Learning Objectives
- 01
Multiply two numbers near a common base.
Close-Together Method
When both factors sit near the same round number.
Topics
Close-together multiplication
Worked Examples
107 × 111=11877
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
100·(107+11) + 7·11
Apply this piece of the shortcut — running product 107.
- →
= 11877
96 × 93=8928
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
100·(96−7) + (−4)·(−7)
Apply this piece of the shortcut — running product 96.
- →
= 8928
27 × 70=1890
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (20)(70)=1400; outer+inner=(20×0)+(7×70)=490; 7×0=0
Run the partial calculation — running product 0.
- →
= 1890
Benjamin, Secrets of Mental Math — cross-multiplication
50 × 71=3550
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (50)(70)=3500; outer+inner=(50×1)+(0×70)=50; 0×1=0
Run the partial calculation — running product 0.
- →
= 3550
Benjamin, Secrets of Mental Math — cross-multiplication
24 × 30=720
Distribute the smaller factor across the place values of the larger number, then add the partial products.
- 01
Cross: (20)(30)=600; outer+inner=(20×0)+(4×30)=120; 4×0=0
Run the partial calculation — running product 0.
- →
= 720
Benjamin, Secrets of Mental Math — cross-multiplication
Talking Points
- •Choose the base both numbers are closest to.
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