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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