Grade: Grade 5 Subject: Mathematics Unit: Fraction Operations SAT: Algebra ACT: Math

Multiplying & Dividing Fractions

Unlike adding and subtracting, multiplying fractions is actually easier! Learn the simple rule for multiplication and the famous "Keep-Change-Flip" method for division.

Multiplying Fractions

The Multiplication Rule

To multiply fractions: Multiply the numerators together. Multiply the denominators together. That's it!

Unlike addition and subtraction, you do NOT need common denominators to multiply fractions. Multiplication is straightforward: just multiply across!

1 Multiply the numerators (top x top)

The product of the numerators becomes your new numerator.

2 Multiply the denominators (bottom x bottom)

The product of the denominators becomes your new denominator.

3 Simplify if needed

Reduce your answer to lowest terms.

Example: 2/3 x 3/4
2 3
x
3 4
=
2 x 3 3 x 4
=
6 12
=
1 2

Simplified: 6/12 = 1/2 (both divisible by 6)

Visual Understanding: Multiplying 2/3 x 3/4 means "2/3 of 3/4". If you shade 3/4 of a rectangle, then shade 2/3 of THAT shaded area, you get the answer!
Visual: 1/2 x 3/4 = 3/8

Shade 3 out of 4 columns (3/4), then shade 1 out of 2 rows (1/2). The overlap is your answer!

Yellow = 3/4 (horizontally). Blue = overlap = 3/8 of the whole!

Dividing Fractions: Keep-Change-Flip

The Division Rule: KCF

To divide fractions, use Keep-Change-Flip: Keep the first fraction, Change division to multiplication, Flip the second fraction. Then multiply!

KEEP

Keep the first fraction exactly as it is

CHANGE

Change the division sign to multiplication

FLIP

Flip the second fraction (swap top and bottom)

Example: 3/4 divided by 1/2

Step 1 - KEEP the first fraction:

3 4

Step 2 - CHANGE division to multiplication:

3 4
x

Step 3 - FLIP the second fraction (1/2 becomes 2/1):

3 4
x
2 1

Step 4 - MULTIPLY:

3 4
x
2 1
=
6 4
=
3 2
= 1 1/2
Why does KCF work? Dividing by a fraction is the same as multiplying by its reciprocal (flipped version). When you divide something into smaller pieces, you actually get MORE pieces - that's why the answer is often bigger than both starting numbers!

Fraction Calculator

Practice multiplying and dividing fractions!

Multiply or Divide Fractions

Click x or ÷ to see the step-by-step solution!

Practice Problems

Problem 1: Multiplication

1 2 x 2 3 = ?

Problem 2: Multiplication

3 5 x 5 6 = ?

Problem 3: Division

1 2 ÷ 1 4 = ?

Problem 4: Division

2 3 ÷ 4 5 = ?

Problem 5: What is the reciprocal of 3/7?

Problem 6: Word Problem

A recipe calls for 3/4 cup of flour. If you want to make 1/2 of the recipe, how much flour do you need?

Check Your Understanding

Do you need common denominators to multiply fractions?

In "Keep-Change-Flip", what do you flip?

What We Learned

x

Multiplication

Multiply top x top and bottom x bottom. No common denominators needed!

÷

Division (KCF)

Keep first fraction, Change ÷ to x, Flip second fraction, then multiply.

🔄

Reciprocal

The "flipped" version of a fraction. The reciprocal of a/b is b/a.

✨

Simplify

Always reduce your final answer to lowest terms.

Next Steps

  • Practice multiplying fractions with whole numbers
  • Try word problems involving fraction multiplication
  • Work on mixed numbers (multiply and divide)
  • Move on to learning about decimals!