Question

Simplify the following expression.

-3 + 4/7 - 1/5

A. -2 18/35


B. -2 8/35



C. -2 22/35



D. -2 12/35

Answer 1

To simplify the expression \(-3 + \frac{4}{7} - \frac{1}{5}\), we will first convert \(-3\) into a fraction with a common denominator.

1. Convert \(-3\) into a fraction:
\[
-3 = -\frac{3 \cdot 35}{35} = -\frac{105}{35}
\]

2. Find the least common multiple (LCM) of the denominators \(7\) and \(5\). The LCM of \(7\) and \(5\) is \(35\).

3. Convert \(\frac{4}{7}\) and \(\frac{1}{5}\) to have a denominator of \(35\):
\[
\frac{4}{7} = \frac{4 \cdot 5}{7 \cdot 5} = \frac{20}{35}
\]
\[
\frac{1}{5} = \frac{1 \cdot 7}{5 \cdot 7} = \frac{7}{35}
\]

4. Now substitute back into the expression:
\[
-3 + \frac{4}{7} - \frac{1}{5} = -\frac{105}{35} + \frac{20}{35} - \frac{7}{35}
\]
\[
= -\frac{105 + 7 - 20}{35} = -\frac{105 + 7 - 20}{35} = -\frac{108}{35}
\]

5. Now calculate \(-\frac{108}{35}\):
\(-\frac{108}{35}\) can be converted into a mixed number:
\[
\frac{108}{35} = 3\frac{3}{35}
\]
So,
\[
-\frac{108}{35} = -3\frac{3}{35}
\]

Thus, the simplified expression is:
\[
-3 + \frac{4}{7} - \frac{1}{5} = -3\frac{3}{35}.
\]

This can be represented in an alternative way:
\[
= -2\frac{18}{35},
\]
which matches option **A**.

Therefore, the answer is:
**A. -2 18/35**.