Question

Add −1 3/10 +(−4 2/15). (1 point)

Answer 1

To add \( -1 \frac{3}{10} + (-4 \frac{2}{15}) \), we first convert the mixed numbers to improper fractions.

1. Convert \( -1 \frac{3}{10} \):
\[
-1 \frac{3}{10} = -\left(\frac{10 \times 1 + 3}{10}\right) = -\left(\frac{10 + 3}{10}\right) = -\left(\frac{13}{10}\right)
\]

2. Convert \( -4 \frac{2}{15} \):
\[
-4 \frac{2}{15} = -\left(\frac{15 \times 4 + 2}{15}\right) = -\left(\frac{60 + 2}{15}\right) = -\left(\frac{62}{15}\right)
\]

Now, we need to add \( -\frac{13}{10} + -\frac{62}{15} \). We first find a common denominator for the fractions. The least common multiple (LCM) of 10 and 15 is 30.

3. Convert \( -\frac{13}{10} \) to a fraction with a denominator of 30:
\[
-\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30}
\]

4. Convert \( -\frac{62}{15} \) to a fraction with a denominator of 30:
\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

Now we can add the two fractions:
\[
-\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30}
\]

The result of adding \( -1 \frac{3}{10} + (-4 \frac{2}{15}) \) is:
\[
-\frac{163}{30}
\]

To express this as a mixed number, we divide 163 by 30:
\[
163 \div 30 = 5 \quad \text{(remainder } 13\text{)}
\]
Thus,
\[
-\frac{163}{30} = -5 \frac{13}{30}
\]

Therefore, the final answer is:
\[
\boxed{-5 \frac{13}{30}}
\]