Question

-1 3/10 + ( -4 2/15)
A. - 2 5/6
B. - 5 1/6
C. 5 1/5
D. - 5 13/30

Answer 1

Are you sure?

Answer 2

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

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

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

Now, we need to add \(-\frac{13}{10} + -\frac{62}{15}\).

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

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

5. Convert \(-\frac{62}{15}\) to have a denominator of 30:
\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

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

6. Now we can convert \(-\frac{163}{30}\) into a mixed number:
\[
-\frac{163}{30} = -5 \frac{13}{30} \quad \text{(since 163 divided by 30 is 5 remainder 13)}
\]

Thus, the result is \(-5 \frac{13}{30}\).

Therefore, the final answer is:
**D. -5 \frac{13}{30}**.

Answer 3

Let me double-check the calculation step-by-step to ensure accuracy.

### Given expression:
\[
-1 \frac{3}{10} + (-4 \frac{2}{15})
\]

### Step 1: Convert the mixed numbers to improper fractions.

1. **Convert \(-1 \frac{3}{10}\)** to an improper fraction:
\[
-1 \frac{3}{10} = -\left(\frac{1 \times 10 + 3}{10}\right) = -\left(\frac{10 + 3}{10}\right) = -\frac{13}{10}
\]

2. **Convert \(-4 \frac{2}{15}\)** to an improper fraction:
\[
-4 \frac{2}{15} = -\left(\frac{4 \times 15 + 2}{15}\right) = -\left(\frac{60 + 2}{15}\right) = -\frac{62}{15}
\]

### Step 2: Find a common denominator

The denominators are 10 and 15. The least common multiple (LCM) of 10 and 15 is 30.

### Step 3: Convert to a common denominator

1. **Convert \(-\frac{13}{10}\)** to a denominator of 30:
\[
-\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30}
\]

2. **Convert \(-\frac{62}{15}\)** to a denominator of 30:
\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

### Step 4: Add the fractions

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

### Step 5: Convert to a mixed number

To convert \(-\frac{163}{30}\) into a mixed number:
1. Divide 163 by 30.
2. 30 goes into 163 a total of 5 times, with a remainder.
3. \( 30 \times 5 = 150\), and \( 163 - 150 = 13\).

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

### Conclusion

The final answer is indeed:
**D. -5 \frac{13}{30}**.

Thank you for your patience!