Multiplying and Dividing Decimals

Multiplying and Dividing Decimals

Learn how to easily multiply and divide decimals in a few simple steps.

Step by step guide to multiply and divide decimals

For Multiplication:

  • Ignore the decimal point and set up and multiply the numbers as you do with whole numbers.
  • Count the total number of decimal places in both of the factors.
  • Place the decimal point in the product.

For Division:

  • If the divisor is not a whole number, move the decimal point to the right to make it a whole number. Do the same for the dividend.
  • Divide similar to whole numbers.

Example 1:

Find the product. \(0.60 \ \times \ 0.20=\)

Solution:

Set up and multiply the numbers as you do with whole numbers. Line up the numbers: \(\begin{array}{r} &60\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \) , Start with the ones place \( → 60 \ \times \ 0=0\), \(\begin{array}{r} &60\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \\ \ \ \ \ \ \ \ 0 \) Continue with other digits \(→ 60 \ \times \ 2=120\), \(\begin{array}{r} &60\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \\ \ \ \ 1,200 \) , Count the total number of decimal places in both of the factors. \((4)\). Then Place the decimal point in the product. Then: \(\begin{array}{r} &0.60\\ \times \!\!\!\!\!\!&0.20\\ \hline \end{array} \\ \ \ \ 0.1200 \) \(→ 0.60 \ \times \ 0.20=0.1200=0.12\)

Example 2:

Find the quotient. \(1.40 \ \div \ 0.2=\)

Solution:

The divisor is not a whole number. Multiply it by \(10\) to get \(2\). Do the same for the dividend to get \(14\).
Now, divide: \(14 \ \div \ 2=7\). The answer is \(7\).

Example 3:

Find the product. \(0.50 \ \times \ 0.20=\)

Solution:

Set up and multiply the numbers as you do with whole numbers. Line up the numbers: \(\begin{array}{r} &50\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \) , Start with the ones place \( → 50 \ \times \ 0=0\), \(\begin{array}{r} &50\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \\ \ \ \ \ \ \ \ 0 \) Continue with other digits \(→ 50 \ \times \ 2=100\), \(\begin{array}{r} &50\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \\ \ \ \ 1,000 \) , Count the total number of decimal places in both of the factors. \((4)\). Then Place the decimal point in the product. Then: \(\begin{array}{r} &0.50\\ \times \!\!\!\!\!\!&0.20\\ \hline \end{array} \\ \ \ \ 0.1000 \) \(→ 0.50 \ \times \ 0.20=0.1000=0.1\)

Example 4:

Find the quotient. \(1.20 \ \div \ 0.2=\)

Solution:

The divisor is not a whole number. Multiply it by \(10\) to get \(2\). Do the same for the dividend to get \(12\).
Now, divide: \(12 \ \div \ 2=6\). The answer is \(6\).

Exercises

Find each Product and Quotient.

1. \(\color{blue}{\begin{array}{r} &4.5\\ \times \!\!\!\!\!\!&1.6\\ \hline \end{array}} \)

2. \(\color{blue}{\begin{array}{r} &7.7\\ \times \!\!\!\!\!\!&9.9\\ \hline \end{array}} \)

3. \(\color{blue}{\begin{array}{r} &2.6\\ \times \!\!\!\!\!\!&1.5\\ \hline \end{array}} \)

4. \(\color{blue}{14.4\div 3.6} \)

5. \(\color{blue}{30.4\div 3.8} \)

6. \(\color{blue}{24.44\div 4.7} \)

Download Multiplying and Dividing Decimals Worksheet

  1. \(\color{blue}{7.2}\)
  2. \(\color{blue}{76.23}\)
  3. \(\color{blue}{3.9}\)
  4. \(\color{blue}{4}\)
  5. \(\color{blue}{8}\)
  6. \(\color{blue}{5.2}\)

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