Question

Find the value of the expression.
two fifths times two thirds plus five fourths times one third

Answer 1

To find the value of the expression \( \frac{2}{5} \times \frac{2}{3} + \frac{5}{4} \times \frac{1}{3} \), we can calculate each part separately and then add the results together.

First, calculate \( \frac{2}{5} \times \frac{2}{3} \):

\[
\frac{2}{5} \times \frac{2}{3} = \frac{2 \times 2}{5 \times 3} = \frac{4}{15}
\]

Next, calculate \( \frac{5}{4} \times \frac{1}{3} \):

\[
\frac{5}{4} \times \frac{1}{3} = \frac{5 \times 1}{4 \times 3} = \frac{5}{12}
\]

Now we need to add \( \frac{4}{15} \) and \( \frac{5}{12} \). To do this, we need a common denominator. The least common multiple of 15 and 12 is 60.

Convert \( \frac{4}{15} \) to have a denominator of 60:

\[
\frac{4}{15} = \frac{4 \times 4}{15 \times 4} = \frac{16}{60}
\]

Convert \( \frac{5}{12} \) to have a denominator of 60:

\[
\frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60}
\]

Now add the two fractions:

\[
\frac{16}{60} + \frac{25}{60} = \frac{16 + 25}{60} = \frac{41}{60}
\]

Thus, the value of the expression is

\[
\boxed{\frac{41}{60}}
\]