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Add −1 3/10 +(−4 2/15)

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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.

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

  2. 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 \(-5 \frac{13}{30}\).

can you try again

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!