Ray's New Higher Arithmetic · Arts. 53–54 · Unit 4: Subtraction
9. Subtraction
Goal: Your student uses the words minuend, subtrahend and difference, subtracts large numbers with borrowing, and proves the work by adding.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Subtraction defined, its terms and five principles, the worked example 827 − 534, the rule, the proof, and 13 examples for practice (answers printed for all but the first).
The lesson, step by step
Warm-up
Mental: 100 − 37; 1000 − 1; 64 − 29.
The idea
Read:
Subtraction is the process of finding the difference between two numbers of the same kind.
A number can be subtracted only from another of the same kind.
The larger number is the minuend, the smaller the subtrahend, and what is left the difference or remainder. The book's example: 2 cents can't be taken from 5 apples.
Work the book's example
From 827 dollars take 534 dollars. Units: 7 − 4 = 3. Tens: 3 tens can't come from 2 tens, so take 1 of the 8 hundreds as 10 tens: 12 − 3 = 9. Hundreds: 7 − 5 = 2. Answer $293.
Rule and proof
Read:
Write the less number under the greater, placing units under units, tens under tens, etc.
Add the remainder to the less number. If the work be correct, the sum will be equal to the greater.
Guided practice
Together:
From 79685 take 30253.
From 2900000 take 777888.
Prove each by adding. (49432 and 2122112.)
Independent practice
Your student works all 13 examples, proving each by addition. Number 7 asks how many years from 1492 to 1776.
Check
Answers are printed for Examples 2 to 13. Example 1 is in the answers below.
Wrap-up
Ask: If you know the difference and the subtrahend, how do you find the minuend? (Add them.)
Tip
Lots of ciphers in the minuend (like 2900000) is where borrowing goes wrong. Go slowly there.
Answers to the book's problems
Example 1: 30020037 − 50009 = 29970028.
Worked out for this site from the scan. If a number in your copy differs, trust the book.