Divide by Decimals
Dividing by decimals seems tricky, but there's a clever trick! You can move the decimal point to make the divisor a whole number - just move it the same amount in both numbers. Let's learn this decimal-shifting magic!
Do this: Read the concept below, then try the quiz or activity.
Concept
The key to dividing by decimals is converting the divisor to a whole number!
🎯 The Strategy: Move the decimal point in the divisor to make it a whole number, then move it the same number of places in the dividend!
📊 Example: 12.5 ÷ 2.5
Step 1: Make divisor a whole number • Divisor: 2.5 → move decimal 1 place right → 25 • Dividend: 12.5 → move decimal 1 place right → 125
Step 2: Now divide whole numbers! 125 ÷ 25 = 5
Answer: 12.5 ÷ 2.5 = 5
Check: 5 × 2.5 = 12.5 ✓
💡 Example 2: 4.8 ÷ 0.6
Step 1: Move decimals • 0.6 → 6 (moved 1 place right) • 4.8 → 48 (moved 1 place right)
Step 2: Divide 48 ÷ 6 = 8
Answer: 4.8 ÷ 0.6 = 8
🌟 Why This Works: Moving the decimal point the same amount in both numbers is like multiplying both by the same power of 10!
4.8 ÷ 0.6 = (4.8 × 10) ÷ (0.6 × 10) = 48 ÷ 6
The division stays equivalent!
🎨 Dividing by Powers of 10:
Special pattern: • ÷ 10: Move decimal ONE place LEFT • ÷ 100: Move decimal TWO places LEFT • ÷ 1000: Move decimal THREE places LEFT
Examples: • 45.6 ÷ 10 = 4.56 (moved 1 left) • 45.6 ÷ 100 = 0.456 (moved 2 left) • 45.6 ÷ 1000 = 0.0456 (moved 3 left)
📏 Step-by-Step Process:
Problem: 15.75 ÷ 0.25
Step 1: Count decimal places in divisor 0.25 has 2 decimal places
Step 2: Move both decimals 2 places right • 0.25 → 25 • 15.75 → 1575
Step 3: Divide 1575 ÷ 25 = 63
Step 4: Check 63 × 0.25 = 15.75 ✓
Answer: 63
🔍 Adding Zeros When Needed:
Example: 5 ÷ 0.2 • 0.2 → 2 (move 1 right) • 5 → 50 (move 1 right, add zero!) • 50 ÷ 2 = 25
Estimation Check: Does 25 make sense? • 5 ÷ 0.5 = 10 • 5 ÷ 0.2 should be bigger (dividing by smaller number) • 25 makes sense! ✓
Real-World Application: You have $18.75 and want to buy items that cost $2.50 each. How many can you buy?
18.75 ÷ 2.50 → 1875 ÷ 250 = 7.5
You can buy 7 complete items (and have $1.25 left over!)
Try it
Practice dividing by decimals!
📝 Dividing by Powers of 10: 1. 45 ÷ 10 = ? 2. 83.5 ÷ 10 = ? 3. 12.4 ÷ 100 = ? 4. 560 ÷ 1000 = ?
🎯 Move the Decimal - What's the Equivalent Division? 5. 6.4 ÷ 0.8 = ___ ÷ ___ (fill in the whole numbers) 6. 12.5 ÷ 2.5 = ___ ÷ ___ 7. 4.2 ÷ 0.6 = ___ ÷ ___
💡 Solve These: 8. 8.4 ÷ 0.7 = ?
9. 15.6 ÷ 1.2 = ?
10. 9.6 ÷ 0.8 = ?
11. 24.5 ÷ 0.5 = ?
📊 More Practice:
12. 18 ÷ 0.6 = ?
(Remember to add zeros!)13. 7.5 ÷ 0.25 = ?
14. 36.4 ÷ 0.4 = ?
15. 5.6 ÷ 0.08 = ?
🏆 Word Problems: 16. A rope is 24.5 feet long. You cut it into pieces that are 3.5 feet each. How many pieces do you get?
17. You have $45.50. Notebooks cost $3.50 each. How many can you buy?
18. A car travels 156.8 miles on 6.4 gallons of gas. How many miles per gallon is that?
19. A recipe uses 2.5 cups of flour. How many batches can you make with 15 cups of flour?
💪 Challenge: 20. 84.6 ÷ 0.06 = ?
21. 125.4 ÷ 0.15 = ?
22. Which is larger: 10 ÷ 0.5 or 10 ÷ 0.2? Why?
(Don't calculate - explain!)23. Without dividing, determine if 45 ÷ 0.9 will be greater or less than 45. Explain your reasoning.
24. Estimate, then solve: 97.3 ÷ 4.8
25. Create a word problem that requires dividing 32.5 ÷ 2.5