# How do you convert the following phrases into math expressions, and then evaluate the expressions: 5 out of 9?

Apr 27, 2017

As a fraction this is $\frac{5}{9}$

As a decimal this is $0.5 \overline{5}$

As a ratio this is $5 : 4$

#### Explanation:

The wording 'out of' means that the 5 is part of the 9, where 9 represents the whole (all of it)

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So as a fraction we have: $\frac{5}{9}$

and as a decimal this is $5 \div 9 = 0.55555 \ldots \to 0.5 \overline{5}$

where the bar over the last 5 means that it is repeated for ever.
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As a ratio we have a relationship or proportion between the 5 and whatever is left after extracting the 5. Which is $9 - 5 = 4$

So as a ratio we have $5 : 4$