Question

Add −1 3/10 +(−4 2/15) .

Answer 1

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

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

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

Now we need to add these two improper fractions: \(-\frac{13}{10} + -\frac{62}{15}\).

To add the fractions, we need a common denominator. 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:
\[
-\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30}
\]

Now we can convert \(-\frac{163}{30}\) to a mixed number:
- \(163 \div 30 = 5\) with a remainder of \(13\).

So,
\[
-\frac{163}{30} = -5 \frac{13}{30}
\]

Finally, the result of \(-1 \frac{3}{10} + (-4 \frac{2}{15})\) is:
\[
\boxed{-5 \frac{13}{30}}
\]