Learning Objectives
- 01
Split a tough multiplication into two easy ones.
Factoring Method
Break one factor into a friendlier product.
Topics
Factoring 2-digit numbers
Worked Examples
43 × 14=602
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
43 × 2 × 7 = 86 × 7
Multiply just the units part (43) by 2. We do one small piece at a time, then add them up at the end. 43 × 2 = 86 — running product 86.
- →
= 602
64 × 15=960
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
64 × 3 × 5 = 192 × 5
Multiply just the units part (64) by 3. We do one small piece at a time, then add them up at the end. 64 × 3 = 192 — running product 192.
- →
= 960
89 × 72=6408
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
89 × 8 × 9
Apply this piece of the shortcut — running product 89.
- →
= 6408
73 × 60=4380
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (70)(60)=4200; outer+inner=(70×0)+(3×60)=180; 3×0=0
Run the partial calculation — running product 0.
- →
= 4380
Benjamin, Secrets of Mental Math — cross-multiplication
52 × 32=1664
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (50)(30)=1500; outer+inner=(50×2)+(2×30)=160; 2×2=4
Run the partial calculation — running product 4.
- →
= 1664
Benjamin, Secrets of Mental Math — cross-multiplication
Talking Points
- •Hunt for the factor pair that makes the rest trivial.
Week 3 · Multiplication Essentials
2×1, 3×1, and factoring methods.
- →Master 2×1 and 3×1
- →Use addition vs subtraction methods
- →Factor for speed
Sample Problems · Week 3
One simple and one intermediate problem to preview the week.
Simple · Day 1
53 × 6=318
Intermediate · Day 5
858 × 6=5148