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Tuesday, May 1, 2012

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

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