Question

(fractions)
Add −1 3/10 +(−4 2/15)

Answer 1

can you try again

Answer 2

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

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

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

Now we need to add \(-\frac{13}{10}\) and \(-\frac{62}{15}\). To do this, we first find a common denominator. The least common multiple of 10 and 15 is 30.

3. Convert both fractions to have a 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, we can add the two fractions:
\[
-\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30}
\]

Now, \(-\frac{163}{30}\) can also be converted back to a mixed number:
\[
-\frac{163}{30} = -5 \frac{13}{30}
\]

Thus, the sum of \(-1 \frac{3}{10} + (-4 \frac{2}{15})\) is \(-5 \frac{13}{30}\).

Answer 3

Certainly! Let's go through the addition of \(-1 \frac{3}{10} + (-4 \frac{2}{15})\) step-by-step again, making sure everything is clear.

1. **Convert mixed numbers to improper fractions**:

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

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

2. **Find a common denominator**:

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

3. **Convert the 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 \(-\frac{62}{15}\):
\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

4. **Now add the fractions**:

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

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

To convert \(-\frac{163}{30}\) to a mixed number, divide \(163\) by \(30\):

\[
163 \div 30 = 5 \quad \text{(which gives a whole part of 5)}
\]
\[
163 - (30 \times 5) = 163 - 150 = 13
\]

Hence, \(-\frac{163}{30} = -5 \frac{13}{30}\).

So, the final answer is:

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

Thank you for your patience, and please let me know if you need further clarification!