<< Chapter < Page Chapter >> Page >
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

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.

A number line, with an arrow, labeled -4, drawn from the mark for 11 to the mark for 7.

The minus symbol

The minus symbol (-) is used to indicate subtraction. For example, 11 4 size 12{"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 11 4 = 7 size 12{"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 size 12{8 - 5=3} {} since 3 + 5 = 8 size 12{3+5=8} {} .

Got questions? Get instant answers now!

9 3 = 6 size 12{9 - 3=6} {} since 6 + 3 = 9 size 12{6+3=9} {} .

Got questions? Get instant answers now!

Practice set a

Complete the following statements.

7 5 = size 12{7 - 5={}} {} since + 5 = 7 size 12{+5=7} {} .

7 - 5 = 2 since 2 + 5 = 7

Got questions? Get instant answers now!

9 1 = size 12{9 - 1={}} {} since + 1 = 9 size 12{+1=9} {} .

9 - 1 = 8 since 8 + 1 = 9

Got questions? Get instant answers now!

17 8 = size 12{"17" - 8={}} {} since + 8 = 17 size 12{+8="17"} {} .

17 - 8 = 9 since 9 + 8 = 17

Got questions? Get instant answers now!

The subtraction process

We'll study the process of the subtraction of two whole numbers by considering the difference between 48 and 35.

Vertical subtraction. 48 - 35 means, 4 tens + 8 ones, minus 3 tens - 5 ones = 1 ten + 3 ones.

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.

    48 - 35 ̲

  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.

    48 - 35 ̲ 13

Got questions? Get instant answers now!

Sample set b

Perform the following subtractions.

275 - 142 ̲ 133

5 2 = 3 . 7 4 = 3 . 2 1 = 1 . alignr { stack { size 12{5 - 2=3 "." } {} #size 12{7 - 4=3 "." } {} # size 12{2 - 1=1 "." } {}} } {}

Got questions? Get instant answers now!

46,042 -   1,031 ̲ 45,011

2 1 = 1 . 4 3 = 1 . 0 0 = 0 . 6 1 = 5 . 4 0 = 4 . alignr { stack { size 12{2 - 1=1 "." } {} #size 12{4 - 3=1 "." } {} # size 12{0 - 0=0 "." } {} #size 12{6 - 1=5 "." } {} # size 12{4 - 0=4 "." } {}} } {}

Got questions? Get instant answers now!

Find the difference between 977 and 235.

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

977 - 235 ̲ 742

The difference between 977 and 235 is 742.

Got questions? Get instant answers now!

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.

1,159 - 809 = 350, with a 1 above the thousands and hundreds columns.

There were 350 more cable television installations in Flags County than in Keys County in 1987.

Got questions? Get instant answers now!

Practice set b

Perform the following subtractions.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask