Question

Cody and Sam mowed the yard on Saturday. Dad told Cody to mow 1/4 of the yard. He told Sam to mow 1/3 of the remainder of the yard. Dad paid each of the boys an equal amount. Sam said, "Dad, that’s not fair! I had to mow one-third, and Cody only mowed one-fourth!" Explain to Sam the error in his thinking.

Draw a picture to support your reasoning.

Answer 1

Explanation:

Dad told Cody to mow
`(1)/(4)` of the yard.

He told Sam to mow
`(1)/(3)` of the remainder of the yard.

Sam might be thinking
`(1)/(3)` is bigger than
`(1)/(4)`

But actually Sam was told to mow :

`(1)/(3)` of (1 -
`(1)/(4)`)

`(1)/(3)` × (1 -
`(1)/(4)`)

=
`(1)/(3)` ×
`(3)/(4)`

=
`(1)/(4)`

Therefore, both mowed the yard in equal amount.