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 1 3/8 × 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 1 1/2 × 2 1/5 ?

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 3 1/4 × 3 1/3 ?

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

This One Has Negatives: What is -1 5/9 × -2 1/7 ?

Convert Mixed to Improper Fractions:

1 5/9 = 9/9 + 5/9 = 14/9
2 1/7 = 14/7 + 1/7 = 15/7

Then multiply the Improper Fractions (Note: negative times negative gives positive) :

-14/9 × -15/7 = -14×-15 / 9×7 = 210/63 

I then decided to simplify next, first by 7 (because I noticed that 21 and 63 are both multiples of 7), then again by 3 (but I could have done it in one step by dividing by 21):

210/63 = 30/9 = 10/3

Finally convert to a Mixed Fraction (because that was the style of the question):

10/3 = (9+1)/3 = 9/3 + 1/3 = 3 1/3