Learning Objectives
- 01
Make change at the register without paper.
Making Change Quickly
Applying complements to real cash transactions.
Goal · 50 mixed +/− problems
Topics
Cash transactionsShopping calculations
Worked Examples
Change from $20 for $13.47=$6.53
Change from $100 for $42.18=$57.82
Complement of 67 to 100=33
Complement-to-100 shortcut (Benjamin): every digit pairs to 9, except the last which pairs to 10.
- 01
6 → 9 − 6 = 3
Pair to 9.
- 02
7 → 10 − 7 = 3
Last digit: complement to 10.
- 03
33 = 33
Read the new digits left-to-right.
- →
= 33
Trachtenberg Speed System — complements
69 − 50=19
Subtract from left to right, rounding to a convenient number when it helps and correcting at the end.
- 01
69 − 50 = 19
Take away the tens (50). Just count down by tens — the ones digit stays the same. 69 − 50 = 19 — running total 19.
- →
= 19
Benjamin, Secrets of Mental Math — left-to-right subtraction
73 + 42=115
Break the second addend into place-value chunks (hundreds, tens, units) and add them one at a time so you only ever track one running total.
- 01
73 + 40 = 113; 113 + 2 = 115
Add the tens (40). Just count up by tens — the ones digit stays the same. 73 + 40 = 115 — running total 115.
- →
= 115
Benjamin, Secrets of Mental Math — left-to-right addition
Talking Points
- •Pennies pair to 10; everything else pairs to 9.
Week 2 · Addition & Subtraction Mastery
Add and subtract rapidly using complements and compensation.
- →Add 2- and 3-digit numbers rapidly
- →Subtract efficiently without borrowing
- →Use complements to 100 and 1000
Sample Problems · Week 2
One simple and one intermediate problem to preview the week.
Simple · Day 3
74 − 29=45
Intermediate · Day 5
Change from $100 for $42.18=$57.82