Page 52 - Basic College Mathematics with Early Integers

S E C T ION 1. 4 I SUBTRACTING WHOLE NUMBERS 29

Subtraction Properties of 0

The difference of any number and that same number is 0. For example,
11 - 11 = 0
The difference of any number and 0 is that same number. For example,

45 - 0 = 45

To subtract whole numbers we subtract the digits in the ones place, then the
tens place, then the hundreds place, and so on. When subtraction involves numbers
of two or more digits, it is more convenient to subtract vertically. For example, to
subtract 893 - 52,

8 9 3 minuend
Line up the numbers vertically so that the minuend is on top and
– 5 2 subtrahend
the place values correspond. Subtract in corresponding place values,
8 4 1 difference starting with the ones place.
3-2
9-5
8-0

To check, add.

difference or 841
+ subtrahend + 52
minuend 893 — Since this is the original minuend,
the problem checks.

Example 2 Subtract: 7826 - 505. Check by adding. PRACTICE 2
Subtract. Check by adding.
Solution: 7826 Check: 7321 a. 9143 - 122
–505 ±505
b. 978 - 851
7321 7826

Work Practice 2

Subtracting by Borrowing
When subtracting vertically, if a digit in the second number (subtrahend) is larger
than the corresponding digit in the first number (minuend), borrowing is necessary.
For example, consider

8 1
- 6 3

Since the 3 in the ones place of 63 is larger than the 1 in the ones place of 81,
borrowing is necessary. We borrow 1 ten from the tens place and add it to the ones
place.

Borrowing
7 11
8 - 1 = 7 : 8 1 ; 1 ten + 1 one = 11 ones
tens ten tens - 6 3 Answer
2. a. 9021 b. 127