Question

A recipe calls for `2 1/2` cups of sugar. You have `2 1/3` cups of sugar Do you have enough sugar? If not, how much more sugar is needed?

Answer 1

`" not enough require another " 1/6" cup"`

Explanation:

Before we can compare these `color(blue)"mixed numbers"` we need to change them to `color(blue)"improper fractions"`

`rArr2 1/2=5/2" and " 2 1/3=7/3`

To compare the fractions `5/2" and " 7/3` we require them to have a `color(blue)"common denominator"`

The lowest common denominator of 2 and 3 is 6 so we have to convert them into fractions with a denominator of 6

`rArr5/2=(5xx3)/(2xx3)=15/6" and " 7/3=(7xx2)/(3xx2)=14/6`

`" Now" 14/6<15/6" thus there is not enough sugar"`

`"amount of sugar needed " =15/6-14/6=1/6" of a cup"`