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Chapter 5: Problem 7

Perform the indicated operation. \(5 \frac{2}{12}+3 \frac{7}{18}\)

Short Answer

Expert verified
Question: Add the mixed numbers \(5 \frac{2}{12}\) and \(3 \frac{7}{18}\). Answer: The sum of the given mixed numbers is \(8 \frac{5}{9}\).

Step by step solution

01

Simplify mixed numbers

Convert the fractions to their simplest form: \(5 \frac{2}{12} = 5 \frac{1}{6}\) (Divide both numerator and denominator by 2) \(3 \frac{7}{18}\) - Already in simplest form.
02

Find common denominator

Find the common denominator for the given simplified fractions. In our case, the least common multiple (LCM) of 6 and 18 is 18.
03

Adjust fractions to have the same denominator

To adjust each fraction to have the same denominator, multiply numerator and denominator by the required number: \(5 \frac{1}{6} = 5 \frac{1 \cdot 3}{6 \cdot 3} = 5 \frac{3}{18}\) \(3 \frac{7}{18}\) - Already has denominator 18.
04

Add the integers and the fractions separately

Add the integer parts (5 + 3) and the fraction parts (\(\frac{3}{18} + \frac{7}{18}\)) separately: Integer part: \(5 + 3 = 8\) Fraction part: \(\frac{3}{18} + \frac{7}{18} = \frac{3+7}{18} = \frac{10}{18}\)
05

Simplify the answer

Simplify the fraction part of the answer: \(\frac{10}{18} = \frac{5}{9}\) (Divide both numerator and denominator by 2) The final answer is: \(8 \frac{5}{9}\).

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