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!
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