Unit 1 · Topic 3

Multiplying & Dividing Fractions

Overview

Multiply straight across. To divide, keep-change-flip.

Topic 3 of 4~15 min
Next: Decimal OperationsAll units
Unit overview

The lesson

Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

Multiplying fractions

Multiply straight across: numerator times numerator, denominator times denominator. Then simplify. For example, 2/3 × 4/5 = 8/15.

The denominator tells you how many equal parts the whole is split into. The numerator tells you how many of those parts you have.

Always ask: "What is the whole?" In 3/4 of a pizza, the whole is one pizza. In 3/4 of 20 students, the whole is 20 students.

Dividing fractions - keep, change, flip

To divide by a fraction, you multiply by its reciprocal (the fraction flipped upside down).

  1. 1Keep the first fraction as it is.
  2. 2Change the ÷ sign to ×.
  3. 3Flip the second fraction (its reciprocal).
  4. 4Multiply across and simplify.
Worked example

3/4 ÷ 2/3

  1. 1Keep 3/4, change ÷ to ×, flip 2/3 → 3/2.
  2. 23/4 × 3/2 = 9/8.
  3. 39/8 = 1 1/8.

Why this matters

Multiply straight across. To divide, keep-change-flip.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Adding numerators and denominators separately (2/3 + 1/4 is not 3/7). Match denominators first, or use a clear model.

Forgetting to simplify the final answer when a smaller equivalent fraction is possible.

Key ideas from this lesson

  1. Multiplying fractions
  2. Dividing fractions - keep, change, flip
  3. Keep the first fraction as it is.
  4. Change the ÷ sign to ×.
  5. Flip the second fraction (its reciprocal).
  6. Multiply across and simplify.

Video walkthroughs

Math Antics

Multiplying Fractions

Multiply across the top and bottom, then simplify.

Watch on YouTube
Math Antics

Dividing Fractions

Flip the second fraction, then multiply (keep-change-flip).

Watch on YouTube
Math Antics

Comparing Fractions

Compare fractions with like or unlike denominators.

Watch on YouTube
Math with Mr. J

How to Simplify Fractions

Put products and quotients of fractions in lowest terms.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

What is 2/5 × 3/7?

Step-by-step solution

  1. 1Multiply numerators: 2 × 3 = 6.
  2. 2Multiply denominators: 5 × 7 = 35.
  3. 3The product is 6/35.

Exercise 2

Try it yourself

What is 4/9 ÷ 2/3?

Step-by-step solution

  1. 14/9 × 3/2 = 12/18.
  2. 2Simplify by dividing numerator and denominator by 6: 2/3.

Exercise 3

Try it yourself

What is 3/4 × 8?

Step-by-step solution

  1. 13/4 × 8/1 = 24/4.
  2. 224 ÷ 4 = 6.

Exercise 4

Try it yourself

A recipe uses 2/3 cup of flour. You want to make half the recipe. How much flour do you need?

Step-by-step solution

  1. 1Half of 2/3 means multiply by 1/2.
  2. 22/3 × 1/2 = 2/6 = 1/3 cup.

Exercise 5

Try it yourself

What is 1 2/3 ÷ 2 1/2?

Step-by-step solution

  1. 11 2/3 = 5/3 and 2 1/2 = 5/2.
  2. 25/3 ÷ 5/2 = 5/3 × 2/5 = 10/15 = 2/3.

Re-read the lesson section if you get stuck, then try again without peeking at the solution.

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Multiplying & Dividing Fractions

Question 1 of 5

Medium

What is 3/4 ÷ 2/3?

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