Question

Jaime has 5 over 11 spaceof a project completed while Tim has finished 7 over 13 spaceof the same project.

a. Who has completed the greater amount of work?

b. How much of the project have they completed together? Show your work.

Answer 1

Part a) Tim has completed the greater amount of work

Part b) They have completed together
`(142)/(143)` of the project or
`99.3\%` of the project

Explanation:

Part a) Who has completed the greater amount of work?

we have

Jaime has 5/11 of a project completed

Tim has 7/13 of a project completed

Multiply 5/11 by 13/13 and 7/13 by 11/11

so

Jaime --->
`(5)/(11)((13)/(13))=(65)/(143)`

Tim --->
`(7)/(13)((11)/(11))=(77)/(143)`

Remember that

When fractions have the same denominator, the larger fraction is the one with the larger numerator

`(77)/(143) >(65)/(143)`

therefore

Tim has completed the greater amount of work

Part b) How much of the project have they completed together?

we have that

Jaime has 65/143 of a project completed

Tim has 77/143 of a project completed

Sum the fraction of the project completed by Jaime plus the fraction of the project completed by Tim

`(65)/(143)+(77)/(143)=(142)/(143)`

Convert to percentage

Multiply by 100

`(142)/(143)(100)=99.3\%`