Multiplying Mixed Fractions
("Mixed Fractions" are also called "Mixed Numbers")
To multiply Mixed Fractions:
- convert to Improper Fractions
- Multiply the Fractions
- convert the result back to Mixed Fractions
Example
What is 1 3/8 × 3 ?
Think of Pizzas.
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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):
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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:
And, lastly, convert to a mixed fraction (only because the original fraction was in that form):
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 x 2 1/5 ?
If you know how to go from Mixed Fraction to Improper Fractions and back again it is easy ...
Step, by step it is:
Convert both to improper fractions
1 1/2 × 2 1/5 = 3/2 × 11/5
Multiply
3/2 × 11/5 = 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 x 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
I was asked to solve this one:
-1 5/9 × -2 1/7 = ?
So, my first step was to 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
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