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Multiplication of Decimals and Whole Numbers

Digits after decimal in product same as in question

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Multiplication of Decimals and Whole Numbers
License: CC BY-NC 3.0

Mrs. Andersen is planning a field trip to the Science Museum for her sixth grade class. The group rate for a student ticket is $8.95 per ticket. If 22 students attend the field trip, how much money should Mrs. Andersen have to cover the cost of admission for the students?

In this concept, you will learn how to multiply decimals and whole numbers together.

Multiplying Decimals and Whole Numbers

Multiplication is a short-cut for repeated addition. It is a way to add the same number of groups several or “multiple” times.

Here is a multiplication equation.

\begin{align*}4 \times 3 =12\end{align*}

This equation tells you that there are 3 groups of 4 or 4 groups of 3. Either grouping results in the same total. The product of 4 multiplied by 3 is 12. A product is the result of multiplying two or more numbers. You can also think of multiplying whole numbers and decimals as groups.

Here is a whole number and decimal multiplication problem. 

\begin{align*}2(0.25) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

Remember that the parentheses tell you the order of operation and can also indicate multiplication. Think of 2 times 0.25 as two groups of twenty-five hundredths. Let’s look at this on a hundreds grid.

License: CC BY-NC 3.0

Each color represents a group of twenty-five hundredths. Two groups of twenty-five hundredths total fifty hundredths.

\begin{align*}2(0.25) = 0.50\end{align*}

This is one way to multiply decimals and whole numbers. You can also multiply a decimal and a whole number just like you would two whole numbers. Afterwards, add the decimal point in the product the same number of places in the decimal number multiplier.

Here is another whole number and decimal multiplication problem.

\begin{align*}4(1.25) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, ignore the decimal and multiply as if this were two whole numbers.

\begin{align*}1.25\\ \underline{\times \;\; 4}\\ \ 500\end{align*} 

Then, add the decimal point in the product. There are two decimal places in 1.25. Count two places from right to left and place the decimal point in the product.

\begin{align*}1.25\\ \underline{\times \;\; 4}\\ 5 {\color{red}.}00\end{align*}

The product of 4 times 1.25 is 5.00.

Examples 

Example 1

Earlier, you were given a problem about Mrs. Andersen’s field trip to the museum.

Mrs. Andersen needs to find the total cost of 22 tickets that cost $8.95 each.

First, write a multiplication problem to find the total cost.

\begin{align*}22(8.95) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

Then, ignore the decimal and multiply as if this were two whole numbers.

\begin{align*}\ \quad \ 8.95\\ \underline{\times \;\;\;\;\; 22}\\ \quad \ 1790\\ \underline{+1790\;\;}\\ \ \ 19690\end{align*}

Next, add the decimal point in the product. There are two decimal places in 8.95.

\begin{align*}\ \quad \ 8.95\\ \underline{\times \;\;\;\;\; 22}\\ \quad \ 1790\\ \underline{+1790\;\;}\\ \ \ 196 {\color{red}.}90\end{align*}

The total cost for 22 student tickets at the group rate is $196.90.

Example 2

Find the product for the following problem.

9 friends decided to go to a movie on Friday night. They each paid the $8.50 for admission. How much money did they spend in all?

First, write a multiplication problem to find the total cost.

\begin{align*}9(8.50) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

Then, ignore the decimal and multiply as if this were two whole numbers.

\begin{align*}& \ 8.50\\ & \ \underline{\times \; \; 9\;}\\ & 7650\end{align*}

Next, add the decimal point in the product. There are two decimal places in 8.50.

\begin{align*}& \ \ 8.50\\ & \ \ \underline{\times \;\; 9\;}\\ & 76 {\color{red}.} 50\end{align*}

The cost of 9 movie tickets was $76.50.

Example 3

Find the product.

\begin{align*}3(4.52) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, ignore the decimal and multiply as if this were two whole numbers.

\begin{align*}& \ 4.52\\ & \ \underline{\times \;\; 3\;}\\ & 1356\end{align*}

Then, add the decimal point in the product.

\begin{align*}& \ 4.52\\ & \underline{\times \;\;\; 3\;}\\ & 13{\color{red}.} 56\end{align*}

The product of 3 times 4.52 is 13.56.

Example 4

Find the product.

\begin{align*}5(2.34) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, ignore the decimal and multiply as if this were two whole numbers.

\begin{align*}& \ 2.34\\ & \underline{\times \;\;\; 5\; }\\ & 1170\end{align*}

Then, add the decimal point in the product.

\begin{align*}& \ \ 2.34\\ & \ \underline{\times \;\;\; 5\; }\\ & 11{\color{red}.}70\end{align*}

The product of 5 times 2.34 is 11.70.

Example 5

Find the product.

 \begin{align*}7(3.561) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, ignore the decimal and multiply as if this were two whole numbers.

\begin{align*}& \ 3.561\\ & \ \underline{\times \;\;\;\; 7\;}\\ & 24927\end{align*}

Then, add the decimal point in the product.

\begin{align*}& \ \ 3.561\\ & \ \ \underline{\times \;\;\;\; 7\;}\\ & 24 {\color{red}.}927\end{align*}

The product of 7 times 3.561 is 24.927.

Review

Find the product for the following problems. 

  1. \begin{align*}5(1.24) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  2. \begin{align*}6(7.81) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  3. \begin{align*}7(9.3) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  4. \begin{align*}8(1.45) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*} 
  5. \begin{align*}9(12.34) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  6. \begin{align*}2(3.56) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  7. \begin{align*}6(7.12) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  8. \begin{align*}3(4.2) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  9. \begin{align*}5(2.4) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  10. \begin{align*}6(3.521) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  11. \begin{align*}2(3.222) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*} 
  12. \begin{align*}3(4.223) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  13. \begin{align*}4(12.34) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  14. \begin{align*}5(12.45) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*} 
  15. \begin{align*}3(143.12) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  16. \begin{align*}4(13.672) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  17. \begin{align*}2(19.901) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
  18. \begin{align*}3(67.321) = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

Review (Answers)

To see the Review answers, open this PDF file and look for section 4.1. 

Resources

 

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Vocabulary

Estimate

To estimate is to find an approximate answer that is reasonable or makes sense given the problem.

multiplication

Multiplication is a simplified form of repeated addition. Multiplication is used to determine the result of adding a term to itself a specified number of times.

Product

The product is the result after two amounts have been multiplied.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0

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