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?

2 Answers
Sep 10, 2016

#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#

Sep 10, 2016

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#