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Key concepts

  • Addition Notation To describe addition, we can use symbols and words.
    Operation Notation Expression Read as Result
    Addition + 3 + 4 three plus four the sum of 3 and 4
  • Identity Property of Addition
    • The sum of any number a and 0 is the number. a + 0 = a 0 + a = a
  • Commutative Property of Addition
    • Changing the order of the addends a and b does not change their sum. a + b = b + a .
  • Add whole numbers.
    1. Write the numbers so each place value lines up vertically.
    2. Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than 9, carry to the next place value.
    3. Continue adding each place value from right to left, adding each place value and carrying if needed.

Practice makes perfect

Use Addition Notation

In the following exercises, translate the following from math expressions to words.

5 + 2

five plus two; the sum of 5 and 2.

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13 + 18

thirteen plus eighteen; the sum of 13 and 18.

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214 + 642

two hundred fourteen plus six hundred forty-two; the sum of 214 and 642

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Model Addition of Whole Numbers

In the following exercises, model the addition.

Add Whole Numbers

In the following exercises, fill in the missing values in each chart.

In the following exercises, add.

  1. 0 + 13
  2. 13 + 0
  1. 13
  2. 13
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  1. 0 + 5,280
  2. 5,280 + 0
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  1. 8 + 3
  2. 3 + 8
  1. 11
  2. 11
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485,012 + 619,848

1,104,860

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24,731 + 592 + 3,868

29,191

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8,015 + 76,946 + 16,570

101,531

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Translate Word Phrases to Math Notation

In the following exercises, translate each phrase into math notation and then simplify.

the sum of 13 and 18

13 + 18 = 31

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the sum of 90 and 65

90 + 65 = 155

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33 increased by 49

33 + 49 = 82

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250 more than 599

250 + 599 = 849

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the total of 628 and 77

628 + 77 = 705

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1,482 added to 915

915 + 1,482 = 2,397

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Add Whole Numbers in Applications

In the following exercises, solve the problem.

Home remodeling Sophia remodeled her kitchen and bought a new range, microwave, and dishwasher. The range cost $1,100 , the microwave cost $250 , and the dishwasher cost $525 . What was the total cost of these three appliances?

The total cost was $1,875.

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Sports equipment Aiden bought a baseball bat, helmet, and glove. The bat cost $299 , the helmet cost $35 , and the glove cost $68 . What was the total cost of Aiden’s sports equipment?

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Bike riding Ethan rode his bike 14 miles on Monday, 19 miles on Tuesday, 12 miles on Wednesday, 25 miles on Friday, and 68 miles on Saturday. What was the total number of miles Ethan rode?

Ethan rode 138 miles.

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Business Chloe has a flower shop. Last week she made 19 floral arrangements on Monday, 12 on Tuesday, 23 on Wednesday, 29 on Thursday, and 44 on Friday. What was the total number of floral arrangements Chloe made?

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Apartment size Jackson lives in a 7 room apartment. The number of square feet in each room is 238 , 120 , 156 , 196 , 100 , 132 , and 225 . What is the total number of square feet in all 7 rooms?

The total square footage in the rooms is 1,167 square feet.

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Weight Seven men rented a fishing boat. The weights of the men were 175 , 192 , 148 , 169 , 205 , 181 , and 225 pounds. What was the total weight of the seven men?

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Salary Last year Natalie’s salary was $82,572 . Two years ago, her salary was $79,316 , and three years ago it was $75,298 . What is the total amount of Natalie’s salary for the past three years?

Natalie’s total salary is $237,186.

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Home sales Emma is a realtor. Last month, she sold three houses. The selling prices of the houses were $292,540 , $505,875 , and $423,699 . What was the total of the three selling prices?

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In the following exercises, find the perimeter of each figure.

An image of a triangle with side lengths of 14 inches, 12 inches, and 18 inches.

The perimeter of the figure is 44 inches.

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A rectangle 21 meters wide and 7 meters tall.

The perimeter of the figure is 56 meters.

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A trapezoid with horizontal top length of 19 yards, the side lengths are 18 yards and are diagonal, and the horizontal bottom length is 16 yards.

The perimeter of the figure is 71 yards.

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This is a rectangle-like image with six sides. Starting from the top left of the figure, the first line runs right for 24 feet. From the end of this line, the second line runs down for 7 feet. Then the third line runs left from this point for 19 feet. The fourth line runs up 3 feet. The fifth line runs left for 5 feet. The sixth line runs up for 4 feet, connecting it at a corner with start of the first line.

The perimeter of the figure is 62 feet.

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Everyday math

Calories Paulette had a grilled chicken salad, ranch dressing, and a 16-ounce drink for lunch. On the restaurant’s nutrition chart, she saw that each item had the following number of calories:

Grilled chicken salad – 320 calories
Ranch dressing – 170 calories
16-ounce drink – 150 calories

What was the total number of calories of Paulette’s lunch?

The total number of calories was 640.

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Calories Fred had a grilled chicken sandwich, a small order of fries, and a 12-oz chocolate shake for dinner. The restaurant’s nutrition chart lists the following calories for each item:

Grilled chicken sandwich – 420 calories
Small fries – 230 calories
12-oz chocolate shake – 580 calories

What was the total number of calories of Fred’s dinner?

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Test scores A students needs a total of 400 points on five tests to pass a course. The student scored 82 , 91 , 75 , 88 , and 70 . Did the student pass the course?

Yes, he scored 406 points.

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Elevators The maximum weight capacity of an elevator is 1150 pounds. Six men are in the elevator. Their weights are 210 , 145 , 183 , 230 , 159 , and 164 pounds. Is the total weight below the elevators’ maximum capacity?

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Writing exercises

How confident do you feel about your knowledge of the addition facts? If you are not fully confident, what will you do to improve your skills?

Answers will vary.

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How have you used models to help you learn the addition facts?

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

After reviewing this checklist, what will you do to become confident for all objectives?

Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
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Sherica
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Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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