problem solving in division of fraction

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Dividing fractions word problems

Dividing fractions word problems arise in numerous situations. We will show you some examples. I recommend that you review the lesson about division of fractions before starting this lesson.

Dividing fractions word problems: a few examples

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

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)

On June 21st, there were 9/10 of a billion stars visible to the naked eye.

On December 21st, there were 4/5 of a billion stars out visible to the naked eye.

How many times more stars were there visible on June 21st than December 21st?

9/10 divided by 4/5 = ?

Find the reciprocal of the divisor.

9/10 × 5/4 = ?

9/10 × 5/4 = 9/2 × 1/4

Solve 9/2 × 1/4 = 9/8

Simplify again

Did you have a hard time understanding the problems above? Did you not understand them at all? Take a look at this figure !

Do you need to master fractions once and for all? Check out my book about fractions .

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Multiplying fractions word problems

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Dividing Fractions Word Problems Worksheets

Toss off solutions to our pdf worksheets on dividing fractions word problems to foster a sense of excellence in identifying the dividend and the divisor and solving word problems on fraction division. Equipped with answer key, our worksheets get children in grade 5, grade 6, and grade 7 rattling their way through the division of fractions and mixed numbers in regular and themed problems. A flurry of everyday scenarios, our free worksheet for dividing fractions word problems is worth a shot!

Dividing Fractions and Whole Numbers Word Problems

Prepare the child through and through so they divide fractions and whole numbers with word problems. Let them take the reciprocal of the divisor and multiply it with the dividend, and they’re good to go!

Dividing Fractions by Cross Cancelling Word Problems

Exceed every learning expectation with our dividing fractions word problems worksheets! Apply cross cancellation after inverting the divisor, find products of what's left, and do write the correct units.

Dividing Mixed Numbers Word Problems

Give 5th grade and 6th grade students a good round of practice to hone their skills in fraction division. Convert mixed numbers into improper fractions, and proceed to divide them as usual.

Dividing Mixed Numbers and Fractions Word Problems

The road to mastery in word problems on dividing mixed numbers and fractions is made smooth with our printable worksheets. Read the problems, identify the dividends and divisors, and find the answers.

Themed Fraction Division Word Problems

If grade 6 and grade 7 learners are bent on proving they're real gifted at tackling fraction division, nothing can stop them! With our themed word problems pdfs, problem-solving is at its most exciting.

Related Worksheets

» Adding Fractions Word Problems

» Subtracting Fractions Word Problems

» Multiplying Fractions Word Problems

» Fraction Word Problems

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Division with unit fractions

Unit fractions word problems.

Unit fractions are fractions with 1 as the numerator. Below are word problems involving the division of whole numbers by unit fractions, or vice versa. 

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Worksheet on Division of Fractions

In worksheet on division of fractions, the questions are based on dividing fractions; to find the reciprocal of the fractions and to classify them as proper, improper and whole numbers; simplifying fractions to its lowest form (if needed) and also word problems on dividing fractions . This exercise sheet on divide the fractions has different types of questions that can be practiced by the seventh grade math students to get more ideas to solve all types of questions in worksheet on division of fractions.

1. Find the reciprocal of each of the following fractions and classify them as proper, improper and whole numbers:  (i) 3/7  (ii) 5/8  (iii) 9/7  (iv) 6/5  (v) 12/7  (vi) 1/8  (vii) 1/11

2. Divide the fractions: 

(i) 3/8 by 5/9 (ii) 7/12 by 3/4 (iii) 1/2 by 2/5 (iv) 3¹/₄ by 2/3 (v) 7/8 by 4¹/₂ (vi) 6¹/₄ by 2³/₅ 3. Dividing fractions:

(i) 3/8 by 4 (ii) 9/16 by 6 (iii) 9 by 3/16 (iv) 10 by 100/3

4. Simplify the fractions:

(i) 3/10 + 10/3 (ii) 4³/₅ + 4/5 (iii) 5⁴/₇ + 1³/₁₀ (iv) 4 ÷ 2²/₅ (v) 2/5 + 1¹/₂ (vi) 3¹/₅ + 1²/₃ (vii) 2¹/₅ + 1¹/₅ (viii) 4³/₇ + 3¹/₂

5. A wire of length 12¹/₂ m is cut into 10 pieces of equal length. Find the length of each piece. 6. The length of a rectangular plot of area 65¹/₃ m² is 12¹/₄ m. What is the width of the plot?

7. By what number should 6²/₉ be multiplied to get 4⁴/₉?

8. The product of two numbers is 25⁵/₆. If one of the numbers is 6²/₃, find the other.

9. The cost of 6¹/₄ kg of apples is $ 400. At what rate per kg are the apples being sold?

10. By selling oranges at the rate of $ 5¹/₄ per orange, a fruit-seller gets $ 630. How many dozens of oranges does he sell?

11. In mid-day meal scheme 3/10 litre of milk is given to each student of a primary school. If 30 litres of milk is distributed every day in the school, how many students are there in the school?

12. In a charity show $ 6496 were collected by selling some tickets. If the price of each ticket was $ 50³/₄, how many tickets were sold?

Students can check the  answers of the worksheet on division of fractions  given below to make sure that the answers are correct. 

1. (i) 7/3, improper (ii) 8/5, improper (iii) 7/9, proper (iv) 5/6, proper (v) 7/12 proper (vi) 8, whole number (vii) 11, whole number

2. (i) 27/40 (ii) 7/9 (iii) 1¹/₄ (iv) 4⁷/₈ (v) 7/36 (vi) 2²¹/₂₂

3. (i) 3/32 (ii) 3/32 (iii) 48 (iv) 3/10

4. (i) 9/100 (ii) 5³/₄ (iii) 4²/₇ (iv) 1²/₃ (v) 4/15 (vi) 1²³/₂₅ (vii) 1⁵/₆ (viii) 1¹³/₄₉

5. 1¹/₄ m 6. 5¹/₃ m 7. 5/7 8. 3⁷/₈ 9. $ 64 10. 10 dozens 11. 100 students 12. 128

If students have any queries regarding the questions given in the worksheet on division of fractions, please fill-up the comment box so that we can help you.

However, suggestions for further improvement, from all quarters would be greatly appreciated.

●   Fractions

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Fraction in Lowest Terms

Addition and Subtraction of Fractions

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