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12 Out of 14 As a Percentage OR

## 12 Out of 14 As a Percentage

We’re now one-quarter through the year, and as I think about our first fourteen months in terms of poetry, this is when we first hear something like “All that is gold does not glitter,” or phrases like that. It’s in these periods of time when the words and phrases we use seem to be the most potent. That’s when “two weeks” starts to take on a different meaning.

### Step

One area that often catches people out is year-on-year percentage increases. For example, Freya has £10 and each year this increases by 5%. How much will she have after 3 years? Some people can be tempted to add together the 5% for the 3 years i.e. 15% and multiply the £10 by 15% giving £11.5. This is incorrect. The correct way of approaching questions like this is to remember that EACH year the initial £10 increased by 5%. So at the end of year 1, Freya would have £10 x 1.05 = £10.5. At the end of year 2, she would have £10.5 x 1.05 = 11.025, and so on. It is important to add in each of these steps to arrive at the correct answer.

Step 2: we write $$\frac{3}{5}$$ as an equivalent fraction over $$100$$. Using the fact that $$100 = 5\times 20$$, we multiply both the numerator and the denominator by $$20$$ to obtain our fraction: $\frac{3}{5} = \frac{3\times 20}{5\times 20} = \frac{60}{100}$ Finally, since $$\frac{60}{100} = 60\%$$ we can state that $$3$$ is $$60\%$$ of $$5$$. (Source: www.radfordmathematics.com)

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