### Simplify a fraction multiplication before multiplying

I'm having difficulty in solving this question which involves calculating fractions - this question relates to finding an arc length.

140 divided by 360, multiplied by 2, multiplied by 22 divided by 7, multiplied by 12:

140

360×2×22

7×12

Solution:

You can either put everything in the calculator, multiplying the top numbers, then dividing by 360 and 7.

Or, you can simplify before you multiply. This process is actually quite handy!

For example, the first fraction 140/360 can be simplified into 14/36, and then further into 7/18 before you multiply.

We get

7

18×2×22

7×12

Now, the 7 in the numerator and the 7 in the denominator cancel out.

Why? Every time we have the same number in the numerator and the denominator, and the only other operation involved is multiplication (like in our example), that number cancels out. It becomes the same situation as if you multiply by 7 and divide by 7: the result is 1. As a shortcut, we can cancel out those numbers and write 1's in their places…

140 divided by 360, multiplied by 2, multiplied by 22 divided by 7, multiplied by 12:

140

360×2×22

7×12

Solution:

You can either put everything in the calculator, multiplying the top numbers, then dividing by 360 and 7.

Or, you can simplify before you multiply. This process is actually quite handy!

For example, the first fraction 140/360 can be simplified into 14/36, and then further into 7/18 before you multiply.

We get

7

18×2×22

7×12

Now, the 7 in the numerator and the 7 in the denominator cancel out.

Why? Every time we have the same number in the numerator and the denominator, and the only other operation involved is multiplication (like in our example), that number cancels out. It becomes the same situation as if you multiply by 7 and divide by 7: the result is 1. As a shortcut, we can cancel out those numbers and write 1's in their places…