Question

9\frac{1}{4} \cdot 9\frac{1}{4}

Explanation:

Step1: Convert mixed numbers to improper fractions

To multiply \( 9\frac{1}{4} \times 9\frac{1}{4} \), first convert each mixed number to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a \times c + b}{c} \). For \( 9\frac{1}{4} \), \( a = 9 \), \( b = 1 \), \( c = 4 \). So, \( 9\frac{1}{4}=\frac{9\times4 + 1}{4}=\frac{36 + 1}{4}=\frac{37}{4} \).

Step2: Multiply the improper fractions

Now, multiply the two improper fractions \( \frac{37}{4} \times \frac{37}{4} \). When multiplying fractions, we multiply the numerators together and the denominators together. So, \( \frac{37\times37}{4\times4}=\frac{1369}{16} \).

Step3: Convert back to a mixed number (optional)

If we want to convert \( \frac{1369}{16} \) back to a mixed number, we divide 1369 by 16. \( 16\times85 = 1360 \), so \( 1369-1360 = 9 \). Thus, \( \frac{1369}{16}=85\frac{9}{16} \).

Answer:

\( 85\frac{9}{16} \) (or \( \frac{1369}{16} \))