Calculate Percent of Range of Numbers

Question

If I have a range from $-4$ to $4$, how can I figure out what $60\%$ of that range is? Pictorially:

I'm looking for $x$ such that the distance from $-4$ to $x$ is $60\%$ of the distance from $-4$ to $4$. How can I find such an $x$?

Answer 1

First, you want to know what the entire range is. That is simply: $$\text{range} = \text{big number} - \text{small number} = 4-(-4) = 8$$

Then, we want sixty percent of the range. In many word problems, one may replace the word of with multiplication. That is, we're first looking for $(60\%)\times(\text{range})$. Recall that $60\%= 0.60$, and the rest should be straightforward.

The above tells us the distance from $-4$ to $x$. To find $x$, then, we simply add that distance to $-4$.