Learning Objectives
- 01
Use overshoot to convert hard divisions to easy ones.
Overshooting Technique
Divide by the next round number, then compensate.
Topics
Overshoot and compensate
Worked Examples
770 ÷ 79=≈ 9.75
Estimate, multiply back, subtract the remainder.
- 01
770 / 80 ≈ 9.625
Apply this piece of the shortcut — running quotient 770.
- →
= ≈ 9.75
490 ÷ 62=≈ 7.9
Estimate, multiply back, subtract the remainder.
- 01
490 / 60 ≈ 8.17
Apply this piece of the shortcut — running quotient 490.
- →
= ≈ 7.9
1444 ÷ 38=38
Estimate, multiply back, subtract the remainder.
- 01
Estimate by leading digits; refine quotient digit-by-digit
Apply this piece of the shortcut — running quotient 1444.
- →
= 38
Benjamin, Secrets of Mental Math — estimated long division
854 ÷ 21=40 r 14
Estimate, multiply back, subtract the remainder.
- 01
Estimate by leading digits; refine quotient digit-by-digit
Apply this piece of the shortcut — running quotient 854.
- →
= 40 r 14
Benjamin, Secrets of Mental Math — estimated long division
1565 ÷ 19=82 r 7
Estimate, multiply back, subtract the remainder.
- 01
Estimate by leading digits; refine quotient digit-by-digit
Apply this piece of the shortcut — running quotient 1565.
- →
= 82 r 7
Benjamin, Secrets of Mental Math — estimated long division
Talking Points
- •Good enough beats exact, when the question is 'about how much?'
Week 4 · Division & Estimation
Mental division, overshooting, and guesstimation.
- →Mental division
- →Overshooting methods
- →Guesstimation
Sample Problems · Week 4
One simple and one intermediate problem to preview the week.
Simple · Day 1
79 ÷ 3=26 r 1
Intermediate · Day 5
8.25% tax on $47=≈ $3.88