Question

Before it started to rain, Bobby cut 1 8 of the grass in his yard and Danny cut 1 5 of the grass in the yard. Both boys were disappointed because they were not able to cut the entire yard.

Which statement is TRUE?

A)Together the boys didn't even cut half the yard. B) The boys were able to cut more than half the yard. C) The boys cut almost three-fourths of the yard. D) Together the boys cut almost the entire yard.

Answer 1

It’s B. The boys were able to cut more than half the yard.

Answer 2

A) Together the boys didn't even cut half the yard.

Explanation:

The amount cut was ...

1/8 + 1/5 = 5/40 +8/40 = 13/40

This amount is less than half = 20/40, so choice A is appropriate.

_____

You can reason about these fractions several ways:

1. half is 2 1/2 fifths. 1/8 is less than 1/5, so 1/5+1/8 < (2 1/2)/5.

2. half is 4/8. 1/5 is more than 1/8 but is less than 2/8. 1/8 + 1/5 < 3/8 < 1/2

3. 1/5 < 1/4; 1/8 < 1/4; 1/2 = 2/4, so two amounts less than 1/4 cannot be more than 1/2.