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BB.1 Add, subtract, multiply, and divide decimals

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Understanding Decimals

Decimals are numbers that show parts of a whole. The decimal point separates whole numbers from parts less than one.

Examples:
  • 0.5 means five-tenths, or half of one.
  • 3.27 means three and twenty-seven hundredths.
  • 7.04 means seven and four hundredths.
Note

The place of each digit matters! Digits to the right of the decimal point show tenths, hundredths, and thousandths.

Adding and Subtracting Decimals

When you add or subtract decimals, always line up the decimal points so each place value matches correctly.

Steps:
  • Write the numbers vertically and line up the decimal points.
  • Add or subtract as with whole numbers.
  • Bring the decimal point straight down into the answer.
Example:
  • 4.23 + 1.7 = 5.93
  • 6.5 − 2.35 = 4.15
Note

Adding zeros can help line up place values. For example, 1.7 can be written as 1.70 before adding or subtracting.

Multiplying Decimals

To multiply decimals, ignore the decimal points and multiply as if they were whole numbers. Then count and place the decimal point in your answer.

Steps:
  • Multiply the numbers as if they were whole numbers.
  • Count the total number of decimal places in both factors.
  • Place the decimal point in the product so it has the same number of decimal places.
Example:
  • 0.6 × 0.4 = 0.24
  • 3.2 × 1.5 = 4.8
Note

Estimate first! 0.6 × 0.4 is close to 0.5 × 0.5 = 0.25, which helps check if your answer makes sense.

Dividing Decimals

When dividing by a decimal, make the divisor a whole number by moving the decimal point. Move the decimal point in the dividend the same number of places.

Steps:
  • Move the decimal point in the divisor to make it a whole number.
  • Move the decimal point in the dividend the same number of places.
  • Divide as you would with whole numbers, and place the decimal point in the quotient directly above its position in the dividend.
Example:
  • 4.8 ÷ 0.6 → move both decimals one place → 48 ÷ 6 = 8
  • 6.25 ÷ 2.5 → move both decimals one place → 62.5 ÷ 25 = 2.5
Note

Check your work by multiplying your quotient by the divisor. The result should be equal to the dividend.

Using Decimals in Real Life

Decimals are used in money, measurement, and science to show precise values. Understanding how to operate with decimals helps solve everyday problems.

Examples:
  • Money: $2.75 + $3.50 = $6.25
  • Measurement: 1.2 meters × 3 = 3.6 meters
  • Division: 5.0 ÷ 2 = 2.5
Note

Whenever you use decimals, estimate first to see if your answer is reasonable. This is a smart math habit!