Ray's New Practical Arithmetic · Art. 26 · Unit 3: Subtraction
12. The rule for subtraction and its proof
Goal: Your child subtracts long numbers using the rule and proves each answer by adding.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The rule for subtraction, the proof, a set of minuends and subtrahends, and story problems. Answers are printed for nearly all.
The lesson, step by step
Warm-up
Mental: 13 − 8? 15 − 9? 11 − 4? 16 − 7?
The rule
Read:
Write the less number under the greater, placing figures of the same order in the same column.
Beginning at the right hand, subtract each figure from the one directly over it, and write the remainder beneath.
The proof
Read:
Add the remainder to the subtrahend; if the sum is equal to the minuend, the work is correct.
Work the first example together: 7640 − 1234 = 6406. Prove it: 6406 + 1234 = 7640.
Guided practice
Do two of the story problems together:
A carriage cost $137, and a horse $65: how much more than the horse did the carriage cost?
A tree 75 feet high was broken; the part that fell was 37 feet long: how high was the stump?
(Answers printed: $72 and 38 ft.)
Independent practice
Assign about ten of the numbered examples, mixing number examples and story problems. Your child proves each by adding.
Check
Answers are printed after most problems. Have your child prove first, then compare.
Wrap-up
Mental: 1000 − 1? 1000 − 250? 500 − 125?
Tip
Long zeros in the minuend (like 10000 − 1) are the hardest. Borrow one step at a time and say each step aloud.