Multiplying Fractions

There are 3 simple steps to multiply fractions 1. Multiply the top numbers (the numerators). 2. Multiply the bottom numbers (the denominators). 3. Simplify the fraction if needed.

 

Example 1

1	×	2
2		5

Step 1. Multiply the top numbers:

1	×	2	=	1 × 2	=	2
2		5

Step 2. Multiply the bottom numbers:

1	×	2	=	1 × 2	=	2
2		5		2 × 5		10

Step 3. Simplify the fraction:

2	=	1
10		5

(If you are unsure of the last step see Equivalent Fractions)

Example 2

1	×	9
3		16

Step 1. Multiply the top numbers:

1	×	9	=	1 × 9	=	9
3		16

Step 2. Multiply the bottom numbers:

1	×	9	=	1 × 9	=	9
3		16		3 × 16		48

Step 3. Simplify the fraction:

9	=	3
48		16

Multiplying Mixed Fractions

("Mixed Fractions" are also called "Mixed Numbers")

To multiply Mixed Fractions:

1. convert to Improper Fractions
2. Multiply the Fractions
3. convert the result back to Mixed Fractions

Example: What is 1³/₈ × 3 ?

Think of Pizzas.

1 3/8 is 1 pizza and 3 eighths of another pizza.

First, convert the mixed fraction (1 ³/₈) to an an improper fraction (¹¹/₈):

Cut the whole pizza into eighths and how many eighths do you have in total? 1 lot of 8, plus the 3 eighths = 8+3 = 11 eighths.

Now multiply that by 3:

1 3/8 × 3 = 11/8 × 3/1 = 33/8 You have 33 eighths.

And, lastly, convert to a mixed fraction (only because the original fraction was in that form):

33 eighths is 4 whole pizzas (4×8=32) and 1 eighth left over.

And this is what it looks like in one line:

1 ³/₈ × 3 = ¹¹/₈ × ³/₁ = ³³/₈ = 4 ¹/₈

Another Example: What is 1¹/₂ x 2¹/₅ ?

Do the steps from above:

1. convert to Improper Fractions
2. Multiply the Fractions
3. convert the result back to Mixed Fractions

Step, by step it is:

Convert both to improper fractions

1 ¹/₂ × 2 ¹/₅ = ³/₂ × ¹¹/₅

Multiply the fractions (multiply the top numbers, multiply bottom numbers):

³/₂ × ¹¹/₅ = ^{(3 × 11)}/_{(2 × 5)} = ³³/₁₀

Convert to a mixed number

³³/₁₀ = 3 ³/₁₀

If you are clever you can do it all in one line like this:

1 ¹/₂ × 2 ¹/₅ = ³/₂ × ¹¹/₅ = ³³/₁₀ = 3 ³/₁₀

One More Example: What is 3¹/₄ x 3¹/₃ ?

Convert both to improper fractions

3 ¹/₄ × 3 ¹/₃ = ¹³/₄ × ¹⁰/₃

Multiply

¹³/₄ × ¹⁰/₃ = ¹³⁰/₁₂

Convert to a mixed number (and simplify):

¹³⁰/₁₂ = 10 ¹⁰/₁₂ = 10 ⁵/₆

Once again, here it is in one line:

3 ¹/₄ × 3 ¹/₃ = ¹³/₄ × ¹⁰/₃ = ¹³⁰/₁₂ = 10 ¹⁰/₁₂ = 10 ⁵/₆