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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

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are you nano engineer ?
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
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in general
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Graphene has a hexagonal structure
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what's the easiest and fastest way to the synthesize AgNP?
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Cied
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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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
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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
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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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