Decimal Division

Grade 5 · decimals · 83 practice problems · read aloud

🔊 Listen to this explanation

Dividing Decimals 🧮

Decimal division helps us split things into equal parts when we're dealing with amounts less than one, like sharing 1.5 liters of juice equally among 3 friends or figuring out how many $0.25 pencils you can buy with $2.00.

How to Divide Decimals: Step-by-Step

  1. Move the Decimal: If the divisor (the number you're dividing by) is a decimal, move its decimal point all the way to the right to make it a whole number.
  2. Move the Other Decimal: Move the decimal point in the dividend (the number you're dividing into) the same number of places to the right.
  3. Divide: Now, divide the new numbers like you would with regular whole numbers.
  4. Place the Decimal: Bring the decimal point straight up into your answer, directly above its new position in the dividend.

Let's See It In Action! ✨

Example 1: 4.8 ÷ 0.6

1. Divisor is 0.6 → Move decimal 1 place: becomes 6
2. Dividend is 4.8 → Move decimal 1 place: becomes 48
3. Divide: 48 ÷ 6 = 8
4. Answer: 8

Example 2: 3.24 ÷ 0.4

1. Divisor is 0.4 → Move decimal 1 place: becomes 4
2. Dividend is 3.24 → Move decimal 1 place: becomes 32.4
3. Divide: 32.4 ÷ 4 = 8.1
4. Bring decimal up: 8.1

Watch Out! Common Mistakes 🚨

Forgetting to move BOTH decimals: You must move the decimal point in the dividend the same number of places as you did in the divisor.

Misplacing the decimal in the answer: Always bring the decimal point straight up from its new position in the dividend.

Dividing by a whole number incorrectly: If the divisor is already a whole number (like 5), you don't need to move any decimals! Just divide and bring the decimal point straight up.

Tips & Tricks for Success 💡

Remember the Rhyme: "Outsider, Insider, Top!" (Move the decimal of the number outside the division bracket, then the one inside, then the decimal goes at the top).

Estimate First: Round the numbers to get a ballpark answer. If 1.8 ÷ 0.9 is about 2 ÷ 1 = 2, your answer should be close to 2.

Check with Multiplication: The best way to check your division is to multiply your answer by the divisor. You should get the dividend back!

Time to Practice! 🏃‍♂️

  • Start with simple problems like 0.8 ÷ 0.2
  • Use grid paper to help keep your decimal points lined up
  • Create your own real-world problems: "If one meter of ribbon costs $1.50, how many meters can I buy with $6.00?"
  • Ask a friend or family member to give you problems to solve

Practice problems

6 of the 83, worked through step by step — try them before opening the answer.

1 8.4 ÷ 4 = ?

Hint: Think about how you would divide a decimal number into equal whole number parts. For example, if you had 6.3 divided by 3, you would first divide the whole number part, then the decimal part.

Show the answer

Answer: 2.1

  1. Write the division problem: 8.4 ÷ 4
  2. Divide the whole number part: 8 ÷ 4 = 2
  3. Bring down the decimal point to the quotient
  4. Divide the decimal part: 0.4 ÷ 4 = 0.1
  5. Add the results: 2 + 0.1 = 2.1
  6. The answer is 2.1

2 12.6 ÷ 3 = ?

Hint: Think about how you can break down the decimal number into equal parts. Consider what happens when you divide both the whole number part and the decimal part separately.

Show the answer

Answer: 4.2

  1. Understand the problem. We are dividing 12.6 by 3. This means we want to split 12.6 into 3 equal parts.
  2. Break 12.6 into whole and decimal parts. 12.6 = 12 + 0.6
  3. Divide the whole number part by 3. 12 ÷ 3 = 4
  4. Divide the decimal part by 3. 0.6 ÷ 3 = 0.2
  5. Add the results from Step 3 and
  6. 4 + 0.2 = 4.2 So, 12.6 ÷ 3 = 4.2 We can check: 4.2 × 3 = 12.6, which is correct.

Let's solve 12.6 ÷ 3 step by step.

3 45.6 ÷ 8 = ?

Hint: Think about how you can break down the decimal number into equal parts using the whole number divisor.

Show the answer

Answer: 5.7

  1. Set up the division problem: 45.6 ÷ 8
  2. Divide the whole number part first: 45 ÷ 8 = 5 with a remainder of 5
  3. Bring down the decimal point and the 6 to make 56
  4. Divide 56 by 8: 56 ÷ 8 = 7
  5. Combine the results: 5.7
  6. Check: 5.7 × 8 = 45.6

The answer is 5.7.

4 14.4 ÷ 6 = ?

Hint: Think about how you can break down the decimal number into equal parts using the whole number divisor.

Show the answer

Answer: 2.4

  1. Set up the division: 14.4 ÷ 6
  2. Divide the whole number part: 14 ÷ 6 = 2 with a remainder of 2
  3. Bring down the decimal point and the 4 to make 2.4
  4. Divide 24 tenths by 6: 24 ÷ 6 = 4
  5. Place the 4 in the tenths place: 2.4
  6. Verify: 2.4 × 6 = 14.4

The answer is 2.4.

5 4.68 ÷ 6 = ?

Hint: Think about how you would divide a decimal by a whole number. Consider what happens to the decimal point when you divide.

Show the answer

Answer: 0.78

  1. Set up the division problem: 6 into 4.68.
  2. Since 6 is larger than 4, we look at the first two digits, 46. How many times does 6 go into 46? 6 × 7 = 42. Write 7 above the 6 in the dividend.
  3. Subtract 42 from 46, which gives 4.
  4. Bring down the next digit, which is 8, making the new number 48.
  5. How many times does 6 go into 48? 6 × 8 = 48. Write 8 above the 8 in the dividend.
  6. Subtract 48 from 48, which gives 0.
  7. Since we started with a decimal point in the dividend, we place the decimal point in the quotient directly above its position in the dividend. This gives us 0.78.

The answer is 0.78.

6 72.6 ÷ 6 = ?

Hint: Think about how to divide a decimal by a whole number. Consider what happens to the decimal point when you divide.

Show the answer

Answer: 12.1

  1. Set up the division problem: 72.6 ÷ 6
  2. Divide the whole number part first. 72 ÷ 6 = 12
  3. Bring down the decimal point directly above into the answer
  4. Now divide the decimal part. 0.6 ÷ 6 = 0.1
  5. Combine the results: 12 + 0.1 = 12.1
  6. Check: 12.1 × 6 = 72.6

The answer is 12.1.

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