Question

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multiplying mixed numbers by fractions
you can multiply a mixed number by a fraction. start by writing the mixed number as an improper fraction to make the multiplication easier. then, multiply. let’s try it! solve $1\frac{3}{4} \times \frac{3}{5}$.
first, write the mixed number as an improper fraction.
$1\frac{3}{4} = \frac{7}{4}$
next, multiply the numerators, and then multiply the denominators. make sure your answer is in simplest form. to simplify an improper fraction, you can rewrite it as a mixed number.
$\frac{7}{4} \times \frac{3}{5} = \frac{7 \times 3}{4 \times 5} = \frac{21}{20} = 1\frac{1}{20}$
try it yourself! multiply. show your work and write your final answer in simplest form.
$4\frac{1}{2} \times \frac{1}{3} =$
$\frac{1}{4} \times 4\frac{4}{5} =$
$3\frac{1}{3} \times \frac{4}{5} =$
$5\frac{1}{2} \times \frac{3}{4} =$
$\frac{5}{8} \times 2\frac{2}{3} =$
$2\frac{4}{9} \times \frac{3}{5} =$
$\frac{3}{4} \times 1\frac{5}{6} =$
$\frac{5}{12} \times 6\frac{2}{5} =$

Explanation:

1. Solve \( 4\frac{1}{2} \times \frac{1}{3} \)

Step1: Convert mixed number to improper fraction

\( 4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2} \)

Step2: Multiply the fractions

\( \frac{9}{2}\times\frac{1}{3}=\frac{9\times1}{2\times3}=\frac{9}{6}=\frac{3}{2}=1\frac{1}{2} \)

Step1: Convert mixed number to improper fraction

\( 4\frac{4}{5}=\frac{4\times5 + 4}{5}=\frac{24}{5} \)

Step2: Multiply the fractions

\( \frac{1}{4}\times\frac{24}{5}=\frac{1\times24}{4\times5}=\frac{24}{20}=\frac{6}{5}=1\frac{1}{5} \)

Step1: Convert mixed number to improper fraction

\( 3\frac{1}{3}=\frac{3\times3 + 1}{3}=\frac{10}{3} \)

Step2: Multiply the fractions

\( \frac{10}{3}\times\frac{4}{5}=\frac{10\times4}{3\times5}=\frac{40}{15}=\frac{8}{3}=2\frac{2}{3} \)

Answer:

\( 1\frac{1}{2} \)

2. Solve \( \frac{1}{4} \times 4\frac{4}{5} \)