Basic Mathematics for College Students

1.3 Subtracting Whole Numbers 29

Subtraction of whole numbers is used by everyone. For example, to find the sale price
of an item, a store clerk subtracts the discount from the regular price. To measure
climate change, a scientist subtracts the high and low temperatures. A trucker
subtracts odometer readings to calculate the number of miles driven on a trip.

SECTION 1.3

Subtracting Whole Numbers

Objectives

1 Subtract whole numbers.

2 Subtract whole numbers with

borrowing.

3 Check subtractions using

addition.

4 Estimate differences of whole

numbers.

5 Solve application problems by

subtracting whole numbers.

6 Evaluate expressions involving

addition and subtraction.

Subtract whole numbers.

To subtract two whole numbers, think of taking away objects from a set. For example,
if we start with a set of 9 stars and take away a set of 4 stars, a set of 5 stars is left.

We can write this subtraction problem in horizontal or vertical form using a
subtraction symbol ,which is read as “minus.” We call the number from which
another number is subtracted the minuend.The number being subtracted is called the
subtrahend,and the answer is called the difference.

Horizontal form Vertical form

Minuend

Subtrahend

 Difference



9 

 4

5

We read each form as

“9 minus 4 equals (or is) 5.”

(^9)   (^4)   (^5) 
Minuend Subtrahend Difference
A set of
5 stars
A set of
9 stars
We take
away 4 stars
to get
this set.
1
The Language of Mathematics The prefix sub means below, as in submarine
or subway. Notice that in vertical form, the subtrahend is written below the
minuend.
To subtract two whole numbers that are less than 10, we rely on our understanding
of basic subtraction facts. For example,
and
To subtract two whole numbers that are greater than 10, we can use vertical form
by stacking them with their corresponding place values lined up. Then we simply
subtract the digits in each corresponding column.

6  3 3, 7  2 5, 9  8  1

EXAMPLE (^1) Subtract: 59  27
Strategy We will write the subtraction in vertical form with the ones digits in a
column and the tens digits in a column. Then we will subtract the digits in each
column, working from right to left.
WHY Like money, where pennies are only subtracted from pennies and dimes are
only subtracted from dimes, we can only subtract digits with the same place
value–ones from ones and tens from tens.
Self Check 1
Subtract:
Now TryProblems 15 and 21

68  31