Question

2
$-\frac{3}{8} + 2\frac{1}{4}$

Explanation:

Step1: Convert mixed number to improper fraction

First, we convert the mixed number \(2\frac{1}{4}\) to an improper fraction. A mixed number \(a\frac{b}{c}\) can be converted to \(\frac{ac + b}{c}\). So for \(2\frac{1}{4}\), we have \(a = 2\), \(b=1\), \(c = 4\). Then \(\frac{2\times4+ 1}{4}=\frac{8 + 1}{4}=\frac{9}{4}\).

Step2: Find a common denominator

The denominators of \(-\frac{3}{8}\) and \(\frac{9}{4}\) are 8 and 4. The least common denominator is 8. We convert \(\frac{9}{4}\) to a fraction with denominator 8. Multiply the numerator and denominator of \(\frac{9}{4}\) by 2: \(\frac{9\times2}{4\times2}=\frac{18}{8}\).

Step3: Add the fractions

Now we add \(-\frac{3}{8}\) and \(\frac{18}{8}\). When adding fractions with the same denominator, we add the numerators and keep the denominator the same. So \(-\frac{3}{8}+\frac{18}{8}=\frac{- 3+18}{8}=\frac{15}{8}\).

Step4: Convert back to mixed number (optional)

We can convert \(\frac{15}{8}\) back to a mixed number. Divide 15 by 8: \(15\div8 = 1\) with a remainder of 7. So \(\frac{15}{8}=1\frac{7}{8}\).

Answer:

\(1\frac{7}{8}\) (or \(\frac{15}{8}\))