Learning Objectives
- 01
Compute complements to 100 and 1000 in one beat.
Complements
Finding the complement to 100 and 1000 instantly.
Topics
Complement to 100Complement to 1000
Worked Examples
Complement of 75 to 100=25
Complement-to-100 shortcut (Benjamin): every digit pairs to 9, except the last which pairs to 10.
- 01
7 → 9 − 7 = 2
Pair to 9.
- 02
5 → 10 − 5 = 5
Last digit: complement to 10.
- 03
25 = 25
Read the new digits left-to-right.
- →
= 25
Complement of 234 to 1000=766
Complement-to-100 shortcut (Benjamin): every digit pairs to 9, except the last which pairs to 10.
- 01
2 → 9 − 2 = 7
Pair to 9.
- 02
3 → 9 − 3 = 6
Pair to 9.
- 03
4 → 10 − 4 = 6
Last digit: complement to 10.
- 04
766 = 766
Read the new digits left-to-right.
- →
= 766
Complement of 670 to 1000=330
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 → 9 − 7 = 2
Pair to 9.
- 03
0 → 10 − 0 = 10
Last digit: complement to 10.
- 04
3210 = 330
Read the new digits left-to-right.
- →
= 330
Complement of 37 to 100=63
Complement-to-100 shortcut (Benjamin): every digit pairs to 9, except the last which pairs to 10.
- 01
3 → 9 − 3 = 6
Pair to 9.
- 02
7 → 10 − 7 = 3
Last digit: complement to 10.
- 03
63 = 63
Read the new digits left-to-right.
- →
= 63
Trachtenberg Speed System — complements
Complement of 38 to 100=62
Complement-to-100 shortcut (Benjamin): every digit pairs to 9, except the last which pairs to 10.
- 01
3 → 9 − 3 = 6
Pair to 9.
- 02
8 → 10 − 8 = 2
Last digit: complement to 10.
- 03
62 = 62
Read the new digits left-to-right.
- →
= 62
Trachtenberg Speed System — complements
Talking Points
- •Each digit pairs to 9, except the last which pairs to 10.
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