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AA.5 Divide decimals by decimals

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Divide decimals by decimals

Dividing decimals by decimals means finding how many times one decimal number fits into another. The goal is to make the divisor (the number you are dividing by) a whole number so the division becomes easier to compute.

Example:
  • 0.6 ÷ 0.2 means “How many groups of 0.2 are in 0.6?”
  • You can think of it as: 0.6 is three groups of 0.2 → 0.6 ÷ 0.2 = 3
Note

Whenever you divide decimals, you can use place-value reasoning to help you understand the size of each number.

How do you prepare decimals for division?

To divide decimals, make the divisor a whole number by moving the decimal point to the right. You must move the decimal point in the dividend the same number of places.

Steps:
  • Problem: 4.56 ÷ 0.12
  • Move the divisor’s decimal two places → 0.12 becomes 12
  • Move the dividend’s decimal two places → 4.56 becomes 456
  • Now divide: 456 ÷ 12 = 38
Note

You are not changing the value of the problem—only the form—because you multiply both numbers by the same power of ten.

Dividing a decimal by a whole number

When the divisor is already a whole number, you divide normally and place the decimal point in the quotient directly above its position in the dividend.

Example:
  • 7.5 ÷ 3 → Divide 75 by 3 = 25
  • Place the decimal: 7.5 ÷ 3 = 2.5
Note

If the dividend does not have enough digits, you may add zeros to continue dividing.

Dividing by decimals less than one

When you divide by a decimal smaller than one, the quotient is often greater than the dividend because you are splitting it into smaller parts.

Example:
  • 3 ÷ 0.5 → Ask “How many halves are in 3?”
  • There are 6 halves in 3 → 3 ÷ 0.5 = 6
Note

This is the opposite of dividing by a number greater than one, where the result becomes smaller.

Using long division with decimals

After making the divisor a whole number, use long division to divide the adjusted numbers. Continue dividing until you reach a remainder of zero or a repeating pattern.

Example:
  • 2.4 ÷ 0.4 → Move both decimals one place → 24 ÷ 4 = 6
  • 1.25 ÷ 0.5 → Move decimals one place → 12.5 ÷ 5 = 2.5
Note

If the division does not come out evenly, continue adding zeros to the right of the dividend to complete the process.

Using decimal division in real-life situations

Decimal division is used in measurement, money, science, recipes, and comparing quantities. Understanding how to divide decimals helps you interpret real-world information accurately.

Examples:
  • If a 1.5-liter bottle is shared equally among 3 people, each gets 1.5 ÷ 3 = 0.5 liters.
  • A ribbon 2.4 meters long cut into pieces of 0.3 meters gives 2.4 ÷ 0.3 = 8 pieces.
Note

Always check whether the divisor is less than one or greater than one—this helps you predict whether your answer should be larger or smaller than the original number.