<< Chapter < Page Chapter >> Page >
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.Objectives of this module: be able to add numbers with like signs and unlike signs, understand addition with zero.

Overview

  • Addition of Numbers with Like Signs
  • Addition with Zero
  • Addition of Numbers with Unlike Signs

Addition of numbers with like signs

Let us add the two positive numbers 2 and 3. We perform this addition on the number line as follows.

We begin at 0, the origin.
Since 2 is positive, we move 2 units to the right.
Since 3 is positive, we move 3 more units to the right.
We are now located at 5.
Thus, 2 + 3 = 5 .

A number line with arrows on each end, labeled from negative two to eight in increments of one. There is a curved arrow starting from zero, and pointing towards two. There is another curved arrow starting from two, and pointing towards five.

Summarizing, we have

( 2 positive units ) + ( 3 positive units ) = ( 5 positive units )

Now let us add the two negative numbers 2 and 3 . We perform this addition on the number line as follows.

We begin at 0, the origin.
Since 2 is negative, we move 2 units to the left.
Since 3 is negative, we move 3 more units to the left.
We are now located at 5 .

Thus, ( 2 ) + ( 3 ) = 5 .

A number line with arrows on each end, labeled from negative seven to three in increments of one. There is a curved arrow starting from zero, and pointing towards negative two. There is another curved arrow starting from negative two, and pointing towards negative five

Summarizing, we have

( 2 negative units ) + ( 3 negative units ) = ( 5 negative units )

These two examples suggest that

( positive number ) + ( positive number ) = ( positive number ) ( negative number ) + ( negative number ) = ( negative number )

Adding numbers with the same sign

To add two real numbers that have the same sign, add the absolute values of the numbers and associate the common sign with the sum.

Sample set a

Find the sums.

3 + 7

Add these absolute values . | 3 | = 3 | 7 | = 7 } 3 + 7 = 10 The common sign is "+ ."

3 + 7 = + 10 or 3 + 7 = 10

Got questions? Get instant answers now!

( 4 ) + ( 9 )

Add these absolute values . | 4 | = 4 | 9 | = 9 } 4 + 9 = 13 The common sign is " ."

( 4 ) + ( 9 ) = 13

Got questions? Get instant answers now!

Practice set a

Find the sums.

( 4 ) + ( 8 )

12

Got questions? Get instant answers now!

( 36 ) + ( 9 )

45

Got questions? Get instant answers now!

14 + ( 20 )

34

Got questions? Get instant answers now!

2 3 + ( 5 3 )

7 3

Got questions? Get instant answers now!

2.8 + ( 4.6 )

7.4

Got questions? Get instant answers now!

Addition with zero

Notice that

Addition with 0

( 0 ) + ( a positive number ) = ( that same positive number ) ( 0 ) + ( a negative number ) = ( that same negative number)

The additive identity is 0

Since adding 0 to a real number leaves that number unchanged, 0 is called the additive identity .

Addition of numbers with unlike signs

Now let us perform the addition 2 + ( 6 ) . These two numbers have unlike signs. This type of addition can also be illustrated using the number line.

We begin at 0, the origin.
Since 2 is positive, we move 2 units to the right.
Since 6 is negative, we move, from the 2, 6 units to the left.
We are now located at 4 .

A number line with arrows on each end, labeled from negative five to five in increments of one. There is a curved arrow starting from zero, and pointing towards two. There is another curved arrow starting from two, and pointing towards negative four.

A rule for adding two numbers that have unlike signs is suggested by noting that if the signs are disregarded, 4 can be obtained from 2 and 6 by subtracting 2 from 6. But 2 and 6 are precisely the absolute values of 2 and 6 . Also, notice that the sign of the number with the larger absolute value is negative and that the sign of the resulting sum is negative.

Adding numbers with unlike signs

To add two real numbers that have unlike signs, subtract the smaller absolute value from the larger absolute value and associate the sign of the number with the larger absolute value with this difference.

Sample set b

Find the following sums.

7 + ( 2 )

| 7 | = 7 Larger absolute value . Sign is " + " . | 2 | = 2 Smaller absolute value .

Subtract absolute values: 7 2 = 5. Attach the proper sign: " + " .

7 + ( 2 ) = + 5 or 7 + ( 2 ) = 5

Got questions? Get instant answers now!

3 + ( 11 )

| 3 | = 3 Smaller absolute value . | 11 | = 11 Larger absolute value . Sign is " " .

Subtract absolute values: 11 3 = 8. Attach the proper sign: " " .

3 + ( 11 ) = 8

Got questions? Get instant answers now!

The morning temperature on a winter's day in Lake Tahoe was 12 degrees. The afternoon temperature was 25 degrees warmer. What was the afternoon temperature?

We need to find 12 + 25 .

| 12 | = 12 Smaller absolute value . | 25 | = 25 Larger absolute value . Sign is "+" .

Subtract absolute values: 25 12 = 13. Attach the proper sign: " + " .

12 + 25 = 13

Thus, the afternoon temperature is 13 degrees.

Got questions? Get instant answers now!

Use a calculator. Add 147 + 84 .                                                      Display Reads

Type 147 147 Press + / 147 Press + 147 Type 84 84 Press = 63

Got questions? Get instant answers now!

Practice set b

Find the sums.

1345.6 + ( 6648.1 )

7993.7

Got questions? Get instant answers now!

Exercises

Find the sums for the the following problems.

( 3 ) + ( 12 )

15

Got questions? Get instant answers now!

( 4 ) + ( 8 )

12

Got questions? Get instant answers now!

( 16 ) + ( 8 )

24

Got questions? Get instant answers now!

( 3 ) + ( 12 )

15

Got questions? Get instant answers now!

9 + ( 6 )

15

Got questions? Get instant answers now!

16 + ( 9 )

25

Got questions? Get instant answers now!

5 + ( 12 ) + ( 4 )

21

Got questions? Get instant answers now!

1221 + ( 44 )

1265

Got questions? Get instant answers now!

47.03 + ( 22.71 )

Got questions? Get instant answers now!

1.998 + ( 4.086 )

6.084

Got questions? Get instant answers now!

[ ( 3 ) + ( 4 ) ] + [ ( 6 ) + ( 1 ) ]

Got questions? Get instant answers now!

[ ( 2 ) + ( 8 ) ] + [ ( 3 ) + ( 7 ) ]

20

Got questions? Get instant answers now!

[ ( 3 ) + ( 8 ) ] + [ ( 6 ) + ( 12 ) ]

Got questions? Get instant answers now!

[ ( 8 ) + ( 6 ) ] + [ ( 2 ) + ( 1 ) ]

17

Got questions? Get instant answers now!

[ 4 + ( 12 ) ] + [ 12 + ( 3 ) ]

Got questions? Get instant answers now!

[ 5 + ( 16 ) ] + [ 4 + ( 11 ) ]

18

Got questions? Get instant answers now!

[ 2 + ( 4 ) ] + [ 17 + ( 19 ) ]

Got questions? Get instant answers now!

[ 10 + ( 6 ) ] + [ 12 + ( 2 ) ]

14

Got questions? Get instant answers now!

14 + [ ( 3 ) + 5 ]

16

Got questions? Get instant answers now!

[ 2 + ( 7 ) ] + ( 11 )

Got questions? Get instant answers now!

[ 14 + ( 8 ) ] + ( 2 )

4

Got questions? Get instant answers now!

In order for a small business to break even on a project, it must have sales of $ 21 , 000 . If the amount of sales was $ 15 , 000 , how much money did this company fall short?

Got questions? Get instant answers now!

Suppose a person has $ 56.00 in his checking account. He deposits $ 100.00 into his checking account by using the automatic teller machine. He then writes a check for $ 84.50 . If an error causes the deposit not to be listed into this person's account, what is this person's checking balance?

$ 28.50

Got questions? Get instant answers now!

A person borrows $ 7.00 on Monday and then $ 12.00 on Tuesday. How much has this person borrowed?

Got questions? Get instant answers now!

A person borrows $ 11.00 on Monday and then pays back $ 8.00 on Tuesday. How much does this person owe?

$ 3.00

Got questions? Get instant answers now!

Exercises for review

( [link] ) Simplify 4 ( 7 2 6 2 3 ) 2 2 .

Got questions? Get instant answers now!

( [link] ) Simplify 35 a 6 b 2 c 5 7 b 2 c 4 .

5 a 6 c

Got questions? Get instant answers now!

( [link] ) Simplify ( 12 a 8 b 5 4 a 5 b 2 ) 3 .

Got questions? Get instant answers now!

( [link] ) Determine the value of | 8 | .

8

Got questions? Get instant answers now!

( [link] ) Determine the value of ( | 2 | + | 4 | 2 ) + | 5 | 2 .

Got questions? Get instant answers now!

Questions & Answers

it is the relatively stable flow of income
Chidubem Reply
what is circular flow of income
Divine Reply
branches of macroeconomics
SHEDRACK Reply
what is Flexible exchang rate?
poudel Reply
is gdp a reliable measurement of wealth
Atega Reply
introduction to econometrics
Husseini Reply
Hi
mostafa
hi
LEMLEM
hello
Sammol
hi
Mahesh
bi
Ruqayat
hi
Ruqayat
Hi fellas
Nyawa
hey
Sammol
hi
God
hello
Jahara
Good morning
Jorge
hi
abubakar
hi
Nmesoma
hi
Mahesh
Hi
Tom
Why is unemployment rate never zero at full employment?
Priyanka Reply
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
Rushawn Reply
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost 6% more than previous year? Provide with reasoning.
Geetha Reply
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
Alii Reply
what is the problem of macroeconomics
Yoal
Economic growth Stable prices and low unemployment
Ephraim
explain inflationcause and itis degre
Miresa Reply
what is inflation
Getu
increase in general price levels
WEETO
Good day How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200. Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
Chisomo Reply
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
Thapase Reply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
Mercy Reply
Hi
Isiaka
Hi
Geli
hy
Man
👋
Bahunda
hy how are you?
Man
ys
Amisha
how are you guys
Sekou
f9 guys
Amisha
how are you guys
Sekou
ys am also fine
Amisha
fine and you guys
Geli
from Nepal
Amisha
nawalparasi district from belatari
Amisha
nd u
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9 no Mpc is greater than 1 Y=100+.9Y+50 Y-.9Y=150 0.1Y/0.1=150/0.1 Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output? discuss your answer using appropriate graph.
Galge Reply
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask