add 3/8×1/4+3/4+1/5

Answer 1

To solve the expression \( \frac{3}{8} \times \frac{1}{4} + \frac{3}{4} + \frac{1}{5} \), we'll handle each part step-by-step.

First, let's deal with the multiplication part: \( \frac{3}{8} \times \frac{1}{4} \).

\[
\frac{3}{8} \times \frac{1}{4} = \frac{3 \times 1}{8 \times 4} = \frac{3}{32}
\]

So the expression now is:

\[
\frac{3}{32} + \frac{3}{4} + \frac{1}{5}
\]

Next, we need a common denominator to add these fractions together. The least common multiple (LCM) of the denominators 32, 4, and 5 is 160.

Let's convert each fraction to have a denominator of 160.

\[
\frac{3}{32} = \frac{3 \times 5}{32 \times 5} = \frac{15}{160}
\]

\[
\frac{3}{4} = \frac{3 \times 40}{4 \times 40} = \frac{120}{160}
\]

\[
\frac{1}{5} = \frac{1 \times 32}{5 \times 32} = \frac{32}{160}
\]

Now we add them together:

\[
\frac{15}{160} + \frac{120}{160} + \frac{32}{160} = \frac{15 + 120 + 32}{160} = \frac{167}{160}
\]

So, the final result is:

\[
\frac{167}{160}
\]

This can also be represented as a mixed number:

\[
1 \frac{7}{160}
\]

Thus, \( \frac{3}{8} \times \frac{1}{4} + \frac{3}{4} + \frac{1}{5} = \frac{167}{160} \) or \( 1 \frac{7}{160} \).