Question

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?

Answer 1

`6312kg`

Explanation:

Let `x=` the total weight of grapes

Last week we picked `1/3` of the grapes or `1/3x`

This week we picked `1/4` of the grapes or `1/4x`

Over these two weeks we have picked
`1/3x + 1/4x= 3682` kg of grapes

To solve, multiply both sides of the equation by the common denominator 12 (`3*4=12`)

`12(1/3x+1/4x)= 12*3682`

Distribute
`4x+3x=44184`

Combine like terms
`7x=44184`

Divide both sides by 7
`(7x)/7=44184/7`

`x=6312kg`

Answer 2

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

`1/12` or "1 part " is `rarr3682 div 7 = 526kg`

`12/12` or "all the parts" is `rarr12xx526 = 6,312kg`

Explanation:

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

Unit = one .

What fraction of grapes have been picked altogether so far?

`1/3 + 1/4 = (4+3)/12`

=`7/12`

If `7/12` or "7 parts" represent 3682 kg

Then `1/12` or "1 part " is `rarr3682 div 7 = 526kg`

`12/12` or "all the parts" is `rarr12xx526 = 6,312kg`