Problem 14 Perform the indicated operation.... [FREE SOLUTION]

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Mathematics in Action, Prealgebra Problem Solving

Addison Wesley

$Math Studyset 91影视 Explanations$ Math

3 Edition

Chapter 5: Problem 14

Perform the indicated operation. $-7 \frac{5}{8}+2 \frac{1}{6}$

Short Answer

Expert verified

Answer: The sum is -5 11/24.

Step by step solution

Convert Mixed Numbers to Improper Fractions

First, let's convert $-7 \frac{5}{8}$ and $2 \frac{1}{6}$ to improper fractions. For $-7 \frac{5}{8}$, the improper fraction will be: $-\frac{7\times 8 + 5}{8} = -\frac{61}{8}$ For $2 \frac{1}{6}$, the improper fraction will be: $\frac{2\times 6 + 1}{6} = \frac{13}{6}$ So the problem becomes: $-\frac{61}{8} + \frac{13}{6}$

Find the Common Denominator and Add the Fractions

Now, we must find the common denominator for both fractions. The least common multiple of 8 and 6 is 24. Let's convert both fractions to have a denominator of 24. $-\frac{61}{8} \times \frac{3}{3} = -\frac{183}{24}$ $\frac{13}{6} \times \frac{4}{4} = \frac{52}{24}$ Now, add the two fractions: $-\frac{183}{24} + \frac{52}{24} = -\frac{131}{24}$

Convert Improper Fraction to Mixed Number

Now, let's convert the improper fraction $-\frac{131}{24}$ back to a mixed number. Divide 131 by 24: $131 \div 24 = 5$ with a remainder of 11. So, $-\frac{131}{24} = -5 \frac{11}{24}$ The final answer is $\boxed{-5 \frac{11}{24}}$.

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91影视

Perform the indicated operation. \(-7 \frac{5}{8}+2 \frac{1}{6}\)

Short Answer

Step by step solution

Convert Mixed Numbers to Improper Fractions

Find the Common Denominator and Add the Fractions

Convert Improper Fraction to Mixed Number

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