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AA.6 Divide decimals: word problems

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What does it mean to divide decimals?

Dividing decimals means splitting a decimal number into equal groups. You use division to find how many groups you can make or how much is in each group when decimals are involved.

Example:
  • If you have 4.8 meters of ribbon and cut it into 6 equal pieces, each piece is 4.8 ÷ 6 = 0.8 meters.
Note

Decimal division often appears in real-life situations like measuring, shopping, and sharing amounts evenly.

How to divide a decimal by a whole number

To divide a decimal by a whole number, divide as you normally would and bring the decimal point straight up into the answer.

Steps:
  • Start with 9.6 ÷ 3
  • Divide: 9 ÷ 3 = 3
  • Bring the decimal point up, then divide 6 ÷ 3 = 2
  • The answer is 3.2
Note

You never move the decimal in the dividend when dividing by a whole number. It simply goes straight up into the quotient.

How to divide a decimal by another decimal

When dividing a decimal by another decimal, make the divisor a whole number by moving its decimal point to the right. Then move the decimal point in the dividend the same number of places.

Example:
  • 0.84 ÷ 0.2
  • Move the decimal in 0.2 one place → 2
  • Move the decimal in 0.84 one place → 8.4
  • Now divide 8.4 ÷ 2 = 4.2
4.2
2
8.4
- 8 ← 4×2
4 ← Bring down
- 4
0
Note

The value of the problem does not change when you move both decimals the same number of places. You are creating an easier division problem.

Types of decimal division word problems

Decimal division word problems can involve finding the number of equal groups, finding the size of each group, comparing quantities, or calculating unit rates.

Situations:
  • Sharing equally: A total amount is split into equal parts. (Example: Sharing 5.4 pounds of apples among 3 people.)
  • Finding the size of one group: You know the number of groups and need one group’s value. (Example: 12.5 gallons poured evenly into 5 containers.)
  • Finding how many groups can be made: You know the size of each group. (Example: How many 0.25-mile laps fit into 1.5 miles.)
  • Unit rate: Dividing to find “per one.” (Example: $7.50 for 3 sandwiches → cost per sandwich.)
Note

Spotting which situation the problem describes helps you choose the correct numbers to divide.

Solving decimal word problems step by step

When solving word problems, carefully identify what the numbers represent and determine whether you are finding each group’s size or the number of groups.

Example:
  • A baker has 7.2 pounds of dough. She divides it into balls that weigh 0.3 pounds each. How many dough balls can she make?
  • Divide: 7.2 ÷ 0.3
  • Move the decimals: 7.2 → 72 and 0.3 → 3
  • Now divide: 72 ÷ 3 = 24
  • She can make 24 dough balls.
Note

Always check that your answer makes sense for the situation. For example, you should not get more groups than the total makes possible.

Common mistakes to avoid

Be careful with decimal placement and be sure you understand what the question is asking before computing.

Watch out for:
  • Forgetting to move the decimal in both numbers when dividing by a decimal.
  • Misreading the problem and dividing the numbers in the wrong order.
  • Changing place values when bringing the decimal point into the quotient.
Note

Reread the question after solving to be sure your answer matches what the problem asked.