How to Multiply Mixed Numbers

How to Multiply Mixed Numbers

You can multiply Mixed numbers in few simple steps.

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Step by step guide to multiply mixed numbers

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

Multiplying Mixed Numbers – Example 1:

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

Solution:

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, \(\frac{9 \ \times \ 7}{4 \ \times \ 2}=\frac{63}{8}=7 \ \frac{7}{8}\)

Multiplying Mixed Numbers – Example 2:

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

Solution:

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

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

Multiplying Mixed Numbers – Example 3:

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

Solution:

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, \(\frac{11×5}{3×2}=\frac{55}{6}=9 \ \frac{1}{6}\)

Multiplying Mixed Numbers – Example 4:

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

Solution:

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 for Multiplying Mixed Numbers

Find each product.

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

ِِDownload Multiplying and Dividing Mixed Numbers Worksheet

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

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