Question

(1/2+1/5) - (3/8 + 1/4) =

Answer 1

To solve the expression \((1/2 + 1/5) - (3/8 + 1/4)\), we will first simplify the two parts separately before combining the results.

**Step 1: Simplify \(1/2 + 1/5\)**

To add the fractions, we need a common denominator. The least common multiple of 2 and 5 is 10.

\[
1/2 = 5/10 \quad \text{and} \quad 1/5 = 2/10
\]

Adding them together:

\[
1/2 + 1/5 = 5/10 + 2/10 = 7/10
\]

**Step 2: Simplify \(3/8 + 1/4\)**

The least common multiple of 8 and 4 is 8.

\[
1/4 = 2/8
\]

Adding these:

\[
3/8 + 1/4 = 3/8 + 2/8 = 5/8
\]

**Step 3: Subtract the two results**

Now, we need to compute:

\[
(7/10) - (5/8)
\]

To subtract these fractions, we need a common denominator. The least common multiple of 10 and 8 is 40.

Convert \(7/10\) and \(5/8\) to have a denominator of 40:

\[
7/10 = 28/40 \quad (\text{since } 7 \times 4 = 28)
\]
\[
5/8 = 25/40 \quad (\text{since } 5 \times 5 = 25)
\]

Now subtract:

\[
28/40 - 25/40 = (28 - 25)/40 = 3/40
\]

Therefore, the final answer is:

\[
\boxed{3/40}
\]