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GRADES 6–7 · MATHEMATICS

Multiplying and Dividing Fractions

Learn how to find a fraction of an amount, multiply two fractions and divide one fraction by another. Follow the worked steps, simplify carefully and use the quiz to check your understanding.

Learning time: approximately 30–35 minutes · Beginner to developing level

What You Will Learn

1. Multiplying a Fraction by a Whole Number

To multiply a fraction by a whole number, multiply the numerator by the whole number and keep the denominator. Then simplify if possible.

Example: 3 × 1/4

Multiply 3 by the numerator 1: 3 × 1 = 3. Keep the denominator 4.

3 ×14=34
Answer: 3/4.

Another example: 4 × 2/5 = 8/5 = 1 3/5. The answer is an improper fraction, which can also be written as a mixed number.

2. Multiply Two Fractions

To multiply fractions, multiply the numerators together and multiply the denominators together. Unlike addition, you do not need a common denominator.

Worked example: 2/3 × 3/5

  1. Multiply the numerators: 2 × 3 = 6.
  2. Multiply the denominators: 3 × 5 = 15.
  3. Write the result: 6/15.
  4. Simplify by dividing top and bottom by 3: 2/5.
23×35=615=25

Answer: 2/5.

Another example: 3/4 × 2/7

Multiply across: (3 × 2)/(4 × 7) = 6/28. Simplify by dividing by 2: 3/14.

3. Simplify Before Multiplying

You can sometimes make a multiplication easier by cancelling common factors diagonally before multiplying. This is called cross-cancellation. You are dividing a numerator and a denominator by the same factor, so the value does not change.

Worked example: 4/9 × 3/8

  1. Look for a common factor between 4 and 8. Divide both by 4 to get 1 and 2.
  2. Look for a common factor between 3 and 9. Divide both by 3 to get 1 and 3.
  3. Multiply the remaining numerators: 1 × 1 = 1.
  4. Multiply the remaining denominators: 3 × 2 = 6.

Answer: 1/6.

Important: Only cancel a factor shared by one numerator and one denominator. Do not cancel two numerators or two denominators with each other.

4. What Does Dividing by a Fraction Mean?

Division asks how many groups of a certain size fit into an amount. For example, 1 ÷ 1/2 asks how many halves fit into one whole. The answer is 2.

One whole contains two halves.
11=12+12

So 1 ÷ 1/2 = 2.

5. Divide Fractions Using the Reciprocal

To divide by a fraction, multiply by its reciprocal. The reciprocal is found by swapping the numerator and denominator. Keep the first fraction, change division to multiplication, and flip the second fraction.

Memory aid: Keep – Change – Flip.

Worked example: 2/3 ÷ 4/5

  1. Keep the first fraction: 2/3.
  2. Change ÷ to ×.
  3. Flip the second fraction: 4/5 becomes 5/4.
  4. Multiply: 2/3 × 5/4 = 10/12.
  5. Simplify: 10/12 = 5/6.
23÷45=23×54=56

Answer: 5/6.

Another example: 3/4 ÷ 1/2

Keep 3/4, change ÷ to ×, and flip 1/2 to 2/1. Then 3/4 × 2/1 = 6/4 = 3/2 = 1 1/2.

6. Solve Everyday Problems

Example 1: Half of a recipe

A recipe needs 2/3 cup of oats. You make half the recipe. How many cups of oats do you need?

1/2 × 2/3 = 2/6 = 1/3. You need 1/3 cup.

Example 2: Ribbon pieces

You have 3/4 metre of ribbon. Each piece is 1/8 metre long. How many pieces can you cut?

3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. You can cut 6 pieces.

Example 3: A garden plot

A rectangular garden is 2/3 metre long and 3/5 metre wide. What is its area?

Area = length × width = 2/3 × 3/5 = 6/15 = 2/5 square metre.

7. Common Mistakes to Avoid

Finding a common denominator for multiplication: You do not need one. Multiply numerators and denominators.
Flipping the wrong fraction: When dividing, flip only the second fraction, the one you are dividing by.
Forgetting to simplify: Reduce the answer when the numerator and denominator share a common factor.
Mixing up multiplication and division: Multiplication uses the fractions as written. Division changes to multiplication by the reciprocal.
Ignoring units in word problems: Area uses square units; lengths use ordinary units.

8. Practice Exercises

Try these before revealing the answers.

  1. 3 × 2/7
  2. 2/5 × 3/4
  3. 5/6 × 3/10
  4. 1/2 ÷ 1/4
  5. 3/5 ÷ 2/3
  6. 4/7 ÷ 2/7
  7. A recipe uses 3/4 cup of flour. You make one half of the recipe. How much flour is needed?
  8. A 2/3-metre strip is cut into pieces that are each 1/6 metre long. How many pieces are made?
Show practice answers and working
  1. 6/7.
  2. 6/20 = 3/10.
  3. 15/60 = 1/4.
  4. 1/2 × 4/1 = 2.
  5. 3/5 × 3/2 = 9/10.
  6. 4/7 × 7/2 = 2.
  7. 1/2 × 3/4 = 3/8 cup.
  8. 2/3 ÷ 1/6 = 2/3 × 6 = 4 pieces.

9. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

1. What is 2/3 × 3/5 in simplest form?
2. What is 3 × 1/4?
3. What is the reciprocal of 2/7?
4. What is 1/2 ÷ 1/4?
5. What is 3/5 ÷ 2/3?

10. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grades 6–7 Mathematics

Multiplying and Dividing Fractions Worksheet

Name: __________________________ Date: _______________

Instructions: Show your working and simplify each answer where possible.

  1. 4 × 2/9
  2. 3/5 × 5/8
  3. 7/10 × 5/14
  4. 2/3 ÷ 1/6
  5. 5/8 ÷ 1/4
  6. 3/4 ÷ 2/5
  7. A recipe needs 2/3 cup of milk. You make one half of the recipe. How much milk do you need?
  8. A 3/4-metre length of string is cut into pieces of 1/8 metre. How many pieces can be cut?

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. 8/9.
  2. 15/40 = 3/8.
  3. 35/140 = 1/4.
  4. 2/3 × 6/1 = 4.
  5. 5/8 × 4/1 = 20/8 = 5/2 = 2 1/2.
  6. 3/4 × 5/2 = 15/8 = 1 7/8.
  7. 1/2 × 2/3 = 1/3 cup.
  8. 3/4 ÷ 1/8 = 3/4 × 8 = 6 pieces.

11. Lesson Summary

Next learning goal: Practise mixed numbers and multi-step fraction problems, then apply fractions to decimals and percentages.

Educational note: This is a curriculum-neutral lesson for Grades 6–7. Teachers and parents can adapt examples and practice to their local curriculum.