# 1.5 Subtraction of whole numbers

 Page 1 / 4
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to subtract whole numbers. By the end of this module, students should be able to understand the subtraction process, subtract whole numbers, and use a calculator to subtract one whole number from another whole number.

## Section overview

• Subtraction
• Subtraction as the Opposite of Addition
• The Subtraction Process
• Subtraction Involving Borrowing
• Borrowing From Zero
• Calculators

## Subtraction

Subtraction is the process of determining the remainder when part of the total is removed.

Suppose the sum of two whole numbers is 11, and from 11 we remove 4. Using the number line to help our visualization, we see that if we are located at 11 and move 4 units to the left, and thus remove 4 units, we will be located at 7. Thus, 7 units remain when we remove 4 units from 11 units. ## The minus symbol

The minus symbol (-) is used to indicate subtraction. For example, $\text{11}-4$ indicates that 4 is to be subtracted from 11.

## Minuend

The number immediately in front of or the minus symbol is called the minuend , and it represents the original number of units.

## Subtrahend

The number immediately following or below the minus symbol is called the subtrahend , and it represents the number of units to be removed .

## Difference

The result of the subtraction is called the difference of the two numbers. For example, in $\text{11}-4=7$ , 11 is the minuend, 4 is the subtrahend, and 7 is the difference.

## Subtraction as the opposite of addition

Subtraction can be thought of as the opposite of addition. We show this in the problems in Sample Set A.

## Sample set a

$8-5=3$ since $3+5=8$ .

$9-3=6$ since $6+3=9$ .

## Practice set a

Complete the following statements.

$7-5=$ since $+5=7$ .

$7-5=2$ since $2+5=7$

$9-1=$ since $+1=9$ .

$9-1=8$ since $8+1=9$

$\text{17}-8=$ since $+8=\text{17}$ .

$\mathrm{17}-8=9$ since $9+8=\mathrm{17}$

## The subtraction process

We'll study the process of the subtraction of two whole numbers by considering the difference between 48 and 35. which we write as 13.

## The process of subtracting whole numbers

To subtract two whole numbers,

The process

1. Write the numbers vertically, placing corresponding positions in the same column.

$\begin{array}{c}\hfill 48\\ \hfill \underline{-35}\end{array}$

2. Subtract the digits in each column. Start at the right, in the ones position, and move to the left, placing the difference at the bottom.

$\begin{array}{c}\hfill 48\\ \hfill \underline{-35}\\ \hfill 13\end{array}$

## Sample set b

Perform the following subtractions.

$\begin{array}{c}\hfill 275\\ \hfill \underline{-142}\\ \hfill 133\end{array}$

$\begin{array}{}5-2=3\text{.}\\ 7-4=3\text{.}\\ 2-1=1\text{.}\end{array}$

$\begin{array}{}2-1=1\text{.}\\ 4-3=1\text{.}\\ 0-0=0\text{.}\\ 6-1=5\text{.}\\ 4-0=4\text{.}\end{array}$

Find the difference between 977 and 235.

Write the numbers vertically, placing the larger number on top. Line up the columns properly.

$\begin{array}{c}\hfill 977\\ \hfill \underline{-235}\\ \hfill 742\end{array}$

The difference between 977 and 235 is 742.

In Keys County in 1987, there were 809 cable television installations. In Flags County in 1987, there were 1,159 cable television installations. How many more cable television installations were there in Flags County than in Keys County in 1987?

We need to determine the difference between 1,159 and 809. There were 350 more cable television installations in Flags County than in Keys County in 1987.

## Practice set b

Perform the following subtractions.

what are the importance of studying economics
To know if the country is growing or not through the country's GDP
Ariel
What is the law of demand
price increase demand decrease...price decrease demand increase
Mujahid
ıf the price increase the demand decrease and if the demand increase the price decrease
MUBARAK
all other things being equal, an increase in demand causes a decrease in supply and vice versa
SETHUAH
yah
Johnson
how is the economy of usa now
Johnson
What is demand
Demand is the quantity of goods and services a consumer is willing and able to purchase at various prices over a given period of time.
Yaw
yea
SETHUAH
Okay congratulations I'll join you guys later .
Aj
yes
MUBARAK
calculate elasticity of income exercises
If potatoes cost Jane $1 per kilogram and she has$5 that could possibly spend on potatoes or other items. If she feels that the first kilogram of potatoes is worth $1.50, the second kilogram is worth$1.14, the third is worth $1.05 and subsequent kilograms are worth$0.30, how many kilograms of potatoes will she purchase? What if she only had $2 to spend? Susan Reply cause of poverty in urban DAVY Reply QI: (A) Asume the following cost data are for a purely competitive producer: At a product price Of$56. will this firm produce in the short run? Why Why not? If it is preferable to produce, what will be the profit-maximizing Or loss-minimizing Output? Explain. What economic profit or loss will the
what is money
money is any asset that is generally acceptable for the exchange of goods and for the settlement of debts
Mnoko
what is economic
economics is the study of ways in which people use resources to satisfy their wants
Falak
what is Price mechanism
what is Economics
ERNESTINA
The study of resource allocation,distribution and consumption.
Emelyn
introduction to economics
welfare definition of economics
Uday
examine the wealth and welfare definitions of economics
Uday
Anand
What do we mean by Asian tigers
Dm me I will tell u
Shailendra
Hi
Aeesha
hi
Pixel
What is Average revenue
KEMZO
How are u doing
KEMZO
it is so fantastic
metasebia
uday
Uday
it is a group of 4 countries named Singapore, South Korea, Taiwan and Hong Kong because their economies are growing very faster
Anand
fyn
EDWARD
Please, average revenue is an amount of money you gained after deducted your total expenditure from your total income.
EDWARD
what's a demand
it is the quantity of commodities that consumers are willing and able to purchase at particular prices and at a given time
Munanag
quantity of commodities dgat consumers are willing to pat at particular price
Omed
demand depends upon 2 things 1wish to buy 2 have purchasing power of that deserving commodity except any from both can't be said demand.
Bashir
Demand is a various quantity of a commodities that a consumer is willing and able to buy at a particular price within a given period of time. All other things been equal.
Vedzi
State the law of demand
Vedzi
The desire to get something is called demand.
Mahabuba
what is the use of something should pay for its opportunity foregone to indicate?
Why in monopoly does the firm maximize profits when its marginal revenue equals marginal cost
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
In the number 779,844,205 how many ten millions are there?
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
7hours 36 min - 4hours 50 min

#### Get Jobilize Job Search Mobile App in your pocket Now! By Donyea Sweets By Brooke Delaney By Robert Murphy By Vanessa Soledad By OpenStax By David Martin By Mistry Bhavesh By John Gabrieli By OpenStax By OpenStax