Multiplying Mixed Numbers

Multiplying Mixed Numbers

You can multiply Mixed numbers in few simple steps.

Step by step guide to multiply mixed numbers

  1. Convert the mixed numbers to improper fractions. (improper fraction is a fraction in which the top number is bigger than bottom number). \(a \ \frac{c}{ \color{ blue }{b} }= a \ \color{blue}{+} \ \frac{c}{\color{ blue }{b}}=\frac{a \color{ blue }{b} \ \color{blue}{+} \ c}{ \color{ blue }{b} }\)
  2. Multiply fractions and simplify if necessary.

Example 1:

Multiply mixed numbers. \(2 \ \frac{1}{4} \ \times \ 3 \ \frac{1}{2}=\)

Answer:

Converting mixed numbers to fractions, \(2 \ \frac{1}{4}=\frac{9}{4}\) and \(3 \ \frac{1}{2}=\frac{7}{2}\).
\(\frac{9}{4} \ \times \ \frac{7}{2}\),

Applying the fractions rule for multiplication, \(\frac{9 \ \times \ 7}{4 \ \times \ 2}=\frac{63}{8}=7 \ \frac{7}{8}\)

Example 2:

Multiply mixed numbers. \(5 \ \frac{2}{3} \ \times \ 3 \ \frac{3}{4}=\)

Answer:

Converting mixed numbers to fractions, \(\frac{17}{3} \ \times \ \frac{15}{4}\),

Applying the fractions rule for multiplication, \(\frac{17 \ \times \ 15}{3 \ \times \ 4}=\frac{255}{12}=21 \ \frac{1}{4}\)

Example 3:

Multiply mixed numbers. \(3 \ \frac{2}{3} \ \times \ 2 \ \frac{1}{2}=\)

Answer:

Converting mixed numbers to fractions, \(3 \ \frac{2}{3}=\frac{11}{3}\) and \(2 \ \frac{1}{2}=\frac{5}{2}\).
\(\frac{11}{3}×\frac{5}{2} \),

Applying the fractions rule for multiplication, \(\frac{11×5}{3×2}=\frac{55}{6}=9 \ \frac{1}{6}\)

Example 4:

Multiply mixed numbers. \(4 \ \frac{3}{5} \ \times \ 2 \ \frac{1}{3}=\)

Answer:

Converting mixed numbers to fractions, \(\frac{23}{5}×\frac{7}{3}\),

Applying the fractions rule for multiplication, \(\frac{23×7}{5×3}=\frac{161}{15}=10 \ \frac{11}{15}\)

Exercises

Find each product.

  • \(\color{blue}{1\frac{2}{3} \times 1\frac{1}{4}}\)
  • \(\color{blue}{1\frac{3}{5} \times 1\frac{2}{3}}\)
  • \(\color{blue}{1\frac{2}{3} \times 3\frac{2}{7}}\)
  • \(\color{blue}{4\frac{1}{8} \times 1\frac{2}{5}}\)
  • \(\color{blue}{2\frac{2}{5} \times 3\frac{1}{5}}\)
  • \(\color{blue}{1\frac{1}{3} \times 1\frac{2}{3}}\)

ِِDownload Multiplying and Dividing Mixed Numbers Worksheet

Answers

  • \(\color{blue}{2\frac{1}{12}}\)
  • \(\color{blue}{2\frac{2}{3}}\)
  • \(\color{blue}{5\frac{10}{21}}\)
  • \(\color{blue}{5\frac{31}{40}}\)
  • \(\color{blue}{7\frac{17}{25}}\)
  • \(\color{blue}{2\frac{2}{9}}\)

Leave a Reply

Your email address will not be published. Required fields are marked *