Problems on Cost Price, Selling Price and Rates of Profit and Loss

Problems on Cost Price, Selling Price and Rates of Profit and Loss | Cost Price and Selling Price Problems with Solutions

Problems on Cost Price, Selling Price, and Rates of Profit and Loss along with solved examples are given in this article with a clear explanation. Students can easily understand the in-depth concepts of C.P., S.P., Profit, and Loss by solving various problems. Also, we have included shortcuts and different methods to solve the problems to help the students while solving questions. Furthermore, all cost price, selling price, profit, and loss formula, solved examples, and practice questions are included here for the best practice of the students.

Cost Price: The price for a product or goods bought by a retailer or merchant is known as the Cost Price.
Selling Price: The price for products or goods sold by a retailer or merchant is known as the Selling Price.
Profit: It is the difference between Selling Price and Cost Price.
Profit = Selling Price – Cost Price = S.P. – C.P.
Profit percent = [(S.P. – C.P)/C.P.] x 100%
Profit percent = (Profit/C.P.) x 100%
Loss: It is the difference between Cost Price and Selling Price.
Profit = Cost Price – Selling Price = C.P. – S.P.
Profit percent = [(C.P – S.P.)/C.P.] x 100%
Profit percent = (Loss/C.P.) x 100%

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Cost Price, Selling Price and Rates of Profit and Loss Questions with Answers

1. A chair is bought for Rs. 300 and sold for Rs. 700. Find the gain percent?
(i) 133.33%
(ii) 73.33%
(iii) 93.33%
(iv) 233.33%

Solution:

Given that a chair is bought for Rs. 300 and sold for Rs. 700. From the given information, the cost price = Rs. 300 and Sale price = Rs. 700.
Now, find the Profit.
Profit or Gain = Selling Price – Cost Price = Rs. 700 – Rs. 300 = Rs. 400
Profit percent or gain percent = (Profit/Cost Price) x 100% = (400/300) x 100% = 133.33%
The gain percent of the book is 133.33%

Therefore, the answer is (i) 133.33%


2. A retailer sells 65 m of cloth for Rs. 8,905 at the profit of Rs. 5/m of cloth. What is the cost price of 1 m of cloth?
(i) Rs. 72
(ii) Rs. 32
(iii) Rs. 132
(iv) Rs. 152

Solution:

Given that a retailer sells 65 m of cloth for Rs. 8,905 at the profit of Rs. 5/m of cloth.
Firstly, find out the Selling Price of the 1 m cloth.
Selling Price of 1m of cloth =  Rs. 8,905/65 = Rs. 137
Now, find the Cost Price of 1m of cloth.
Cost Price of 1m of cloth = Selling Price of 1m of cloth – profit on 1m of cloth
Cost Price of 1m of cloth = Rs. 137 – Rs. 5 = Rs. 132
The cost price of 1 m of cloth is Rs. 132

Therefore, the answer is (iii) Rs. 132


3. By selling a fan at Rs. 1600, a shopkeeper makes a profit of 25%. At what price should he sell the fan so as to make a loss of 25%?
(i) Rs. 690
(ii) Rs. 960
(iii) Rs. 540
(iv) Rs. 1200

Solution:

Given that by selling a fan at Rs. 1600, a shopkeeper makes a profit of 25%.
The selling price of a fan = Rs. 1600.
The shopkeeper makes a profit of 25%.
Firstly, find out the Cost Price.
Cost Price = (Selling Price) x [100/(100+Profit)]
Cost Price = (1600) x [100/(100+25)] = 1600 x [100/(125)]
Cost Price = 1280.
Now, find the Loss.
Loss = 25% = 25% of 1280 = Rs. 320.
Now, find the Selling Price.
Selling Price = Cost Price – Loss = 1280 – 320 = Rs. 960
The selling price of the fan to make a loss of 25% is Rs. 960

Therefore, the answer is (ii) Rs. 960


4. Alex bought 140 bottles at the rate of Rs. 200/bottle. The transport expenditure was Rs. 1,200. He paid an octroi at the rate of Rs. 1.55/bottle and labor charges were Rs. 300. What should be the selling price of 1 bottle, if he wants a profit of 20%?
(i) Rs. 247.125
(ii) Rs. 274.659
(iii) Rs. 245.687
(iv) Rs. 254.712

Solution:

Given that Alex bought 140 bottles at the rate of Rs. 200/bottle. The transport expenditure was Rs. 1,200. He paid an octroi at the rate of Rs. 1.55/bottle and labor charges were Rs. 300.
Total Cost Price per bottle = 200 + 1200/140 + 1.55 + 300/140 = 212.26
Selling Price = Cost Price[(100 + profit%)/100] = 212.26[(100 + 20%)/100] = 254.712
The selling price of 1 bottle, if he wants a profit of 20% is Rs. 254.712.

Therefore, the answer is (iv) Rs. 254.712


5. A man sold two cars for Rs. 5.8 lakhs each. On the one, he gained 10% and on the other, he lost 10%. What percent is the effect of the sale on the whole?
(i) 25% loss
(ii) 25% gain
(iii) 0.25% gain
(iv) 0.25% loss

Solution:

Given that a man sold two cars for Rs. 5.8 lakhs each. On the one, he gained 10% and on the other, he lost 10%.
Find out the loss%.
Loss% = (5/10)^2 = 1/4% = 0.25%.
The loss% that effect of the sale, on the whole, is 0.25%.

Therefore, the answer is (iv) 0.25% loss


6. A bike is sold at 25% profit. If the CP and the SP of the bike are increased by Rs 80 and Rs 50 respectively, the profit% decreases by 10%. Find the cost price of the bike?
(i) 260
(ii) 240
(iii) 320
(iv) 220

Solution:

Given that a bike is sold at 25% profit. If the CP and the SP of the bike are increased by Rs 80 and Rs 50 respectively.
Let the Cost Price = x, then Selling Price = (125/100) × x  = 5x/4
New Cost Price (CP) = (x + 60), new Selling Price (SP) = (5x/4 + 30), new profit% = 25 – 15 = 10
So (5x/4 + 30) = (110/100) × (x + 60)
Solve, x = 240

Therefore, the answer is (ii) 240


7. A man bought some pens at the rate of 20 for Rs. 60 and sold them at 5 for Rs. 30. Find his gain or loss percent.

Solution:

Given that a man bought some pens at the rate of 20 for Rs. 60 and sold them at 5 for Rs. 30.
Cost price of 20 pens = Rs. 60 → Cost price (CP) of 1 pen = Rs. 3.
Selling price of 5 pens = Rs. 30 → Selling price (SP) of 1 pen = Rs. 30/5 = Rs. 6
Therefore, Gain = 6 – 3 = 3.
Gain percent = 3/3 * 100 = 100%

Therefore, the answer is 100%


8. A shopkeeper buys batteries from a dealer at a rate of Rs 350 per battery. He sells them at a rate of Rs 425 per battery. He buys 5 batteries of the same type and at the same rate. Find the overall profit/loss. Also profit percent/ loss percent.

Solution:

Given that a shopkeeper buys batteries from a dealer at a rate of Rs 350 per battery.
The cost price rate = Rs 350 per battery.
Total cost price = Rs 350 x 5 = Rs 1750
He sells them at a rate of Rs 425 per battery.
Selling price rate = Rs 425 per battery
Total selling price = Rs 4250
He buys 5 batteries of the same type and at the same rate.
Profit = total selling price – total cost price
= Rs 4250 – Rs 1750
= Rs 2500
Profit percent = (2500/1750) x 100 % = 142.85%


9. A shopkeeper sells a TV for Rs. 8,500 with a loss of Rs. 500. Find the price at which he had bought it from the dealer. Also, calculate the loss percent?

Solution:

Given that a shopkeeper sells a TV for Rs. 8,500 with a loss of Rs. 500. Find the price at which he had bought it from the dealer.
The selling price of the TV = Rs 8,500
The loss suffered by the shopkeeper = Rs 500
Now, find the Cost price.
We know that, Selling price = Cost Price – Loss
So, Cost Price = Selling Price + Loss
Cost Price = Rs 8,500 + Rs 500
= Rs 9,000
Loss percent = (Loss/Cost price) x 100% = (500/9000) x 100% = 5.55


Successive Discounts

Successive Discounts – Definition, Formula, Tips & Tricks | How do you Calculate Successive Discounts?

A successive discount is a discount that is given on the selling price of the product that has already had the discount on the marked price. While you cross a garment store, you come across the offers like 20% or 30% in blocks. The percentage we find on it is the discount offered by the shopkeeper to their customers.

For example, Suppose that a shopkeeper bought a shirt from the retailer at $500 and he decided to sell it at $800 and again put the discount of 20% where the final selling price will be $640. The customer feels that he got it for 20% off, but the shopkeeper sells it for a profit of $140 even after offering the discount. In short, we can say that, if the discount is again applied to the selling price, then it is determined as successive discounts. Successive discount is the amount of discount which is offered on the discount.

Successive Discounts Formula

To find the total discount in successive discounts case, Suppose that the first discount is x% and the second discount is y%, then the formula can be written as:
Total discount = x + y – \(\frac {xy}{100} \)%
There is another scenario like, Consider the original price of the shirt as ‘x’ and the first discount offered as ‘y’ and again the discount offered as ‘z’ on the new price. Then the selling price of the shirt is calculated as:
x-(y + z – \(\frac {yz}{100} \)) * x

Example:
Suppose that the online shopping website sells a product and it offers a discount of 10% on that product and again it offers more than 20% on the discounted value. Know the final value of the product.

In this case, let us suppose that the initial value is 100.
Given that the shopkeeper offered a discount of 10%, therefore it is (100-10) = 90
Then the shopkeeper again offered a discount of 20%, therefore it is 90 – 2(9) = 72
Hence the final value of the product is 72.
We can also calculate the final value by using the formula
Total discount = (x + y – xy / 100)%
x = 10% and y = 20%
Total discount = (10 + 20 – (10)(20) / 100)%
= (30 – 200/100)% = 28%

Successive Discounts Examples

Example 1:
Store is offering a t-shirt at the price of Rs.950. Successive discounts offered by the store are 30% and 50%. Calculate the selling price and total discount offered by the store?

Solution:
Given that, the price of the t-shirt = Rs. 950
Successive discounts are 30% and 50%
Total discounts = (x + y – xy / 100)%
= (30 + 50 – (30)(50) /100)% = 80 – 1500/100% = 65%
Discount = 65% of Rs. 950 = 65/100 * 950 = Rs. 617.5
Therefore, the selling price of the shirt = Rs. 950 – 617.5 = Rs. 332.5
Hence, the total discount offered is Rs. 617.5

The selling price is Rs. 332.5

Example 2:
Successive discounts on the product are 5%, 10%, and 15%. The price of the product in the store is $1000. Calculate the overall selling price and discount of the product?

Solution:
Given that, the price of the product = $1000
Successive discounts are 5%, 10% and 15%
Total discount of 5% and 10% are (x + y – xy / 100)% = 5 + 10 – (5)(10) / 100% = 15 – (50)/100% = 14.5%
Overall discount due to 14.5% and 15% = 14.5 + 15 – (14.5) * (15) /100%
= 29.5 – (217.5)/100% = 27.325%
Discount = 27.325 of $1000 = $273. 25
Total selling price of the product = Store price – overall discount
= $1000 – 273.25 = $726.75
Hence, the total discount offered = $273.25

The total selling price of the product = $726.75

Example 3:
The price of the product is $2250. The successive discounts are 10% and 20%. Find the selling price?

Solution:
Given that, the price of the product is $2250
The successive discounts are 10% and 20%
Total discount = (x + y – xy / 100)%
x = 10% and y = 20%
Total discount = 10 + 20 – (10)(20) 100% = (30 -200/100)%
Total discount = 28%
Discount = 28% of 2250 = (28/100) * 2250
Discount = 630
Therefore, the discount earned is 630
Selling Price = Marked Price – Discount = 2250 – 630 = 1620
Selling Price = 1620

Therefore, Selling Price = 1620
Discount = 630

Example 4:
Successive discounts of 30% and 20% are offered by the trader. Find the total discount offered?

Solution:
Given that, the successive discounts are 30% and 20%
Suppose that MRP = 100
Discount 1 = 30% of 100
Discount = 30
Hence, the price is 100-30 = 70
Now, the discount amount is 20%
Discount = 20% of 70
Discount = 14
Hence, the final price is 70-14 = 56
Total discount offered by the trader = MRP – Selling Price
= 100 – 56 = 44

Hence, the total discount offered = Rs. 44

Example 5:
3 successive discounts of 50%, 20%, and 10% are offered by a trader. Find the total discount percent?

Solution:
Suppose that MRP = 100
Given that, First discount = 50% of 100
Discount = 50
Hence, the price = 100-50 = 50
Second discount = 20% of 50 = 10
Hence, the price = 50 – 10 = 40
Final Discount = 10% of 40 = 4
Hence, the total price = 40 – 4 = 36
Therefore, total discount = MRP – Selling Price = 100 – 36 = 64
Total discount = 64/100 * 100 = 64%

Hence the total discount offered = 64%

We have mentioned all the tricks and tips to solve successive discount problems. Practice all the questions and improve your skills in solving the problems on successive discounts.

Frequently Asked Questions on Successive Discounts

1. How are successive discounts calculated?

Suppose that successive discounts are d1, d2 and d3, then the selling price is SP = (1-d1/100) * (1-d2/100) * (1-d3/100) * Marked Price

2. Is 30 or 40 successive discounts better?

The discount of 70% is better than the successive discounts of 30% and 40%.

3. How do you calculate two successive discount formulas?

The two discount formula is (x + y – xy / 100)%
Where x is the first discount and y is the second discount

4. What is the meaning of successive discounts?

Successive discount is the discounted price on the already given discount which is similar to compound interest.

Understanding Discount and Markups

Understanding Discount and Markup – Definition, Examples | How do you do Discount and Markup?

If you are wondering what is the difference between discounts and markup then you have come the right way? Here we will give you insight on discount and markups definition, formulae, and solved examples explaining step by step on how to approach. Follow the concept and know the real-time examples of discount and markup by checking the below sections for detailed information.

Also, check:

What is meant by Discount?

Discount is the reduction in the price/rate of some product/item. The main purposes of providing discounts are:

  • Increase in sales
  • Clear the old stock
  • Encourage distributors
  • Reward potential customers

Discount is considered the easiest way to increase the product demand and plays an important role in online products. We can check amazing offers while shopping for various products. These offers mainly concentrate to attract customers which are named as discounts. It is considered as the value/price of the total amount/quantity which is generally less than the original value. In general words, we can tell that the total amount is sold at a particular discount to attract customers.

Discount Formula

The discount formula is as follows:
Discount = Marked Price – Selling Price
where Marked Price (M.P) is the actual value of the product without the discount value.
Selling Price is what the customers pay for the product.
Discount is the percentage of the marked price.

Markup

Markup is considered as the total profit or gross on a particular service or commodity. It is defined as the percentage over cost price. For suppose, if the product cost is Rs. 100 and its selling price is Rs. 150, then the markup will be 50%. It is also defined as the difference between CP(cost price) and SP(selling price) of the product. It estimates the profit and loss of the business.

What is meant by Markup Price?

Markup is the difference between the retail price of a commodity and cost. The amount that is added to the cost determines the retail prices of particular items. Markup is combined with total C.P to meet the business costs and generation of profit. Markup represents the percentage or fixed amount of selling price or cost price.

Markup Formula

As mentioned above, markup value is the difference between the SP(selling price) and CP(cost price) of the product.
Markup = Retail – Cost

Markup Percentage

The formula to calculate the markup percentage is:
Sale Price = Cost * (1 + Markup) or Markup = 100 * (Sale Price – Cost Price)/Cost

Markup and Discount Examples

Example 1.
Lara wanted to gift her mom a dress. The cost of the dress was Rs. 450 and it is marked as 20% off on the dress. How much is the discount amount?

Solution:
Given that, Cost of the dress = Rs. 450
Discount Percentage = 20%
Discount Amount = Original Price * Discount Rate
Discount Amount = 450 * 20% = 450 * (20/100) = 90
Therefore, the discount amount is Rs. 90
Hence the final cost of the dress is Cost Price – Discount Amount
= 450 – 90 = 340

The final cost is 340.

Example 2.
Soheal bought a watch which was originally Rs. 5000. He got a discount of 50% on the total amount. How much is the discount amount?

Solution:
Given that, the cost of the watch = Rs. 5000
Discount he got = 50%
Discount Amount = Original Price * Discount Rate
Discount Amount = 5000 * 50%
= 5000 * (50/100)
= 2500
Therefore, the discount amount is 2500
Hence the final cost of the watch is Cost Price – Discount Amount
= 5000 – 2500
= 2500

The final cost of the watch is 2500.

Example 3.
The original price of the book is Rs. 400. I got 20% on the total amount. How much is the discount amount?

Solution:
Given that, the cost of the book is Rs. 400
The discount I got = 20%
Discount Amount = Original Price * Discount Rate
Discount Amount = 400 * 20% = 400 * (20/100) = 80
Therefore, the discount amount is Rs. 80
Hence the final cost of the book is Cost Price – Discount Amount
= 400 – 80 = 320

The final cost of the book is Rs. 320

Example 4.
A car dealer advertises a 7% markup over cost. Find the selling price of the car that cost the dealer $13,000.

Solution:
Given that, Markup = 7% of 13,000 = (7/100) * 13000 = 910
The markup price is 910
Selling Price = Cost Price + Markup Price
=13,000 + 900
=13,900

The selling price of car = 13,900

Example 5.
A ring that costs the jeweler $360 sells for $630. Find the markup rate?

Solution:
Given that, Cost of the ring = $360
Selling Price = $630
Markup Price = Selling Price – Cost Price
= 630 – 360 = 270
The markup price = $270
Markup Percentage = Markup Price / Cost Price
= 270/360 = 75%

Therefore, the markup percentage = 75%

Example 6.
A person got a loan from a bank at a rate of 3% per year for some period. In how much period of time his loan of Rs. 65,000 will become Rs. 68,000.

Solution:
Given that, Principal amount = Rs. 65,000
Profit for bank = Rs. 68,000 – 65000 = 3900
Markup rate = 3/100per year
Profit per year = 650 * 3 = Rs. 1,950
The total amount of time period to clear a loan is 3900 – 1950 = 1950

Therefore, it takes 2 years to become Rs. 68,000 from Rs. 65,000 is 2 years.

Hence, the complete information is given on discount and markup. Check our page for more new concepts and information. Discount and Markup are used in day-to-day life and solve various problems of business.

Understanding Overheads Expenses

Understanding Overheads Expenses – Definition, Types, Examples | How do you Calculate Overhead Expenses?

Overhead expenses are business and other costs which are not related to direct materials, labor, and production. Overhead expenses are some of the indirect costs which are not related to particular business activities. Calculating the overhead expenses is not only important for budgeting but also to determine the charge or investment for a product or service. Suppose that you have a good business that is service-based. Apart from the direct investments or costs, indirect costs like insurance, rent, utilities are considered as overheads expenses.

To understand it better we will consider another example, ie., Suppose a person bought a TV at the cost price of Rs 12,000. Now, he took cable connection for the TV. He has to pay the cable bill every month which is considered as an overhead expense.

What are Overhead Expenses?

Overhead Expenses support the business but they do not generate any revenue. These expenses are mandatory and you have to pay them irrespective of your revenue. The main examples of overhead expenses are property taxes, utilities, office supplies, insurance, rent, accounting and legal expenses, advertising expenses, government licenses and fees, depreciation, and property taxes.

Types of Overhead Expenses

Among the overhead expenses, not all the expenses are the same or equal. These expenses are divided into 3 categories. Know the different expenses and their types which can create a meaningful budget for the business. The different types of overhead expenses are:

  • Fixed Overhead
  • Variable Overhead
  • Semi-Variable Overhead

1. Fixed Overhead Expense

These expenses are something which won’t change from month to month. If a fixed overhead has to change then it changes only annually during the renewal period. Examples of fixed overhead are insurance, salaries, rent. These overhead expenses are easy to budget and plan. These fixed overheads are tough to reduce or restrict the cash flow.

2. Variable Overhead Expense

These expenses are mostly affected by business activities and not by sales. Some of the examples of variable overhead expenses are office supplies, legal expenses, repairs, advertising expenses, and maintenance expenses. It is no guarantee that office supplies will not change according to sales volume. In the same way, advertising expenses may increase during peak sales. The drawback of variable expense is that it is difficult to predict while budgeting.

3. Semi-Variable Expenses

These expenses are also not the same from month to month. These semi-variable expenses are also not completely unpredictable and some examples of these expenses are many utilities, hourly wages, some commissions, and vehicle expenses.

Also, See:

Calculating Overhead Rate

Calculating overhead rate is an important factor in the business. It determines the exact amount of sales that goes into overhead expenses. To calculate it, we have to add all the overhead expenses and divide that number with your sales. The formula of overhead rate is:

Overhead Rate = Overhead Expenses / Sales

Overhead Charges Examples

Example 1.
An industry estimated the factory overhead for the period of 10 years at 1,60,000. The estimation of materials produced for 40,000 units is 200,000. Production requires 40,000 hours of man work at the estimated wage cost of 80,000. Machines will run for 25,000 hours approximately. Calculate the overhead rate on each of the following bases:
i. Direct labor cost
ii. Machine hours
iii. Prime Cost

Solution:

To find the direct labour cost, machine hours and prime cost we have to calculate the overhead rate.
(i) Direct Labour Cost
= (Estimated Factory OverHead / Estimated Direct Labour Cost) * 100
= (1,60,000 / 80,000) * 100
= 200%
(ii) Machine hours
= (Estimated Factory Overhead / Estimated Machine hours)
= 1,60,000 / 25,000
= 6.40 per machine hour
(iii) Prime Cost Basis
= Estimated Factory Overhead / Estimated prime cost
= 1,60,000 / (2,00,000 + 80,000)) * 100
= 89%

Example 2.
A shopkeeper purchased a second hand car for Rs. 1,40,000. He spent Rs. 15,000 on its repair and painting and then sold it for Rs. 17,000. Find his profit or loss?

Solution:
Cost Price = Rs. 1,40,000
Overhead Charges = Rs. 15,000
C.P.N = (1,40,000 + 15,000) = Rs. 1,55,000
S.P = Rs. 17,000
Therefore, S.P > C.P
Hence, it is profit
Profit Percent = S.P – C.P
P = 170000 – 155000
P = Rs. 15000
P% = P / C.P.N * 100
P% = 15000/155000 * 100
P% = 300/31%
Therefore, the profit percentage is 300/31%

Example 3.
A retailer buys a radio for Rs. 225. His overhead expenses are Rs. 15. If he sells the radio for Rs. 300. Determine his profit percentage?

Solution:
Cost Price of radio = Rs. 225
Overhead expenses = Rs. 15
Selling Price of radio = Rs. 300
Net Cost Price = Rs. 225 + 15 = 240
Profit % = Selling Price – Cost Price / Cost Price * 100
P% = 300 – 240 / 240 * 100
P% = 60/240 * 100
P% = 25%
Therefore, the profit percentage = 25%

Frequently Asked Questions on Overhead Costs

1. What are the examples of overhead expenses?

The examples of overhead expenses are interest, labor, advertising, insurance, accounting fees, travel expenditure, telephone bills, supplies, utilities, taxes, legal fees, repairs, legal fees, etc.

2. What are the types of overhead?

The types of overheads are fixed overhead expense, semi-variable overhead expense, and variable overhead expense.

3. What is the minimum percentage for overhead?

The minimal percentage is that it should not exceed 35% of the total revenue. In growing or small businesses, the overhead percentage factor is usually considered as the critical figure which is of concern.

4. How will overhead affect profit?

Overhead represents the supporting costs of production or service delivery. If there is an increase in overhead, it reduces profits by the exactly same amount.

Successor and Predecessor

Successor and Predecessor – Definition, Examples | Difference between the Successor and Predecessor

Successor and Predecessor are the terms that are mentioned just before and after the number or term. Learn the definition, examples, and differences of successor and predecessor. Know the logic to find the successor and predecessor of the number. We are explaining the concept with images and solved examples to make it more clear and easy. Check it out!!

Do Refer: Successor and Predecessor of a Whole Number

Successor and Predecessor in Maths

Check out the What is the Successor and Predecessor from the below details. Also, find out different examples to understand deep about Predecessor and Successor.

What is Predecessor?

The predecessor is the value that comes immediately before/right before the particular value. Suppose that the particular value is x, then the predecessor value is before the value of that particular value i.e., x-1. Therefore, to find the predecessor value of any number, we have to subtract 1 from the given value.

Examples:

If x = 15, then the predecessor value of 15 is 15 – 1 = 14
If x = 21, then the predecessor value of 21 is 21 – 1 = 20
If x = 49, then the predecessor value of 49 is 49 – 1 = 48
If x = 90, then the predecessor value of 90 is 90 – 1 = 90
If x = 115, then the predecessor value of 115 is 115 – 1 = 114

Therefore, the predecessor of any number is one less than the original whole number.

What is Successor?

The successor is the value that comes immediately after/right after the particular value. Suppose that the particular value is x, then the successor value is after the value of that particular value i.e., x + 1. Therefore, to find the successor value of any number, we have to add 1 to the given value.

Examples:
If x = 15, then the successor value of 15 is 15 + 1 = 16
If x = 21, then the successor value of 21 is 21 + 1 = 22
If x = 49, then the successor value of 49 is 49 + 1 = 50
If x = 90, then the successor value of 90 is 90 + 1 = 91
If x = 115, then the successor value of 115 is 115 + 1 = 116

Therefore, the successor of any number is one greater than the original whole number.

How to find the Successor and Predecessor of a Number?

To find the predecessor and successor of any value, we apply the basic subtraction and addition methods.

To evaluate the successor and predecessor of any value, we have to apply the basic method of addition and subtraction, respectively. For the successor, we need to add 1 to the given number whereas for the predecessor we have to subtract 1 from the given number. Finding a successor and predecessor is very easy and quick.

  • Successor = Given number + 1
  • Predecessor = Given number – 1

Let us see some solved examples here to understand better.

Successor and Predecessor Examples

Example 1.
Find the successor of the following numbers:
(i) 15
(ii) -11
(iii) -85
(iv) 91
(v) 149
(vi) 44
(vii) 87
(viii) 78

Solution:
The successor values of the numbers are as follows:
(i) 15 + 1 = 16
The successor value of 15 is 16
(ii) -11 + 1 = -10
The successor value of -11 is – 10
(iii) -85 + 1 = -84
The successor value of -85 is -84
(iv) 91 + 1 = 92
The successor value of 91 is 92
(v) 149 + 1 = 150
The successor value of 149 is 150
(vi) 44 + 1 = 45
The successor value of 44 is 45
(vii) 87 + 1 = 88
The successor value of 87 is 88
(viii) 78 + 1 = 79
The successor value of 78 is 79

Example 2.
Find the predecessor of the following numbers:
(i) -15
(ii) -81
(iii) 65
(iv) -9
(v) 22
(vi) 198
(vii) 55

Solution:
The predecessor values of the numbers are as follows:
(i) -15 – 1 = -16
The predecessor value of -15 is -16
(ii) -81 – 1 = -82
The predecessor value of -81 is -82
(iii) 65 – 1 = 64
The predecessor value of 65 is 64
(iv) – 9 – 1 = -10
The predecessor value of -9 is -10
(v) 22 – 1 = 21
The predecessor value of 22 is 21
(vi) 198 – 1 = 197
The predecessor value of 198 is 197
(vii) 55 – 1 = 54
The predecessor value of 55 is 54

Example 3.
Write the successor and predecessor of the following numbers:
(i) 94
(ii) 114
(iii) 32
(iv) 65
(v) 78

Solution:
The successor and predecessor of the numbers are as follows:
(i) The number is 94
Successor value of 94 is 94 + 1 = 95
Predecessor value of 94 is 94 – 1 = 93
(ii) The number is 114
Successor value of 114 is 114 + 1 = 115
Predecessor value of 114 is 114 – 1 = 113
(iii)The number is 32
Successor value of 32 is 32 + 1 = 33
Predecessor value of 32 is 32 – 1 = 31
(iv)The number is 65
Successor value of 65 is 65 + 1 = 66
Predecessor value of 65 is 65 – 1 = 64
(v)The number is 78
Successor value of 78 is 78 + 1 = 79
Predecessor value of 78 is 78 – 1 = 77

FAQs on Successor and Predecessor

1. What is the main difference between successor and predecessor

The successor is the number that comes after the original number. The predecessor is the number that comes before the original number.

2. Is there any natural number available that has no predecessor value?

Yes, there is a natural number that has no predecessor value i.e., 1. The reason for this is that natural numbers start from 1.

3. Is there any natural number available that has no successor value?

No, there is no natural number that has no successor value. As the natural numbers are infinite and it has no last value.

4. What is the formula for successor and predecessor numbers?

The formula for successor and predecessor are

  • Successor = Original number + 1
  • Predecessor = Original number – 1
Conversion of Mixed into Improper Fractions

Conversion of Mixed into Improper Fractions | How to Turn a Mixed Fraction to an Improper Fraction?

Do you want to know the Conversion of Mixed into Improper Fractions? Then, check the entire article where you can get a bulk knowledge of converting mixed fractions to improper fractions. You will come to know the detailed explanation with images and examples. Conversion of mixed fractions into improper fractions helps for everyday use. Generally, Mixed fractions will have both the fraction and whole numbers.

Mixed Fractions = Integer(Numerator/Denominator)

Example:

Suppose that a group of 8 friends ordered 2 pizzas of 6 pieces each. Each of them took one piece from it and so 8 pieces were remaining. For the next round, only 4 people were interested to eat and the total number of pieces left was 8.

Hence, each of them gets \(\frac {1}{2} \) piece of the remaining pizza. Therefore, the total amount of pizza 4 people ate was 1 \(\frac {1}{2} \). Here 1 \(\frac {1}{2} \) is the mixed fraction.

Also, find

How to Convert Mixed Fractions into Improper Fractions?

Converting the mixed fractions into improper fractions involves various steps. The steps are as follows:

Step 1:
Obtain the mixed fraction and multiply the whole part with the fraction’s denominator.
Step 2:
Add the resultant value to the numerator
Step 3:
The result in step 2 will be the numerator of the improper fraction
Step 4:
The denominator will be the same as the mixed fraction. Hence  it forms an improper fraction

Converting Mixed Fractions into Improper Fractions Problems

Check out all the examples given here. We have explained every question with a clear explanation and with images.

Example 1:

Convert the mixed fraction 5\(\frac {7}{12} \) into improper fractions?

Solution:

Step 1: Multiply the whole number with a denominator
Start converting the mixed fraction into an improper fraction. Multiply the whole number part which is present before the fraction with the denominator of the fraction. Suppose that you need to turn 5\(\frac {7}{12} \) into the improper fraction, then the result of step 1 will be
5 * 12 ⇒ 60

Step 2: Add the resultant to the numerator
The resultant in step 1, should be added to the numerator in the mixed fraction. From the example fraction of 5\(\frac {7}{12} \), we obtain the result of step 2 as
5 * 12 ⇒ 60
60 + 7 = 67

Step 3: Find the numerator of the improper fraction
The resultant value of step 3 is the numerator of the improper fraction.

Step 4: Find the denominator and form the improper fraction
Make use of the numerator in step 3 and the denominator will be the same value of the mixed fraction. In the above step, the numerator is 67 and the denominator is 12. Hence the resultant improper fraction is \(\frac {67}{12} \).

Conversion of Mixed into Improper Fractions

Example 2:

Convert the mixed fraction 5\(\frac {2}{3} \) into improper fraction?

Solution:

Conversion of mixed fractions to improper fractions involves the following steps:

  1. Multiply the whole number with the denominator of the fraction ⇒ 5 * 3 = 15
  2. Add the resultant to the numerator ⇒ 15 + 2 = 17
  3. The resultant is the numerator and the improper fraction is \(\frac {17}{3} \)

Conversion of Mixed into Improper Fractions example

Example 3:

Convert the mixed fraction 3\(\frac {1}{4} \) into improper fraction?

Solution:

Conversion of mixed fractions to improper fractions involves the following steps:

  1. Multiply the whole number with the denominator of the fraction ⇒ 3 * 4 = 12
  2. Add the resultant to the numerator ⇒ 12 + 1 = 13
  3. The resultant is the numerator and the improper fraction is \(\frac {13}{4} \)

Conversion of Mixed into Improper Fractions examples

Example 4:

Convert the mixed fraction 64\(\frac {1}{4} \) into improper fraction?

Solution:

Conversion of mixed fractions to improper fractions involves the following steps:

  1. Multiply the whole number with the denominator of the fraction ⇒ 64 * 4 = 256
  2. Add the resultant to the numerator ⇒ 256 + 1 = 257
  3. The resultant is the numerator and the improper fraction is \(\frac {257}{4} \)

Conversion of Mixed into Improper Fractions solved example

Example 5:

Convert the mixed fraction 11\(\frac {3}{8} \) into improper fraction?

Solution:

Conversion of mixed fractions to improper fractions involves the following steps:

  1. Multiply the whole number with a denominator of the fraction ⇒ 11 * 8 = 88
  2. Add the resultant to the numerator ⇒ 88 + 3 = 91
  3. The resultant is the numerator and the improper fraction is \(\frac {91}{8} \)

Conversion of Mixed into Improper Fractions solved examples

FAQs on How to Convert Mixed Fractions into Improper Fractions

1. How to change mixed fractions into improper fractions?

  1. Multiply the whole number with the denominator.
  2. Add the resultant to the numerator
  3. Form the improper fraction with the resultant value as numerator and denominator of mixed fraction as the original denominator.

2. What is the improper fraction of 8\(\frac {6}{5} \)?

8\(\frac {6}{5} \) can be written as \(\frac {46}{5} \) in the improper fraction.

3. What is the rule for improper fractions?

Step 1: You have to divide the numerator by denominator.
Step 2: The quotient value must be written as the whole number.
Step 3: In the final step, use the remainder as the final numerator of the proper fraction.

Fraction as Division

Understanding Fraction as Division Problems | How do you Convert Fractions to Division?

Fraction as Division is the representation of fractions as division rule (÷). You can convert any fraction to division with the simple steps provided. By dividing the numerator (upper part of the fraction) with the denominator (lower part of the fraction) can get you the division.

Check the detailed explanation of the concept of fraction as division on this page. For a better understanding of the division concept with fractions, we have listed all of them explaining step by step along with images in the next sections.

Example:
\(\frac {6}{5} \) = 6 ÷5

How to Interpret a Fraction as Division?

You can convert the Fractions into Divisions by using the division rule. Firstly, find out the numerator and denominator of the fraction. Then, use the division symbol to show the fraction as the division. If you wish to simplify, you can simplify the division.

Fractions Expressed as Division
Check out the below examples to find out the examples of Fractions Expressed as Division.
(i) 11/9 = 11 ÷ 9
(ii) 5/13 = 5 ÷ 13
(iii) 92/65 = 92 ÷ 65
(iv) 3/7 = 3 ÷ 7
(v) 16/19 = 16 ÷ 19

Divisions Expressed as Fractions
Find the below examples to find out the Divisions Expressed as Fractions examples.
(i) 10 ÷ 4 = 10/4;
(ii) 14 ÷ 6 = 14/6
(iii) 7 ÷ 5 = 7/5
(iv) 17 ÷ 7 = 17/7
(v) 13 ÷ 21 = 13/21

See More:

Fractions as Division Problems

We have given different examples with explanations and images below.

Example 1:
Raju has 2 packets of biscuits and each of the packets has 9 biscuits. He wants to divide the two packets of biscuits into 3. How many biscuits will each packet contain when divided into 3 packets?

Solution:

Raju has 18 biscuits with him.
He wants to divide it into 3 packets.
We can show the division with a fraction as follows:
18 ÷ 3 which is a fraction
On further simplification of fraction, we get the result as 6.

Therefore, when divided into 3 packets, each of the packets contain 6 biscuits.

Fractions as Division Questions and Answers

Example 2:
Suppose that there are 64 chocolates in the box. We have to pack them into 4 boxes. Thus many chocolates do each box contains and how do you represent them in the form of fractions?

Solution:

Given that the No of total chocolates in a box = 64
No of boxes these chocolates are to be divided = 4
The total no of chocolates in each box can be represented with fractions i.e., \(\frac {64}{4} \) = 64 ÷ 4
On further division, we get the result as 16

Therefore, there are 16 chocolates in each box.

Fraction as Division

Example 3:

There are 96 cupcakes in a box. 12 cupcakes are to be packed in each box. How many boxes do we need?

Solution:
Given that the total no of cupcakes in a box = 96
No of cupcakes to be packed in each box = 12
The total no of boxes can be represented with fractions i.e., \(\frac {96}{12} \) = 96 ÷12
On further division, we get the result as 8

Therefore, 8 boxes are needed to pack 96 cupcakes.

Fraction as Division Examples

Example 4:
2496 nails are packed into 6 boxes. Find the number of nails in each box?

Solution:

Given that the total no of nails = 2496
No of boxes = 6
Total no of nails in each box can be represented with fractions i.e., \(\frac {2496}{6} \) = 2496 ÷ 6
On further division, we get the result as 416

Therefore, 416 nails are there in each box.

Fraction as Division Example

Example 4:
176 bottles should be placed in 8 trays. Find the number of bottles in each tray?

Solution:
Given that the total number of bottles = 176
No of trays = 8
Total number of bottles in each tray can be represented with fractions i.e., \(\frac {176}{8} \) = 176 ÷ 8
On further division, we get the result as 22

Therefore, 22 bottles should be placed in each tray.

Solved Examples on Fraction as Division

Example 5:
4404 boxes of oranges should be placed in 6 trucks. Find the total number of boxes placed in each truck?

Solution:
Given that the total no of boxes of oranges = 4404
No of trucks = 6
The total no of boxes placed in each truck can be represented with fractions i.e., \(\frac {4404}{6} \) = 4404 ÷ 6
On further division, we get the result as 734

Therefore, 734 boxes are to be placed in each truck.

How do you Convert Fractions to Division

FAQs on Understanding Fractions as Division

 1. How to convert fractions as division?

To convert the fractions as division, use the calculator and divide the upper part of the fraction (numerator) by the bottom part of the fraction (denominator).

2. Give an example of fractions as division?

 Suppose that \(\frac {3}{4} \) is the fraction, then write the numerator “3” followed by the division symbol and then followed by “4”.

Division of \(\frac {3}{4} \) is 3 ÷ 4

 3. Arefractions as division and division of fractions the same?

The answer is no. Fractions as division are the representation of fractions as division rules (÷). Division of fractions represents breaking down the fraction into further parts.

Representation of Fractions on a Number Line

Representations of Fractions on a Number Line | How to Represent Fractions on a Number Line?

Representation of Fractions on a number line helps to understand how the fractions can be represented as part of a whole. As we know that fraction is not a whole number as it is represented as (\(\frac {1}{2} \), \(\frac {1}{3} \), \(\frac {1}{4} \)) etc. You can know how these fraction numbers can be easily represented on a number line. We have included all the images and also step by step procedure to Representation Fractions on a Number Line.

Example:
Represent the fraction \(\frac {2}{5} \) on a number line?
Solution:
Given that the fraction is \(\frac {2}{5} \)
As the denominator of the fraction is 5, divide the intervals into 5 between every pair of consecutive integers on the number line. Each part represents the fraction \(\frac {1}{5} \)

Also, check

How to Represent Fractions on a Number Line?

To represent the fractions on a number line, various steps are to be followed. They are:

Step 1: Find the suitable length and draw the number line of that length.
Step 2: Determine whether the fraction is proper or improper, if it is an improper fraction then convert it into a mixed fraction and mark the integers that lie between the fraction values. For example, if the fraction is \(\frac {3}{2} \), then note it as 1\(\frac {1}{2} \). Then mark 1 and 2 points on the number line.
Step 3: Consider the denominator of the fraction and draw the equal number of parts marked in step 2.
Step 4: Now, consider the number in the numerator and count forward starting from the left.
Step 5: Finally, mark the point on the number line.

Representing Fractions on a Number Line Examples

Check out the examples given below to understand how to Represent a Fractions on a Number Line.

Example 1:

Represent the fraction \(\frac {3}{5} \)?

Solution:
Follow the below steps to represent fractions on a number line:
Step 1: Draw the number line of length 4
Representations of Fractions on a Number Line
Step 2: As the fraction is a proper fraction, we have to mark points on the number line.
Representations of Fractions on a Number Line example
Step 3: The denominator value is 5, hence we have to make an equal number of parts between numbers.
Representations of Fractions on a Number Line examples
Step 4: As the numerator value is 3, we have to move forward to 3.
Representations of Fractions on a Number Line solved example
Step 5: Mark the point on the number line.
Representations of Fractions on a Number Line solved examples

Example 2:

Represent the fraction \(\frac {1}{4} \)?

Solution:
Check the following steps to represent the fraction on a number line
Step 1: Draw the number line of length 5.
Step 2: As the fraction is a proper fraction, we have to mark points on the number line.
Step 3: The denominator value is 4, hence we have to make an equal number of parts between numbers.
Step 4: As the numerator value is 1, we have to move forward to 1.
Representations of Fractions on a Number Line problem
Step 5: Mark the point on the number line.
Representations of Fractions on a Number Line problems

Example 3:

Represent the fraction \(\frac {2}{4} \)?

Solution:
Check the following steps to represent the fraction on a number line
Step 1: Draw the number line of length 4
Step 2: As the fraction is a proper fraction, we have to mark points on the number line.
Step 3: The denominator value is 4, hence we have to make an equal number of parts between numbers.
Step 4: As the numerator value is 2, we have to move forward to 2.
Representations of Fractions on a Number Line question and answer
Step 5: Mark the point on the number line.
Representations of Fractions on a Number Line question and answers

Example 4:

Represent the fraction \(\frac {1}{8} \)?

Solution:
Check the following steps to represent the fraction on a number line
Step 1: Draw the number line of length 9
Step 2: As the fraction is a proper fraction, we have to mark points on the number line.
Step 3: The denominator value is 8, hence we have to make an equal number of parts between numbers.
Step 4: As the numerator value is 1, we have to move forward to 1.
Representations of Fractions on a Number Line questions and answers
Step 5: Mark the point on the number line.
Representations of Fractions on a Number Line questions and solved answers

Example 5:

Represent the fraction \(\frac {1}{2} \)?

Solution:
Check the following steps to represent the fraction on a number line
Step 1: Draw the number line of length 3
Step 2: As the fraction is proper fraction, we have to mark points on the number line.
Step 3: The denominator value is 2, hence we have to make an equal number of parts between numbers.
Step 4: As the numerator value is 1, we have to move forward to 1.
How to Represent Fractions on a Number Line
Step 5: Mark the point on the number line.
How to Represent Fractions on a Number Line examples

FAQs on Representation of Fractions on a Number Line

 1. What does representing fractions on the number line shows?

If the fractions are represented on a number line, it shows the regular intervals between the integers. It also helps to understand the basic concept of fractional numbers formation.

2. What are the steps to represent the fraction \(\frac {3}{4} \) on a number line?

Step 1: Draw the number line of length 5.
Step 2: As the fraction is a proper fraction, we have to mark points on the number line.
Step 3: The denominator value is 3, hence we have to make an equal number of parts between numbers.
Step 4: As the numerator value is 3, we have to move forward to 3.
Step 5: Mark the point on the number line.

3. How do you represent on a number line?

  1. Draw a straight line of suitable length.
  2. Now, mark the point at the extreme left at zero(0).
  3. Mark the remaining points to the right of zero and label them as 1, 2, 3, …. Make sure that the distance between these points must be uniform which is said to be a unit distance.
Division as the Inverse of Multiplication

Division as the Inverse of Multiplication | How do you teach Division the Inverse of Multiplication?

Division and multiplication are very closely related. As we know that division is the inverse property of multiplication. Let a and b be two whole numbers. Dividing the number a by number b means finding the whole number when multiplied by b gives the value a and we represent it as a ÷ b = c (or) a = b * c. Division as the Inverse of Multiplication problems and theory is explained here in this article.

Example:

Divide 30 by 6 and find the inverse of multiplication?

Solution:

Given that we have to divide the value 30 by 6.
It means that finding a whole number which when multiplied by 6 gives 30. The number which divides 30 by 6 is 5. Therefore, we can write 30 ÷ 6 = 5.

The inverse of multiplication is 5 * 6 = 30

How to teach Division as the Inverse of Multiplication?

Division and multiplication are inverse operations because dividing and multiplying by the same number won’t change the original value. For example, 15 * 4/4 = 15 and 24 * 4/4 = 24. Dividing and multiplying by 4 cancels each other, so the result does not change.

See More:

Relationship between Multiplication and Division Examples

The below examples will let you know the complete details of Division as the Inverse of Multiplication concept.

Example 1:

96 rupees are equally distributed among six candidates. How much amount does each person get. Also, define the inverse of multiplication here?

Solution:

Given that the total amount of rupees = 96
No of candidates = 6
Amount of rupees each person get = 96 ÷ 6 = 16
With the division property of the above question, we get the result as 16
For the above solution, we can apply the inverse of multiplication ie., 16 * 6 = 96

Therefore division is the inverse of multiplication.

Division as inverse of multiplication example

Example 2:

The cost of the pen is 10 rupees. Find the cost of 5 such boxes?

Solution:

Given that the cost of pen = 10
No of boxes = 5
Cost of 5 such boxes = 10 * 5 = 50
With the multiplication property, the result is 50
For the above solution, we can apply the division rule i.e., 50 ÷ 5 = 10

Therefore multiplication is the inverse of division.

Division as inverse of multiplication examples

Example 3:

The cost of 9 litres of diesel is Rs.1080. Find the cost of 1 litre of diesel?

Solution:

Given that the total cost of diesel = Rs. 1080
No of litres = 9
Cost of 1 litre of diesel = 1080 ÷ 9 = 120
With the division rule, the result is 120
For the above solution, we can apply the inverse of multiplication i.e., 120* 9 = 1080

Therefore division is the inverse of multiplication.

Division as inverse of multiplication solved example

Example 4:
If 25 watches cost Rs. 10,500. How much will 5 watches cost?

Solution:

Given that the total cost for watches = 10,500
No of watches = 25
Cost of 5 watches = 10,500 ÷ 5 = 420
With the division rule, the result is 420
For the above solution, we can apply the inverse of multiplication i.e., 420 * 25 = 10,500

Therefore, the division is the inverse of multiplication.

Division as inverse of multiplication solved examples

Example 5:

6400 litres of milk in the tank are filled in bottles. Find the capacity of each bottle if filled in 80 bottles?

Solution:

Given that the total litres of milk = 6400
No of bottles = 80
Capacity of each bottle = 6400 ÷ 80 = 80
With the division rule, the result is 80
For the above solution, we can apply the inverse of multiplication i.e., 80 * 80 = 6400

Therefore, the division is the inverse of multiplication.

Division as inverse of multiplication question and answers

FAQs on Teaching Division as Inverse of Multiplication

1. What makes the difference between division and multiplication?

The multiplication is the product of two factors and division is to find the missing factor if the product of other fraction is known. Dividing and multiplying with the same number does not change the original value.

2. What is the example of the inverse of multiplication?

An example of inverse multiplication is

54 ÷ 6 = 9, since 9 * 6 = 54

3. How is the division as the inverse multiplication?

The division is inverse multiplication. If a given number is divided and then multiplied by the same number, you will result with the same number you started with. Multiplication comes with the opposite effect to division.

Conversion of Improper Fractions Into Mixed Fractions

Conversion of Improper Fractions Into Mixed Fractions – Definition, Facts, Examples | How do you Change a Improper Fraction to a Mixed Fraction?

Conversion of Improper fractions into mixed fractions helps to understand the result of algebraic problems in a better way. Improper fractions will have high-value numerators compared to denominators. Mixed fractions will have both whole numbers and a fraction. Examples of Converting Improper Fractions to Mixed Fractions are given here along with explanations and images. Read the concept and practice all the problems for a better understanding of the concept.

Example:
Suppose if you ordered a pizza of 6 slices and your friend ate it all and you didn’t get any of the pieces. So, you ordered another pizza and ate 1 slice from it. Hence the total pizza eaten is 7/6 parts.

It is the improper fraction as the numerator is greater than the denominator. Leftover pizzas, half-filled glasses of water are examples of mixed fractions.

How to Convert an Improper Fraction Into a Mixed Number?

We are providing the steps to convert an improper fraction into a mixed fraction in the following sections:

  1. In the first step, you have to divide the denominator with the numerator.
  2. Identify the divisor, quotient, and remainder.
  3. Now, write the mixed number in the form of remainder/divisor.

Converting Improper Fractions Into Mixed Fractions – Solved Examples

Example 1.
Convert the improper fraction \(\frac { 7 }{ 5 } \) into mixed fractions?

Solution:
Step 1. Divide the numerator by the denominator

Start converting by writing the improper fraction. Divide the numerator value by the denominator value and include the remainder. Suppose that you need to turn the fraction of \(\frac { 7 }{ 5 } \) into a mixed number, We apply the division rule and divide the numerator 7 by denominator 5, in this way:
\(\frac { 7 }{ 5 } \) → \(\frac { 7 }{ 5 } \) = 1 R2

Step 2. Write the answer as a whole number

The highest number present at the left of the fraction is the whole number answer of the problem. In other words, we can justify writing the division problem without the remainder. In step 1, the answer is 1 R2, so we leave the remainder and write the whole part 1.

Step 3. Make the fraction from the original remainder and denominator:

Make use of the remainder from step 2 and put it in the numerator and use the denominator from the original improper fraction. Now, add the fraction next to the whole number and you will have the mixed number. In the above example, the remainder is 2, put 2 in the numerator and original denominator 5. Hence, the fraction is \(\frac { 2 }{ 5 } \). Now, put the fraction next to the whole number i.e., 1 \(\frac { 2 }{ 5 } \) which is a mixed fraction.

Example 2:
Convert the improper fraction \(\frac { 11 }{ 4 } \) into mixed fractions?

Solution:
To convert the improper fraction \(\frac { 11 }{ 4 } \) into a mixed fraction, we use the following steps:
1. Divide the denominator with numerator ⇒ \(\frac { 11 }{ 4 } \) = 2 and it gives the remainder as 3.
2. Write the result whole number 2, then write the remainder 3 in the numerator above the denominator value.
3. 2 \(\frac { 3 }{ 4 } \) is the mixed fraction for the improper fraction \(\frac { 11 }{ 4 } \).

Improper to MIxed fraction example

Example 3:
Convert \(\frac { 10 }{ 3 } \) into a mixed fraction?

Solution:
To convert the improper fraction \(\frac { 10 }{ 3 } \) into a mixed fraction, we use the following steps:
1. Divide the denominator with numerator ⇒ \(\frac { 10 }{ 3 } \) and it gives the remainder as 1.
2. Write the result whole number 3, then write the remainder 1 in the numerator above the denominator value.
3. 3 \(\frac { 1 }{ 3 } \) is the mixed fraction for the improper fraction \(\frac { 10 }{ 3 } \).

Improper to MIxed fraction examples

Example 4:
Convert \(\frac { 23 }{ 4 } \) into a mixed fraction?

Solution:
To convert the improper fraction \(\frac { 23 }{ 4 } \) into a mixed fraction, we use the following steps:
1. Divide the denominator with numerator ⇒ \(\frac { 23 }{ 4 } \) and it gives the remainder as 3.
2. Write the result whole number 5, then write the remainder 3 in the numerator above the denominator value.
3. 5 \(\frac { 3 }{ 4 } \) is the mixed fraction for the improper fraction \(\frac { 23 }{ 4 } \).

Improper to Mixed fraction solved Example

Example 5:
Convert the improper fraction \(\frac { 115 }{ 6 } \) into a mixed fraction?

Solution:
To convert the improper fraction \(\frac { 115 }{ 6 } \) into a mixed fraction, we use the following steps:
1. Divide the denominator with numerator ⇒ \(\frac { 115 }{ 6 } \) and it gives the remainder as 1.
2. Write the result whole number 19, then write the remainder 1 in the numerator above the denominator value.
3. 19 \(\frac { 1 }{ 6 } \) is the mixed fraction for the improper fraction \(\frac { 115 }{ 6 } \)

Improper to Mixed fraction solved Examples

FAQs on Improper Fraction to Mixed Fraction Conversion

1. How to change the improper fraction into a mixed fraction?

1. Divide the numerator value by the denominator value.
2. Use the quotient value as the whole number.
3. Now, use the remainder as the numerator of the proper fraction.

2. What is 7/4 as a mixed fraction?

7/4 can be written as 1 ¾ in the mixed fraction.

3. What is the rule for mixed fractions?

Step 1: Multiply the denominator with the whole number of the mixed fraction.
Step 2: Add the numerator to the product received from step 1.
Step 3: Finally, write the improper fraction with the sum obtained from step 2 in the numerator/denominator form.