Question

Each week, Dwight calculated that he spends 2/3 of his allowance on food and 1/9 on video games. How much did he spend on food and video games?

Answer 1

`2/3+1/9=2/3(1)+1/9=2/3(3/3)+1/9=6/9+1/9=7/9`

Explanation:

To answer this, we need to make the fractions use the same size of slice, and it's the denominator that determines how big the slice is. Right now, we know that the food portion of his budget, if we slice the budget into 3 pieces, takes up 2 of them. And we also know that if we slice up his budget 9 ways, video games take up 1 of them. We can't compare the two amounts because we are slicing his allowance into two different sizes. So let's change the fractions so that they are the same size.

So how do we get `2/3 and 1/9` to slice up the same way? Through a clever use of the number 1:

`2/3+1/9=2/3(1)+1/9=2/3(3/3)+1/9=6/9+1/9=7/9`