Question

a. $2\frac{3}{4}$ $2\frac{7}{8}$

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \( 2\frac{3}{4} \) to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So for \( 2\frac{3}{4} \), we have \( \frac{2\times4 + 3}{4}=\frac{8 + 3}{4}=\frac{11}{4} \).

For \( 2\frac{7}{8} \), using the same formula, we get \( \frac{2\times8+7}{8}=\frac{16 + 7}{8}=\frac{23}{8} \).

Step2: Find a common denominator

The denominators are 4 and 8. The least common denominator is 8. We convert \( \frac{11}{4} \) to a fraction with denominator 8 by multiplying the numerator and denominator by 2: \( \frac{11\times2}{4\times2}=\frac{22}{8} \).

Step3: Subtract the fractions

Now we subtract \( \frac{23}{8}-\frac{22}{8} \). When subtracting fractions with the same denominator, we subtract the numerators: \( \frac{23 - 22}{8}=\frac{1}{8} \).

Answer:

\( \frac{1}{8} \)