Question

. $\frac{9}{10} + \frac{7}{8} + 2\frac{3}{4}$

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(2\frac{3}{4}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(2\frac{3}{4}\), we have \(a = 2\), \(b = 3\), \(c = 4\). Then \(2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{8 + 3}{4}=\frac{11}{4}\).

Step2: Find a common denominator

The denominators of the fractions are \(10\), \(8\), and \(4\). The least common multiple (LCM) of \(10\), \(8\), and \(4\) is \(40\). Now convert each fraction to have a denominator of \(40\):

• For \(\frac{9}{10}\), multiply numerator and denominator by \(4\): \(\frac{9\times4}{10\times4}=\frac{36}{40}\)
• For \(\frac{7}{8}\), multiply numerator and denominator by \(5\): \(\frac{7\times5}{8\times5}=\frac{35}{40}\)
• For \(\frac{11}{4}\), multiply numerator and denominator by \(10\): \(\frac{11\times10}{4\times10}=\frac{110}{40}\)

Step3: Add the fractions

Now add the three fractions with the common denominator: \(\frac{36}{40}+\frac{35}{40}+\frac{110}{40}=\frac{36 + 35+110}{40}=\frac{181}{40}\)

Step4: Convert back to mixed number (optional)

Convert \(\frac{181}{40}\) to a mixed number. Divide \(181\) by \(40\): \(181\div40 = 4\) with a remainder of \(21\). So \(\frac{181}{40}=4\frac{21}{40}\)

Answer:

\(4\frac{21}{40}\) (or \(\frac{181}{40}\))