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Chapter 5: Problem 89

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(2 \frac{2}{3}+1 \frac{3}{4}\)

Short Answer

Expert verified
The result of \(2 \frac{2}{3}+1 \frac{3}{4}\) is \(4 \frac{5}{12}\).

Step by step solution

01

Convert to Improper Fractions

Convert the mixed numbers to improper fractions. In general, an improper fraction is formed by multiplying the integer part by the denominator of the fraction and then adding the numerator of the fraction. So, \(2 \frac{2}{3}\) becomes \( \frac{(2*3)+2}{3} = \frac{8}{3}\) and \(1 \frac{3}{4}\) will become \(\frac{(1*4)+3}{4}=\frac{7}{4}\).
02

Find a Common Denominator and Add

When adding fractions, the denominators must be the same. The least common multiple of 3 and 4 is 12. Convert both fractions to have this denominator: \(\frac{8}{3} * \frac{4}{4} =\frac{32}{12}\); \(\frac{7}{4}*\frac{3}{3} =\frac{21}{12}\). Now add the two fractions together: \(\frac{32}{12} + \frac{21}{12} = \frac{53}{12}\)
03

Reduce to Lowest Terms and Convert to Mixed Number

The fraction can be expressed as a mixed number by dividing the numerator by the denominator. So, \(\frac{53}{12}\) will be \(4 \frac{5}{12}\). This is already reduced to its lowest terms since the numerator and denominator have no common factors other than 1.

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