To multiply fractions: 1) Multiply the numerators together to get the new numerator 2) Multiply the denominators together to get the new denominator 3) Simplify the resulting fraction if possible by cancelling common factors in the numerator and denominator.

1. October 4, 2012
Multiplication and division of fractions
1. Multiplying fractions
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2. Explanation October 4, 2012
A simple fraction 3 Numerator
2×
8 Denominator
You can think of any as the number number 1 multiplied
this fraction as the 2 multiplied by the
by the numerator, then divided by the denominator.
numerator, then divided by the denominator.
1×3÷8
1 3 1×3
This is the same as × or
1 8 1×8
What happens when you multiply by a fraction?
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3. Explanation October 4, 2012
What happens when you multiply by a fraction? 2× 3
8
You can think of this as the number 2 multiplied by the
numerator, then divided by the denominator.
2×3÷8
2×3
This is the same as × or
1×8
6 3
= 8 = 4
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4. Explanation October 4, 2012
When you multiply two fractions together, you can think
of it as working out what amount the first fraction of the
second fraction would be.
1 1
of = =
2 8
or
1 1 1
× =
2 4 8
Notice that all you have to do is first multiply the two
numerators and then multiply the two denominators.
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5. Examples October 4, 2012
3 1 3
× =
5 2 10
In the next example, you can simplify your answer…
3 1 3 1
× = =
4 3 12 4
Remember, when you have mixed fractions, you must
multiply the whole number by the denominator, then add
your answer to the numerator…
3 3 8 15 120
1 5
× 3 = × =
4 5 4 20
= 6
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6. Explanation October 4, 2012
Simplifying by cancelling
These two fractions have been multiplied together, then
the answer simplified.
13 3
1 1 1
× = =
4 62 24 8
8
If a numerator in one fraction has a common factor with
the denominator in the other fraction, you can cancel
down the fractions, before carrying out the multiplication.
Cross out the numbers with the common factor 3 and
replace them with the quotients for that factor .
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End