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-1 3/10 + ( -4 2/15)

A. - 2 5/6
B. - 5 1/6
C. 5 1/5
D. - 5 13/30

3 answers

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 \(-\frac{13}{10} + -\frac{62}{15}\).

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

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

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

  1. 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}.

Are you sure?

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!