Question

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

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

Together the boys cut three-fourths of the yard.
Together the boys cut three-fourths of the yard.

The boys cut exactly half of the yard.
The boys cut exactly half of the yard.

Together the boys did not cut half of the yard.

Answer 1

To determine the correct statement, we need to add the fractions of the grass that Amnar and Aayush cut.

Amnar cut \( \frac{1}{6} \) of the grass and Aayush cut \( \frac{1}{3} \) of the grass. To add these fractions, we need a common denominator. The least common multiple of 6 and 3 is 6.

In terms of sixths:
- \( \frac{1}{6} \) is already in sixths.
- \( \frac{1}{3} \) can be converted to sixths:
\[
\frac{1}{3} = \frac{2}{6}
\]

Now we can add the fractions:
\[
\frac{1}{6} + \frac{2}{6} = \frac{3}{6}
\]

This simplifies to:
\[
\frac{3}{6} = \frac{1}{2}
\]

Now we can evaluate the true statements based on our calculations:
1. **The boys cut almost the whole yard.** - This is not true, as they cut \( \frac{1}{2} \) of the yard.

2. **Together the boys cut three-fourths of the yard.** - This is false; they cut \( \frac{1}{2} \).

3. **The boys cut exactly half of the yard.** - This is true since \( \frac{3}{6} = \frac{1}{2} \).

4. **Together the boys did not cut half of the yard.** - This is false; they cut half of the yard.

The true statement is:
**The boys cut exactly half of the yard.**