Learning Objectives
- 01
Extend cross-multiplication to 3-digit numbers.
3-Digit Cross Multiplication
Same principle, one more cross.
Topics
3×3 cross-multiplication
Worked Examples
314 × 159=49,926
41 × 39=1599
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (40)(30)=1200; outer+inner=(40×9)+(1×30)=390; 1×9=9
Run the partial calculation — running product 9.
- →
= 1599
Benjamin, Secrets of Mental Math — cross-multiplication
83 × 44=3652
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (80)(40)=3200; outer+inner=(80×4)+(3×40)=440; 3×4=12
Run the partial calculation — running product 12.
- →
= 3652
Benjamin, Secrets of Mental Math — cross-multiplication
77 × 50=3850
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (70)(50)=3500; outer+inner=(70×0)+(7×50)=350; 7×0=0
Run the partial calculation — running product 0.
- →
= 3850
Benjamin, Secrets of Mental Math — cross-multiplication
85 × 74=6290
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (80)(70)=5600; outer+inner=(80×4)+(5×70)=670; 5×4=20
Run the partial calculation — running product 20.
- →
= 6290
Benjamin, Secrets of Mental Math — cross-multiplication
Talking Points
- •Practise the cross pattern slowly before adding the timer.
Week 5 · Advanced Paper-and-Mental Techniques
Verification, cross-multiplication, close-together method.
- →Verify quickly
- →Cross-multiplication
- →Close-together multiplication
Sample Problems · Week 5
One simple and one intermediate problem to preview the week.
Simple · Day 1
22 × 8=176
Intermediate · Day 4
107 × 111=11877