Question

Add −1 3/10 +(−4 2/15).(1 point)
Responses

a.−5 1/5

b.−5 1/6

c.−2 5/6

d.−5 13/30

Answer 1

To solve the problem of adding \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), we first convert both mixed numbers into improper fractions.

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

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

Now, we need to add these two fractions:
\[
-\frac{13}{10} + (-\frac{62}{15})
\]
This simplifies to:
\[
-\frac{13}{10} - \frac{62}{15}
\]

Next, we need a common denominator to add these fractions. The least common multiple of 10 and 15 is 30.

3. Convert both fractions to have a denominator of 30:
- For \(-\frac{13}{10}\):
\[
-\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30}
\]

- For \(-\frac{62}{15}\):
\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

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

Now we can convert \(-\frac{163}{30}\) back into a mixed number:
- 30 goes into 163 five times (since \(30 \times 5 = 150\)), leaving a remainder of 13.
- Therefore:
\[
-\frac{163}{30} = -5 \frac{13}{30}
\]

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

The answer is \(d. -5 \frac{13}{30}\).