Question

Add Fractions & Decimals Quick Check
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Question
Add −1 3/10 +(−4 2/15).

Answer 1

To add the fractions \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), let's follow these steps:

1. First, convert the mixed numbers to improper fractions.

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

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

2. Now we need to add the two improper fractions:
\[
-\frac{13}{10} + -\frac{62}{15}
\]

3. To add these fractions, we need a common denominator. The least common multiple (LCM) of 10 and 15 is 30.

4. Convert each fraction:
\[
-\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30}
\]
\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

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

6. Convert the improper fraction back to a mixed number:
\(-\frac{163}{30}\) can be converted by dividing \(163\) by \(30\):
\[
163 \div 30 = 5 \text{ remainder } 13
\]
So,
\[
-\frac{163}{30} = -5 \frac{13}{30}
\]

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