College

Samantha is preparing a fruit salad. She has the following ingredients:

- [tex]\frac{3}{5}[/tex] of the fruit salad is made up of strawberries.
- [tex]\frac{1}{4}[/tex] of the fruit salad is made up of blueberries.
- The remaining portion of the fruit salad is made up of kiwi.

What fraction of the fruit salad is made up of kiwi?

Answer :

First, note that strawberries make up [tex]$\frac{3}{5}$[/tex] of the salad and blueberries make up [tex]$\frac{1}{4}$[/tex] of the salad.

To find the fraction of the salad that consists of kiwi, we first add the fractions for strawberries and blueberries:

[tex]$$
\text{Total fraction (strawberries and blueberries)} = \frac{3}{5} + \frac{1}{4}.
$$[/tex]

To add these fractions, we convert them to have a common denominator. The least common denominator for [tex]$5$[/tex] and [tex]$4$[/tex] is [tex]$20$[/tex]:

[tex]$$
\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}, \quad \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}.
$$[/tex]

Now add the two fractions:

[tex]$$
\frac{12}{20} + \frac{5}{20} = \frac{12 + 5}{20} = \frac{17}{20}.
$$[/tex]

Since the entire salad represents the whole, which is [tex]$1$[/tex], the fraction of the salad that is made up of kiwi is the remaining portion:

[tex]$$
\text{Fraction for kiwi} = 1 - \frac{17}{20} = \frac{20}{20} - \frac{17}{20} = \frac{3}{20}.
$$[/tex]

Thus, the fraction of the fruit salad that is made up of kiwi is:

[tex]$$
\boxed{\frac{3}{20}}.
$$[/tex]