# I came across this sum in the Unitary Method With Fractions exercise in my Math Textbook. What am I supposed to do here?

## Last week we picked 1/3 of our grapes and this week we picked 1/4 of them. So far we have picked 3682 kg of grapes. What is the total weight of grapes we expect to pick?

Sep 10, 2016

$6312 k g$

#### Explanation:

Let $x =$ the total weight of grapes

Last week we picked $\frac{1}{3}$ of the grapes or $\frac{1}{3} x$

This week we picked $\frac{1}{4}$ of the grapes or $\frac{1}{4} x$

Over these two weeks we have picked
$\frac{1}{3} x + \frac{1}{4} x = 3682$ kg of grapes

To solve, multiply both sides of the equation by the common denominator 12 ($3 \cdot 4 = 12$)

$12 \left(\frac{1}{3} x + \frac{1}{4} x\right) = 12 \cdot 3682$

Distribute
$4 x + 3 x = 44184$

Combine like terms
$7 x = 44184$

Divide both sides by 7
$\frac{7 x}{7} = \frac{44184}{7}$

$x = 6312 k g$

Sep 10, 2016

Find what 1 part is, then find the value of ALL the parts:

$\frac{1}{12}$ or "1 part " is $\rightarrow 3682 \div 7 = 526 k g$

$\frac{12}{12}$ or "all the parts" is $\rightarrow 12 \times 526 = 6 , 312 k g$

#### Explanation:

The "Unitary method" means to find out what ONE part represents.

Unit = one .

What fraction of grapes have been picked altogether so far?

$\frac{1}{3} + \frac{1}{4} = \frac{4 + 3}{12}$

=$\frac{7}{12}$

If $\frac{7}{12}$ or "7 parts" represent 3682 kg

Then $\frac{1}{12}$ or "1 part " is $\rightarrow 3682 \div 7 = 526 k g$

$\frac{12}{12}$ or "all the parts" is $\rightarrow 12 \times 526 = 6 , 312 k g$