Add −13/10 +(−42/15) .(1 point)

Question

Responses

−5 1/5
negative 5 Start Fraction 1 over 5 End Fraction

−2 5/6
negative 2 Start Fraction 5 over 6 End Fraction

−5 1/6
negative 5 Start Fraction 1 over 6 End Fraction

−5 13/30

Answer 1

To add the fractions \( -\frac{13}{10} + \left(-\frac{42}{15}\right) \), we first need a common denominator.

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

Next, we convert each fraction to have a denominator of 30:

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

2. Convert \( -\frac{42}{15} \): \[ -\frac{42}{15} = -\frac{42 \times 2}{15 \times 2} = -\frac{84}{30} \]

Now we can add the two fractions: \[ -\frac{39}{30} + \left(-\frac{84}{30}\right) = -\frac{39 + 84}{30} = -\frac{123}{30} \]

Next, we simplify \( -\frac{123}{30} \). We can divide both the numerator and the denominator by 3: \[ -\frac{123 \div 3}{30 \div 3} = -\frac{41}{10} \]

Finally, we can convert \( -\frac{41}{10} \) into a mixed number: \[ -\frac{41}{10} = -4 \frac{1}{10} \]

So the answer is: \[ -4 \frac{1}{10} \]

Based on the options provided, there is no direct match. Please double-check the calculations or provided choices.