Before it started to rain, John cut 1/6 of the grass and Eugene cut 1/3 of the grass. Which statement is true?

Question

Responses

The boys cut almost the whole yard.
The boys cut almost the whole yard.

Together the boys cut 3/4 of the yard.
Together the boys cut 3 fourths of the yard.

The boys cut exactly 1/2 of the yard.

Together the boys did not cut 1/2 of the yard.

Answer 1

To find out how much grass John and Eugene cut together, we need to add the fractions of the yard they each cut.

John cut \( \frac{1}{6} \) of the grass, and Eugene cut \( \frac{1}{3} \) of the grass.

First, we need to convert \( \frac{1}{3} \) to a fraction with a denominator of 6 so we can easily add the fractions:

\[ \frac{1}{3} = \frac{2}{6} \]

Now we can add the two fractions:

\[ \frac{1}{6} + \frac{2}{6} = \frac{3}{6} \]

We can simplify \( \frac{3}{6} \) to \( \frac{1}{2} \).

So, the boys cut exactly \( \frac{1}{2} \) of the yard.

The true statement is:

The boys cut exactly 1/2 of the yard.