Learn on PengiReveal Math, Course 1Module 3: Compute with Multi-Digit Numbers and Fractions

3-2 Compute With Multi-Digit Decimals

In this Grade 6 lesson from Reveal Math, Course 1, students learn to apply standard algorithms for addition, subtraction, multiplication, and division with multi-digit decimals, including numbers extending to the thousandths place. Key techniques covered include aligning decimal points, annexing zeros, and determining correct decimal placement in products by summing the decimal places of each factor. Students also practice using estimation to verify the reasonableness of their solutions.

Section 1

Adding Decimals to the Thousandths

Property

To add decimals, align the decimal points vertically. Add the digits in each place value column, starting from the right, and regroup as needed. Place the decimal point in the sum directly below the decimal points in the numbers being added.

Examples

  • 2.458+1.321=3.7792.458 + 1.321 = 3.779
2.458+1.3213.779\begin{array}{r} &2&.&4&5&8 &\\ +&1&.&3&2&1 \\ \hline &3&.&7&7&9 \end{array}
  • 0.785+0.462=1.2470.785 + 0.462 = 1.247
01.7185+0.4621.247\begin{array}{r} &\overset{1}{0}&.&\overset{1}{7}&8&5 \\ +&0&.&4&6&2 \\ \hline &1&.&2&4&7 \end{array}
  • 4.5+3.298=7.7984.5 + 3.298 = 7.798
4.500+3.2987.798\begin{array}{r} &4&.&5&0&0 \\ +&3&.&2&9&8 \\ \hline &7&.&7&9&8 \end{array}

Explanation

This method for adding decimals is an application of place value. Aligning the decimal points ensures that you are adding digits with the same place value: thousandths to thousandths, hundredths to hundredths, and so on. If numbers have a different number of decimal places, you can add trailing zeros as placeholders. This process is similar to adding whole numbers, with the additional step of placing the decimal point in the final answer.

Section 2

Subtracting Decimals to the Thousandths

Property

To subtract decimals, align the numbers by their decimal points. Subtract as you would with whole numbers, starting from the rightmost place value, and regroup (borrow) when necessary. Place the decimal point in the difference directly below the decimal points in the numbers being subtracted.

Examples

  • 5.432−2.1565.432 - 2.156
5.43312212−2.1563.276\begin{array}{rcccccc} & 5 & . & \overset{3}{\cancel{4}} & \overset{12}{\cancel{3}} & \overset{12}{\cancel{2}} \\ -& 2 & . & 1 & 5 & 6 \\ \hline & 3 & . & 2 & 7 & 6 \\ \end{array}
  • 12.5−3.48112.5 - 3.481
10212.5409010−3.4819.019\begin{array}{rccccccc} & \overset{0}{\cancel{1}} & \overset{12}{\cancel{2}} & . & \overset{4}{\cancel{5}} & \overset{9}{\cancel{0}} & \overset{10}{\cancel{0}} \\ -& & 3 & . & 4 & 8 & 1 \\ \hline & & 9 & . & 0 & 1 & 9 \\ \end{array}

Section 3

How to Multiply Decimal Numbers

Property

How to multiply decimal numbers:
Step 1. Write the numbers in vertical format, lining up the numbers on the right.
Step 2. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
Step 3. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.

Examples

Book overview

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Module 3: Compute with Multi-Digit Numbers and Fractions

  1. Lesson 1

    3-1 Divide Multi-Digit Whole Numbers

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  2. Lesson 2Current

    3-2 Compute With Multi-Digit Decimals

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  3. Lesson 3

    3-3 Divide Whole Numbers by Fractions

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  4. Lesson 4

    3-4 Divide Fractions by Fractions

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  5. Lesson 5

    3-5 Divide with Whole and Mixed Numbers

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Lesson overview

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Section 1

Adding Decimals to the Thousandths

Property

To add decimals, align the decimal points vertically. Add the digits in each place value column, starting from the right, and regroup as needed. Place the decimal point in the sum directly below the decimal points in the numbers being added.

Examples

  • 2.458+1.321=3.7792.458 + 1.321 = 3.779
2.458+1.3213.779\begin{array}{r} &2&.&4&5&8 &\\ +&1&.&3&2&1 \\ \hline &3&.&7&7&9 \end{array}
  • 0.785+0.462=1.2470.785 + 0.462 = 1.247
01.7185+0.4621.247\begin{array}{r} &\overset{1}{0}&.&\overset{1}{7}&8&5 \\ +&0&.&4&6&2 \\ \hline &1&.&2&4&7 \end{array}
  • 4.5+3.298=7.7984.5 + 3.298 = 7.798
4.500+3.2987.798\begin{array}{r} &4&.&5&0&0 \\ +&3&.&2&9&8 \\ \hline &7&.&7&9&8 \end{array}

Explanation

This method for adding decimals is an application of place value. Aligning the decimal points ensures that you are adding digits with the same place value: thousandths to thousandths, hundredths to hundredths, and so on. If numbers have a different number of decimal places, you can add trailing zeros as placeholders. This process is similar to adding whole numbers, with the additional step of placing the decimal point in the final answer.

Section 2

Subtracting Decimals to the Thousandths

Property

To subtract decimals, align the numbers by their decimal points. Subtract as you would with whole numbers, starting from the rightmost place value, and regroup (borrow) when necessary. Place the decimal point in the difference directly below the decimal points in the numbers being subtracted.

Examples

  • 5.432−2.1565.432 - 2.156
5.43312212−2.1563.276\begin{array}{rcccccc} & 5 & . & \overset{3}{\cancel{4}} & \overset{12}{\cancel{3}} & \overset{12}{\cancel{2}} \\ -& 2 & . & 1 & 5 & 6 \\ \hline & 3 & . & 2 & 7 & 6 \\ \end{array}
  • 12.5−3.48112.5 - 3.481
10212.5409010−3.4819.019\begin{array}{rccccccc} & \overset{0}{\cancel{1}} & \overset{12}{\cancel{2}} & . & \overset{4}{\cancel{5}} & \overset{9}{\cancel{0}} & \overset{10}{\cancel{0}} \\ -& & 3 & . & 4 & 8 & 1 \\ \hline & & 9 & . & 0 & 1 & 9 \\ \end{array}

Section 3

How to Multiply Decimal Numbers

Property

How to multiply decimal numbers:
Step 1. Write the numbers in vertical format, lining up the numbers on the right.
Step 2. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
Step 3. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 3: Compute with Multi-Digit Numbers and Fractions

  1. Lesson 1

    3-1 Divide Multi-Digit Whole Numbers

    LearnPractice
  2. Lesson 2Current

    3-2 Compute With Multi-Digit Decimals

    LearnPractice
  3. Lesson 3

    3-3 Divide Whole Numbers by Fractions

    LearnPractice
  4. Lesson 4

    3-4 Divide Fractions by Fractions

    LearnPractice
  5. Lesson 5

    3-5 Divide with Whole and Mixed Numbers

    LearnPractice