Anton is making a fruit salad. He uses 2/3 cup of grapes and 1/2 cup of strawberries. What is the total amount of fruit Anton uses?

Jul 2, 2017

A total of $\frac{7}{6}$, or $1 \frac{1}{6}$ cups of fruit was used to make the fruit salad.

Explanation:

Let $x$ equal the total amount of fruit.

$x = \frac{2}{3} c + \frac{1}{2} c$

In order to add fractions, the denominators must be the same. In this case, we can multiply the denominators to get the least common denominator (LCD). The least common denominator is $3 \times 2 = 6$. Multiply each fraction by an equivalent fraction, color(red)(a/a, that will give each fraction a denominator of $6$.

x=2/3cxxcolor(red)(2/2)+1/2cxxcolor(red)(3/3

Simplify.

$x = \frac{4}{6} c + \frac{3}{6} c$

$x = \frac{7}{6} c$

The improper fraction $\frac{7}{6}$ can be converted to a mixed fraction by dividing the numerator by the denominator. The whole number quotient is the whole number for the fraction, and the remainder becomes the new numerator over the same denominator.

$x = 7 \div 6$

$x = 1 R 1$

$x = 1 \frac{1}{6}$

Jul 2, 2017

$\frac{2}{3} c G r + \frac{1}{2} c S t = 1 \frac{1}{6} c S A L A D \to$ the total amount of fruit used.

Explanation:

For Anton to calculate the total amount of fruit in the salad, he will have to add the components by first changing the given measurements to those which will add easily. He must express the two numbers in common terms.

$\frac{2}{3}$ will not add to $\frac{1}{2}$ directly.

so we need to make the terms match each other.

If we multiply the denominator (bottom number) $3$ by the denominator $2$ we will get $3 \times 2 = 6$.

Because we multiplied the $3$ and the $2$ to get the $6$, we know that $6$ is common to both terms.

So now we can make both terms common by multiplying each one so both have a denominator of $6$.

Starting with $\frac{2}{3}$, we will need to multiply the $3$ by $2$.

To multiply the entire fraction by $2$ we would only double the amount of grapes in the salad, and we would still end up with denominator $3$.

We will need a better way. How about multiplying by $\frac{2}{2}$?

We know that $\frac{2}{2} = 1$, so we do not double the grapes.

And using multiplication of numerators (top) and denominators (bottom) then we get:

$\frac{2}{3} \times \frac{2}{2} = \frac{4}{6} \to$ so we have Anton's grapes in a common term.

For the strawberries we use the same reasoning to multiply:

$\frac{1}{2} \times \frac{3}{3} = \frac{3}{6}$ so we have Anton's strawberries in a common term.

Now we can add them into the salad with cups $c$ as measure:

$\frac{4}{6} c G r + \frac{3}{6} c S t = \frac{7}{6} c S A L A D \to$ and we know $\frac{6}{6} c = 1 c$

$\frac{4}{6} c G r + \frac{3}{6} c S t = 1 \frac{1}{6} c S A L A D \to$ and replacing our given terms

$\frac{2}{3} c G r + \frac{1}{2} c S t = 1 \frac{1}{6} c S A L A D$