Question

equation practice (show your work)

1. $2\frac{1}{3} \times 1\frac{1}{2} = \underline{quadquad}$
2. $3\frac{3}{4} \times \frac{2}{5} = \underline{quadquad}$
3. $1\frac{5}{6} \times 2\frac{1}{4} = \underline{quadquad}$

Explanation:

Problem 1: \( 2\frac{1}{3} \times 1\frac{1}{2} \)

Step1: Convert mixed numbers to improper fractions

\( 2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{7}{3} \)
\( 1\frac{1}{2}=\frac{1\times2+1}{2}=\frac{3}{2} \)

Step2: Multiply the improper fractions

\( \frac{7}{3}\times\frac{3}{2}=\frac{7\times3}{3\times2} \)

Step3: Simplify the fraction

Cancel out the common factor \( 3 \) in the numerator and denominator: \( \frac{7\times\cancel{3}}{\cancel{3}\times2}=\frac{7}{2}=3\frac{1}{2} \)

Problem 2: \( 3\frac{3}{4} \times 2\frac{2}{5} \)

Step1: Convert mixed numbers to improper fractions

\( 3\frac{3}{4}=\frac{3\times4 + 3}{4}=\frac{15}{4} \)
\( 2\frac{2}{5}=\frac{2\times5+2}{5}=\frac{12}{5} \)

Step2: Multiply the improper fractions

\( \frac{15}{4}\times\frac{12}{5}=\frac{15\times12}{4\times5} \)

Step3: Simplify the fraction

Factor and cancel common factors: \( \frac{3\times5\times3\times4}{4\times5}=3\times3 = 9 \)

Problem 3: \( 1\frac{5}{6} \times 2\frac{1}{4} \)

Step1: Convert mixed numbers to improper fractions

\( 1\frac{5}{6}=\frac{1\times6 + 5}{6}=\frac{11}{6} \)
\( 2\frac{1}{4}=\frac{2\times4+1}{4}=\frac{9}{4} \)

Step2: Multiply the improper fractions

\( \frac{11}{6}\times\frac{9}{4}=\frac{11\times9}{6\times4} \)

Step3: Simplify the fraction

Factor and cancel common factors: \( \frac{11\times3\times3}{2\times3\times4}=\frac{11\times3}{2\times4}=\frac{33}{8}=4\frac{1}{8} \)

Answer:

\( \frac{7}{2} \) or \( 3\frac{1}{2} \)