Question

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

−516
negative 5 Start Fraction 1 over 6 End Fraction

−515
negative 5 Start Fraction 1 over 5 End Fraction

−256
negative 2 Start Fraction 5 over 6 End Fraction

−51330

Answer 1

To add the numbers \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), let's 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 \(-\frac{13}{10}\) and \(-\frac{62}{15}\). To do this, we need a common denominator. The least common multiple of 10 and 15 is 30.

3. Convert the fractions to have the common denominator of 30:
\[
-\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30}
\]
\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

4. Now, add the two fractions:
\[
-\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30}
\]

Finally, we can convert \(-\frac{163}{30}\) to a mixed number:
\[
-\frac{163}{30} = -5 \frac{13}{30}
\]

Thus, the answer is:
\[
\text{negative 5 } \frac{13}{30}
\]

Based on the responses provided, none of them match \(-5 \frac{13}{30}\), but if we're looking for the closest option, we have:

- \(-5 \frac{1}{6}\) is close but doesn’t match our result.

Please double-check to see if the options provided are different. If modifying fractions is acceptable, \(-5 \frac{1}{5}\) could be rounded, but it's not equivalent.

None of the provided options are correct based on the calculations made.