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August 14th, 2014, 10:09 AM   #1
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How to simplify a fraction times by a fraction

Hi please can someone explain how to simplify the following -

4/3 x 3/8

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August 14th, 2014, 10:49 AM   #2
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To multiply a fraction by the fraction, we need to multiply their numerators, and write result as a numerator, and multiply their denominators, and write result as a denominator:

Now we can use the rule: if we divide the numerator and denominator of the certain fraction by the same number, we get the same fraction:
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August 15th, 2014, 02:46 AM   #3
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Skaa is correct, but you might find the following method a lot easier to pick up.

When multiplying two fractions together, follow these steps:

Step 1: cancel any bottom with any top. Repeat until you can't cancel anymore.
Step 2: multiply all the top numbers together and bottom numbers together


Example 1:

So, we have

$\displaystyle \frac{4}{3} \times \frac{3}{8}$

Step 1: cancel any bottom with any top.

Cancelling is a process where you cross out two numbers and replace them with smaller ones by diving each one by the same number.

Can we cancel the 4 with the 3 on the bottom? No, because there is no number that we can divide both of them by. We could divide by 1, but that's not going to do anything.
Can we cancel the 4 with the 8? Yes, because 4 goes into both of these.

If we divide the 4 and the 8 by 4, we get 1 and 2. We replace the numbers by crossing out the old ones and writing the new one next to it

$\displaystyle \frac{^1\cancel{4}}{3} \times \frac{3}{\cancel{8}^2}$

We can also cancel the 3 on the top with the 3 on the bottom because we can divide both of these by 3, giving 1 and 1.

We are left with

$\displaystyle \frac{^1\cancel{4}}{\cancel{3}^1} \times \frac{^1\cancel{3}}{\cancel{8}^2}$

and we can't cancel anymore numbers.

It can sometimes look a bit messy with all the crossing out, so try and keep it neat! Don't scribble the numbers out completely because you need to see the old number to check your answer if you made a mistake, so crossing it out with a single diagonal line is enough.

Step 2: multiply all the top numbers together and bottom numbers together

$\displaystyle \frac{^1\cancel{4}}{\cancel{3}^1} \times \frac{^1\cancel{3}}{\cancel{8}^2} = \frac{1\times 1}{1\times 2} = \frac{1}{2}$

Example 2:

$\displaystyle \frac{63}{25} \times \frac{35}{81}$

Same process, but we have bigger numbers:

What goes into 63 and 81? 9! So we divide the 63 and 81 by 9 to get 7 and 9...

$\displaystyle \frac{^7\cancel{63}}{25} \times \frac{35}{\cancel{81}^9}$

What goes into 25 and 35? 5! So we divide the 25 and 35 by 5 to get 5 and 7...

$\displaystyle \frac{^7\cancel{63}}{\cancel{25}^5} \times \frac{^7\cancel{35}}{\cancel{81}^9}$

Now multiply top numbers together and bottom numbers together

$\displaystyle \frac{^7\cancel{63}}{\cancel{25}^5} \times \frac{^7\cancel{35}}{\cancel{81}^9} = \frac{7\times 7}{5\times 9} = \frac{49}{45} = 1 \frac{4}{45}$

Because the top number was bigger than the bottom number we needed to convert the improper fraction to a mixed number.
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