To multiply fractions, simply multiply the numerators; then multiply the denominators. Simplify to lowest terms if possible.
Multiply
This answer had to be simplified because it wasn't in lowest terms.
When multiplying fractions, you can cancel (do early simplifying) first, which eliminates the need to simplify your answer later. To cancel, find a number that divides evenly into one numerator and one denominator. In Example , 2 will divide evenly into 2 in the numerator (it goes in one time) and 12 in the denominator (it goes in six times). Thus,
Whole numbers can also be written as fractions
Multiply
Multiply
Remember: You may cancel only when multiplying fractions.
To multiply mixed numbers, first change any mixed number to an improper fraction. Then multiply the numerators together and the denominators together, as shown in Example .
Multiply
Multiply
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 138 × 3 ?
Think of Pizzas.
First, convert the mixed fraction (138) to an improper fraction (118):
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:
138 × 3 = 118 × 31 = 338
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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:
138 × 3 = 118 × 31 = 338 = 418
Another Example: What is 112 × 215 ?
Do the steps from above:
- convert to Improper Fractions
- Multiply the Fractions
- convert the result back to Mixed Fractions
Step, by step it is:
Convert Mixed to Improper Fractions:
112 = 22+12 = 32
215 =105+15 =115
Multiply the fractions (multiply the top numbers, multiply bottom numbers):
32 × 115 = 3 × 112 × 5 = 3310
Convert to a mixed number
3310 = 3310
If you are clever you can do it all in one line like this:
112 × 215 = 32 × 115 = 3310 = 3310
One More Example: What is 314 × 313 ?
Convert Mixed to Improper Fractions:
314 = 134
313 = 103
Multiply
134 × 103 = 13012
Convert to a mixed number:
13012 = 101012
And simplify:
101012 = 1056
Here it is in one line:
314 × 313 = 134 × 103 = 13012 = 101012 = 1056
This One Has Negatives: What is −159 × −217 ?
Convert Mixed to Improper Fractions:
159 = 99 + 59 = 149
217 = 147 + 17 =
157
Then multiply the Improper Fractions (Note: negative times negative gives positive) :
−149 × −157 = −14 × −159 × 7 = 21063
We can simplify now. Here we use two steps, first by 7 (21 and 63 are both multiples of 7), then again by 3. But it could be done in one step by dividing by 21:
21063 = 309 = 103
Finally convert to a Mixed Fraction (because that was the style of the question):
103 = (9+1)3 = 93 + 13 = 313