Divide by 2-Digit Numbers Using Partial Quotients
Dividing by 2-digit numbers can seem tricky, but partial quotients makes it manageable! Instead of finding the exact answer all at once, we subtract friendly multiples until we get there. It's like taking stairs instead of a giant leap!
Do this: Read the concept below, then try the quiz or activity.
Concept
Partial quotients is a flexible, friendly way to divide that lets you work with multiples you know!
🎯 The Strategy: Instead of dividing all at once, subtract multiples of the divisor until you can't anymore!
📊 Example: 156 ÷ 12
Think: What times 12 is easy to calculate? • 12 × 10 = 120 (a good start!) • 12 × 5 = 60
Step-by-Step: 1. Start with 156 2. Subtract 120 (that's 10 groups of 12) 156 - 120 = 36 3. Subtract 24 (that's 2 groups of 12) 36 - 24 = 12 4. Subtract 12 (that's 1 group of 12) 12 - 12 = 0
Add up the groups: 10 + 2 + 1 = 13
So 156 ÷ 12 = 13 ✓
💡 Visual Representation:
___13___
12 | 156
-120 (10 groups)
----
36
-24 (2 groups)
----
12
-12 (1 group)
----
0🌟 Choosing Your Multiples: You can use ANY friendly multiples! • Conservative approach: 10s and 5s • Aggressive approach: larger chunks • Mixed: whatever feels comfortable
Alternative solution for 156 ÷ 12: - Subtract 60 (5 groups): 156 - 60 = 96 - Subtract 60 (5 groups): 96 - 60 = 36 - Subtract 36 (3 groups): 36 - 36 = 0 - Total: 5 + 5 + 3 = 13 groups
Same answer, different path!
🎨 Pro Tips: • Always start with a multiple you're confident about • Multiples of 10 are usually easiest • It's okay to take small steps • Keep track of your groups on the side
Try it
Let's practice division using partial quotients!
📝 Identify Friendly Multiples: 1. List three easy multiples of 15: (Hint: ×10, ×5, ×2) 2. What's 23 × 10? 23 × 5? 23 × 2? 3. Which is easier to subtract from 250: 24 × 10 or 24 × 7? Why?
🎯 Divide Using Partial Quotients: 4. 132 ÷ 11 = ? • Try subtracting 110 (10 groups) first • Keep going!
5. 168 ÷ 14 = ? Show all your partial quotients
6. 195 ÷ 13 = ?
💡 Multiple Paths: 7. Solve 144 ÷ 12 two different ways using different multiples
📊 With Remainders: 8. 157 ÷ 15 = ? R? 9. 203 ÷ 18 = ? R?
🏆 Word Problems: 10. A school has 336 students. They want to organize field day with 24 students per team. How many teams can they make?
11. A factory packed 375 toys. Each box holds 25 toys. How many boxes did they fill?
💪 Challenge:
12. 847 ÷ 22 = ?
Estimate first, then solve13. Explain why partial quotients is helpful: Write 2-3 sentences about why this method works well for you.
14. 504 ÷ 36 = ?
Try to solve it efficiently (using larger multiples)