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2. Operations with Rational numbers
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United States of America
Grade 6

2.09 Subtract decimals

Lesson
Practice

Subtract decimal numbers

When we subtract numbers with decimals, we follow the same process as working with whole numbers and use place value columns, only now there are values in the columns after the decimal point.

Let's watch a video to see how to subtract decimals with values in the tenths and hundredths columns.

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In our next video, we are going to work through a subtraction where we need to regroup. When we are subtracting using the standard algorithm and need to take a larger number away from a smaller number, we need to exchange a value from the previous place value column.

For example, we could exchange 1 tenth for 10 hundredths. Let's take a look at this process in more detail.

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We always start our calculations from the smallest place value column.

Examples

Example 1

Find 0.64-0.3 giving your answer as a decimal.

Worked Solution
Create a strategy

Use the standard algorithm for subtraction.

Apply the idea

Write 0.3 as 0.30 in the standard algorithm so that it has the same number of decimal places as 0.64. Make sure to align the decimal points.

\begin{array}{c} & &0 &. &6 &4 \\ &- &0 &. &3 &0\\ \hline & \\ \hline \end{array}

Begin in the hundredths column and move left. Subtract 0 from 4 to get 4 hundredths: \begin{array}{c} & &0 &. &6 &4 \\ &- &0 &. &3 &0\\ \hline & & & & &4 \\ \hline \end{array}

Subtract 3 from 6 to get 3 tenths: \begin{array}{c} & &0 &. &6 &4 \\ &- &0 &. &3 &0\\ \hline & & & &3 &4 \\ \hline \end{array}

Copy the decimal point down to the answer. \begin{array}{c} & &0 &. &6 &4 \\ &- &0 &. &3 &0\\ \hline & & &. &3 &4 \\ \hline \end{array}

Subtract 0 from 0 to get 0:\begin{array}{c} & &0 &. &6 &4 \\ &- &0 &. &3 &0\\ \hline & &0 &. &3 &4 \\ \hline \end{array}

0.64 - 0.3 = 0.34

Example 2

Find 3.12-0.04, leaving your answer in decimal form.

Worked Solution
Create a strategy

Use the standard algorithm for subtraction.

Apply the idea

Write it using the standard algorithm and align the decimal points.\begin{array}{c} & &3 &. &1 &2 \\ &- &0 &. &0 &4 \\ \hline & \\ \hline \end{array}

In the hundredths column, 2 is less than 4, so we need to take away 1 from the tenths, and carry it to the ones which gives us 12.

\begin{array}{c} & &3 &. &0 &\text{}^1 2 \\ &- &0 &. &0 &4 \\ \hline & & & & & \\ \hline \end{array}

So now we have 12-4=8:\begin{array}{c} & &3 &. &0 &\text{}^12 \\ &- &0 &. &0 &4 \\ \hline & & & & &8 \\ \hline \end{array}

Subtract the tenths, 0-0=0:\begin{array}{c} & &3 &. &0 &\text{}^12 \\ &- &0 &. &0 &4 \\ \hline & & & &0 &8 \\ \hline \end{array}

Bring down the decimal point and subtract the ones, 3-0=3:\begin{array}{c} & &3 &. &0 &\text{}^1 2 \\ &- &0 &. &0 &4 \\ \hline & &3 &. &0 &8 \\ \hline \end{array}

3.12 - 0.04 = 3.08

Example 3

What is 87-5.45?

Worked Solution
Create a strategy

Before we begin subtracting, it's helpful to estimate what our final answer will be so that we can feel confident in our final answer. For example, since 87 is close to 90, and 5.45 is close to 5, we can assume that our final answer will be close to 90 - 5 = 85.

Apply the idea

To begin the subtraction, rewrite 87-5.45 as 87.00-5.45 and use the standard algorithm to subtract.

\begin{array}{c} &&8&7&.&0&0 \\ &-&&5 &.&4&5 \\ \hline &&8&1&.&5&5 \\ \hline \end{array}

Reflect and check

By adding trailing zeros to our whole number, we were were able to subtract a number with decimals from it. Our calculated answer fits with our expectation that the answer would be a little bit more than 81.

Idea summary

To subtract decimals using the standard algorithm:

  • Align the decimal points, so that all the numbers are in columns according to their place values.

  • Subtract the numbers, beginning on the right and moving to the left.

  • Write the decimal point in the answer so it is aligned with the decimal points in the question.

Outcomes

6.NS.B.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

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