Question

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

−5 1/6

−5 1/5

−2 5/6

−5 13/30

Answer 1

To add the fractions \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), we can first convert these mixed numbers into improper fractions and then find a common denominator.

1. Convert the mixed numbers to improper fractions:

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

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

2. Now we want to add these two improper fractions:

\[
-\frac{13}{10} + \left(-\frac{62}{15}\right)
\]

3. Find a common denominator. The least common multiple of 10 and 15 is 30.

Convert the fractions:

\[
-\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30}
\]

\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

4. Now add the two fractions:

\[
-\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30}
\]

5. Convert \(-\frac{163}{30}\) back into a mixed number:

\(-\frac{163}{30}\) means that \(163\) divided by \(30\) is \(5\) with a remainder of \(13\):

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

So the answer is:

\(-5 \frac{13}{30}\)

Thus the correct response is \(-5 \frac{13}{30}\).