Learn how to break numbers into smaller, easier parts!
This strategy is also called:
• The Break Apart Method
• The Distributive Property
• Partial Products
The break apart strategy helps you multiply by splitting one number into place values (tens, ones, hundreds, etc.) and multiplying each part separately, then adding the results.
50 × 63
Instead of solving this all at once:
• Break 63 into: 60 + 3
• Multiply each part: 50 × 60 = 3,000 and 50 × 3 = 150
• Add them together: 3,000 + 150 = 3,150
By breaking the harder number into friendly pieces, the math becomes much easier!
This works because of the distributive property, which says that multiplying a number by a sum is the same as multiplying by each part and adding.
50 × 63 is the same as 50 × (60 + 3)
50 × 60 + 50 × 3
3,000 + 150 = 3,150
Step 1: Break 27 into 20 + 7
Step 2: Multiply each part:
• 40 × 20 = 800
• 40 × 7 = 280
Step 3: Add: 800 + 280 = 1,080
This strategy is especially helpful when:
Great candidates: 50 × 63, 30 × 48, 60 × 35, 20 × 74
Also works well for: 25 × 36, 15 × 42, any multi-digit multiplication!
Break apart 45:
45 = 40 + 5
Multiply each part by 30:
• 30 × 40 = 1,200
• 30 × 5 = 150
Add the products:
1,200 + 150 = 1,350
Problem 1: 20 × 34 = ?
Solution:
• Break 34 into: 30 + 4
• 20 × 30 = 600
• 20 × 4 = 80
• Add: 600 + 80 = 620
Problem 2: 30 × 25 = ?
Solution:
• Break 25 into: 20 + 5
• 30 × 20 = 600
• 30 × 5 = 150
• Add: 600 + 150 = 750
Problem 3: 40 × 22 = ?
Solution:
• Break 22 into: 20 + 2
• 40 × 20 = 800
• 40 × 2 = 80
• Add: 800 + 80 = 880
Problem 4: 50 × 16 = ?
Solution:
• Break 16 into: 10 + 6
• 50 × 10 = 500
• 50 × 6 = 300
• Add: 500 + 300 = 800
Problem 5: 60 × 14 = ?
Solution:
• Break 14 into: 10 + 4
• 60 × 10 = 600
• 60 × 4 = 240
• Add: 600 + 240 = 840
Problem 6: 30 × 19 = ?
Solution:
• Break 19 into: 10 + 9
• 30 × 10 = 300
• 30 × 9 = 270
• Add: 300 + 270 = 570
Problem 7: 50 × 63 = ?
Solution:
• Break 63 into: 60 + 3
• 50 × 60 = 3,000
• 50 × 3 = 150
• Add: 3,000 + 150 = 3,150
Problem 8: 40 × 57 = ?
Solution:
• Break 57 into: 50 + 7
• 40 × 50 = 2,000
• 40 × 7 = 280
• Add: 2,000 + 280 = 2,280
Problem 9: 70 × 48 = ?
Solution:
• Break 48 into: 40 + 8
• 70 × 40 = 2,800
• 70 × 8 = 560
• Add: 2,800 + 560 = 3,360
Problem 10: 60 × 35 = ?
Solution:
• Break 35 into: 30 + 5
• 60 × 30 = 1,800
• 60 × 5 = 300
• Add: 1,800 + 300 = 2,100
Problem 11: 80 × 43 = ?
Solution:
• Break 43 into: 40 + 3
• 80 × 40 = 3,200
• 80 × 3 = 240
• Add: 3,200 + 240 = 3,440
Problem 12: 90 × 52 = ?
Solution:
• Break 52 into: 50 + 2
• 90 × 50 = 4,500
• 90 × 2 = 180
• Add: 4,500 + 180 = 4,680
Once you master the basic strategy, you can break both numbers into parts. This creates a box method or area model.
Break both numbers:
23 = 20 + 3
45 = 40 + 5
Multiply all four parts:
• 20 × 40 = 800
• 20 × 5 = 100
• 3 × 40 = 120
• 3 × 5 = 15
Add all products:
800 + 100 + 120 + 15 = 1,035
Problem 13: 24 × 36 = ?
Solution:
Break both: 24 = 20 + 4, and 36 = 30 + 6
• 20 × 30 = 600
• 20 × 6 = 120
• 4 × 30 = 120
• 4 × 6 = 24
• Add: 600 + 120 + 120 + 24 = 864
Problem 14: 32 × 15 = ?
Solution:
Break both: 32 = 30 + 2, and 15 = 10 + 5
• 30 × 10 = 300
• 30 × 5 = 150
• 2 × 10 = 20
• 2 × 5 = 10
• Add: 300 + 150 + 20 + 10 = 480
Key Takeaways:
✓ Break numbers into tens and ones
✓ Multiply each part separately
✓ Add the products together
✓ Works great with multiples of 10
✓ Can break apart one or both numbers
Pro Tip:
This strategy is the foundation for how we multiply larger numbers on paper! Keep practicing! 🌟