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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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
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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