Question

Matthew helped clean the kitchen for 1/3 hour. He helped with the laundry for 1 1/2 hours.

Altogether, how many hours did Matthew help clean the kitchen and help with laundry?

Answer 1

To find the total hours Matthew helped with cleaning the kitchen and doing laundry, we first need to convert the time he spent on each task into a common format.

Matthew helped clean the kitchen for \( \frac{1}{3} \) hour.

Matthew helped with the laundry for \( 1 \frac{1}{2} \) hours, which can be converted to an improper fraction:
\[
1 \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \text{ hours.}
\]

Now we can add the two times together:
\[
\frac{1}{3} + \frac{3}{2}.
\]

To add these fractions, we need a common denominator. The least common multiple of 3 and 2 is 6.

Now we convert each fraction:
\[
\frac{1}{3} = \frac{2}{6} \quad \text{(multiply the numerator and denominator by 2)},
\]
\[
\frac{3}{2} = \frac{9}{6} \quad \text{(multiply the numerator and denominator by 3)}.
\]

Now we can add:
\[
\frac{2}{6} + \frac{9}{6} = \frac{2 + 9}{6} = \frac{11}{6} \text{ hours.}
\]

Finally, we can express \( \frac{11}{6} \) hours as a mixed number:
\[
\frac{11}{6} = 1 \frac{5}{6} \text{ hours.}
\]

So, altogether, Matthew helped for \( \frac{11}{6} \) hours or \( 1 \frac{5}{6} \) hours.