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Chapter 5: Problem 13

Perform the indicated operation. \(4 \frac{3}{11}-2 \frac{9}{22}\)

Short Answer

Expert verified
Question: Subtract the mixed numbers \(4 \frac{3}{11}\) and \(2 \frac{9}{22}\). Answer: \(1 \frac{19}{22}\)

Step by step solution

01

Convert the mixed numbers to improper fractions

First, we need to convert both \(4 \frac{3}{11}\) and \(2 \frac{9}{22}\) into improper fractions. To convert a mixed number to an improper fraction, we can use the following formula: \(ImproperFraction = (WholeNumber \times Denominator) + Numerator\) For \(4 \frac{3}{11}\): \((4 \times 11) + 3 = 47\) So, the improper fraction is \(\frac{47}{11}\). For \(2 \frac{9}{22}\): \((2 \times 22) + 9 = 53\) So, the improper fraction is \(\frac{53}{22}\).
02

Find a common denominator

In order to subtract these fractions, we need to find a common denominator. The least common multiple (LCM) of \(11\) and \(22\) is \(22\). Now we will convert both fractions to equivalent fractions with the denominator \(22\): For \(\frac{47}{11}\), we need to multiply both the numerator and the denominator by \(2\) (since \(11 \times 2 = 22\)): \(\frac{47}{11} \times \frac{2}{2} = \frac{94}{22}\) For \(\frac{53}{22}\), the denominator is already \(22\), so we don't need to change anything: \(\frac{53}{22}\) Now, we can rewrite the original problem as: \(\frac{94}{22}-\frac{53}{22}\)
03

Subtract the fractions

Since the denominators are the same, we can subtract the numerators directly: \(\frac{94}{22}-\frac{53}{22}=\frac{94-53}{22}=\frac{41}{22}\)
04

Simplify the fraction and convert back to a mixed number if needed

The improper fraction \(\frac{41}{22}\) cannot be simplified further, so we can leave it as it is. However, if needed or required, we can convert it back to a mixed number: \(MixedNumber = \frac{Numerator}{Denominator} = WholeNumber \frac{RemainingNumerator}{Denominator}\) \(MixedNumber = \frac{41}{22} = 1 \frac{19}{22}\) So our final answer is: \(\frac{41}{22}\) or \(1 \frac{19}{22}\)

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