Question

What is 67.5% of 80?

Answer 1

`54`

Explanation:

Multiply 80 with 67.5% in decimal form, which is `67.5/100" or "0.675.`

So we now have:

`80 xx 0.675 = 54`

Answer 2

54

Explanation:

The % symbol is like a unit of measurement that is worth `1/100`

So `67.5%" is the same as "67.5xx1/100 = 67.5/100`

Consider the word 'of' in 65% of 80 as being the same as multiply

As an example: 3 of 78 is the same as `78+78+78 -> 3xx78`

So 67.6% of 80 `-> 67.5%xx80 -> 67.5/100xx80`

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Let me introduce you to a trick to work this out without using a calculator.

Write as `67.5xx80/100`

`67.5xx(8xx10)/100`

`67.5xx8/10`

8 is the same as `2xx2xx2`

First doubling of 67.5 = 135.0
Second doubling = 270
Third doubling = 540

Now we have:

`540/10 = 54`
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Check by calculator: `67.5/100xx80= 54`

`color(brown)("Sometimes the numbers do not lend themselves to this type of approach")`