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

Answer:

Step-by-step explanation:

Dad told Cody to mow $\frac{1}{4}$ of the yard.

He told Sam to mow $\frac{1}{3}$ of the remainder of the yard.

Sam might be thinking $\frac{1}{3}$ is bigger than $\frac{1}{4}$

But actually Sam was told to mow :

$\frac{1}{3}$ of (1 - $\frac{1}{4}$)

$\frac{1}{3}$ × (1 - $\frac{1}{4}$)

= $\frac{1}{3}$ × $\frac{3}{4}$

= $\frac{1}{4}$

Therefore, both mowed the yard in equal amount.