Question

multiply:
$2\frac{2}{4} \times 1\frac{1}{3}$
provide an answer as a simplified proper fraction or mixed number.

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \( 2\frac{2}{4} \) to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So for \( 2\frac{2}{4} \), \( a = 2 \), \( b=2 \), \( c = 4 \). Then \( 2\frac{2}{4}=\frac{2\times4 + 2}{4}=\frac{8 + 2}{4}=\frac{10}{4}=\frac{5}{2} \) (simplified by dividing numerator and denominator by 2). For \( 1\frac{1}{3} \), \( a = 1 \), \( b = 1 \), \( c=3 \), so \( 1\frac{1}{3}=\frac{1\times3+1}{3}=\frac{3 + 1}{3}=\frac{4}{3} \).

Step2: Multiply the improper fractions

Now we multiply \( \frac{5}{2}\times\frac{4}{3} \). When multiplying fractions, we multiply the numerators together and the denominators together: \( \frac{5\times4}{2\times3}=\frac{20}{6} \).

Step3: Simplify the result

Simplify \( \frac{20}{6} \) by dividing numerator and denominator by their greatest common divisor, which is 2. So \( \frac{20\div2}{6\div2}=\frac{10}{3} \). Then convert \( \frac{10}{3} \) to a mixed number: \( 3\frac{1}{3} \) (since \( 10\div3 = 3 \) with a remainder of 1).

Answer:

\( 3\frac{1}{3} \)