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# Dividing Fractions Word Problems

The order of operations is the set of rules that defines the order in which calculations must be carried out in a mathematical expression. The order of operations is important because it determines how calculations are performed, which can affect the result.

• The Standard Order of Operations
• Parentheses
• Exponents
• Multiplication and Division
• Order of Operations Solved Examples
• Order of Operations Practice Problems
• FAQs

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Before proceeding to word problems, let’s know how to divide fractions.

To divide one fraction by another, multiply the first one by the reciprocal of the second. To find the reciprocal of a fraction, switch its numerator and denominator. The following example shows how to divide fractions using whole numbers, fractions and mixed numbers

Steps to divide fractions:

1) Flip the Divisor: To divide by a fraction, you need to multiply by its reciprocal (flipped version). So, if you have the division problem a/b ÷ c/d, you can rewrite it as a/b x d/c.

2) Multiply the Numerators: Multiply the fractions’ numerators (top numbers) together.

3) Multiply the Denominators: Multiply the denominators (bottom numbers) of the fractions together.

4) Simplify the Result: If possible, simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Now, let’s begin dividing fractions in real-life situations with word problems.

The following example diagram shows simple division of fractions using word problem. There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.

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Example 1: Baking a Cake

You have a recipe that calls for 3/4 cup of sugar, and you want to make half of the recipe. How much sugar do you need?

Solution: To find half of 3/4 cup, you divide 3/4 by 2:

(3/4) ÷ 2 = (3/4) * (1/2) = 3/8 cup

So, you would need 3/8 cup of sugar.

Example 2: Sharing a Pizza

You and your friend are sharing a pizza. If the pizza is divided into 8 equal slices and you want to split it evenly, how many slices will each of you get?

Solution:

To divide the pizza evenly, you need to divide 1 pizza (8 slices) by 2:

(8/1) ÷ 2 = (8/1) * (1/2) = 8/2 = 4

Each of you will get 4 slices.

Example 3: Traveling Distance

You’re driving a distance of 2/3 of a mile, and you’ve covered 1/4 of the distance so far. How much more distance do you need to cover?

Solution:

To find out how much more distance you need to cover, subtract the distance covered from the total distance:

(2/3) – (1/4) = (8/12) – (3/12) = 5/12 mile

You need to cover 5/12 miles more.

Example 4: Cooking Time

A recipe says you should cook a dish for 3/5 of an hour. What would it be if you want to know the cooking time for 2 dishes?

Solution:

To find the cooking time for 2 dishes, simply multiply the cooking time for 1 dish by 2:

(3/5) x 2 = 6/5 hours

So, the cooking time for 2 dishes would be 6/5 hours, which is 1 hour and 12 minutes.

Example 5 :

Tim has 1 1/2 liters of juice in a jug. He has to pour the juice into cups. Each cup can hold 1/4 liters of juice. How many cups will he need to pour all the juice?

Solution:

Number of cups needed = Total quantity of juice ÷ Capacity of 1 cup

= 3/2 ÷ 1/4 (as 1 ½ = 3/2)

= 3/2 x 4/1

= 12/2

= 6

Therefore, the number of cups required to pour the juice is 6.

Example 6 :

3 friends share 4/5 of a pizza. What fraction of pizza does each person get?

Solution:

The amount to share is 4/5

Since the amount will be shared between 3 friends, the amount must be divided between 3 people.

So each person must get 4/5 divided by 3

(4/5) / 3 = (4/5) / (3/1) = 4/5 × 1/3 = (4 × 1) / (5 × 3) = 4/15

Each person will eat 4/15.

Indeed, 4/15 + 4/15 + 4/15 = 12/15 = 4/5 (divide 12 and 15 by 3 to get 4/5)

Example 7 :

The cost of 6  dozen bananas is \$302 2/5? What is the cost of 2 bananas?

Solution :

6 dozen bananas = 6 x 12 = 72 bananas

Cost of 6 dozen bananas = Cost of 72 bananas = 302 2/5 = 1512/5

Cost of 1 banana = (1512/5)/72 = 1512/360 = \$4 1/5

Cost of 2 bananas = 2 x 4 1/5 = 2 x 21/5 = 42/5 = \$8 2/5 = \$8.4

Two bananas costs 8 dollars and 40 cents.

Example 8 :

The length of a rectangular plot of area 65 1/3 m² is 12 1/4 m. What is the width of the plot?

Solution:

Area of rectangular plot = 65 1/3 = 196/3

Length = 12 1/4 = 49/4

Width = Area/length = (196/3) ÷ (49/4) = (196/3) x (4/49) = 5 1/3 m

Example 9 :

By what number should 6 2/9 be multiplied to get 4 4/9?

Solution:

The number that must be multiplied = (6 2/9) ÷ (4 4/9)

= (56/9) ÷ (40/9)

= (56/9) x (9/40)

=  7/5

= 1 2/5

Example 10:

The product of two numbers is 25 5/6. If one of the numbers is 6 2/3, find the other.

Solution:

Let m be the number

According to the questions, m x 6 2/3= 25 5/6

=> m = (25 5/6)/(6 2/3)

= (155/6) x (3/20)

= 31/8

= 3 7/8

Example 11:

The cost of 6 1/4 kg of apples is \$400. At what rate per kg are the apples being sold?

Solution:

6 1/4 = 25/4

Cost of 25/4 kg of apples = \$400

Cost of 1 kg of apples = Total amount/(Total weight)

= 400/(25/4)

= 400 x 4/25

= 16 x 4

= \$64

Example 12

In a charity show, \$6496 was collected by selling some tickets. If the price of each ticket was \$50 3/4, how many tickets were sold?

Solution:

50 3/4 = 203/4

Number of tickets sold = Amount collected / (price per ticket)

= 6496 ÷ (203/4)

= 6496 x 4/203

= 32 x 4

= 128

## FAQs

#### How do I deal with mixed numbers when dividing fractions?

To deal with mixed numbers, convert them into improper fractions before proceeding with the division. For example, convert 2 1/2 to the fraction 5/2 and then divide as usual.

#### When should I invert the second fraction in a division problem?

Invert the second fraction when dividing fractions. It means if you have a problem like 1/3 ÷ 2/5, you should invert the second fraction to get 1/3 x 5/2. It is because division is equivalent to multiplying by the reciprocal.

#### How do I multiply fractions once I've inverted the second fraction?

Multiplying fractions is straightforward. Multiply the numerators (the top numbers) together to get the new numerator, and multiply the denominators (the bottom numbers) together to get the new denominator. For example, 1/3 x 5/2 equals 5/6.

#### What if the result is an improper fraction?

If the result is an improper fraction (numerator is larger than the denominator), you can convert it to a mixed number for clarity or leave it as an improper fraction, depending on the problem’s requirements.

#### How do I simplify the final fraction in a word problem?

To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator and divide both by this factor. Keep simplifying until the fraction is in its simplest form. For example, if you have 10/20, the GCF is 10, so you simplify to 1/2.

#### Can you provide an example of a word problem involving dividing fractions?

Certainly! Here’s an example: If you have 3/4 of a pizza and you want to share it equally among 2 friends, how much pizza will each person get? To solve it, you would divide 3/4 by 2 (3/4 ÷ 2), which becomes 3/4 x 1/2 = 3/8. So, each person gets 3/8 of the pizza. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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