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Mathematics LibreTexts

1.2: Add Whole Numbers (Part 2)

  • Page ID
    5767
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    Translate Word Phrases to Math Notation

    Earlier in this section, we translated math notation into words. Now we’ll reverse the process. We’ll translate word phrases into math notation. Some of the word phrases that indicate addition are listed in Table \(\PageIndex{2}\).

    Table \(\PageIndex{1}\)
    Operation Words Example Expression
    Addition plus 1 plus 2 1 + 2
    sum the sum of 3 and 4 3 + 4
    increased by 5 increased by 6 5 + 6
    more than 8 more than 7 7 + 8
    total of the total of 9 and 5 9 + 5
    added to 6 added to 4 4 + 6

    Example \(\PageIndex{12}\): translate and simplify

    Translate and simplify: the sum of 19 and 23.

    Solution

    The word sum tells us to add. The words of \(19\) and \(23\) tell us the addends.

    The sum of 19 and 23
    Translate. 19 + 23
    Add. 42
    The sum of 19 and 23 is 42.

    Exercise \(\PageIndex{23}\)

    Translate and simplify: the sum of \(17\) and \(26\).

    Answer

    Translate:

    Exercise \(\PageIndex{24}\)

    Translate and simplify: the sum of \(28\) and \(14\).

    Answer

    Translate: \(28+14\); Simplify: \(42\)

    Example \(\PageIndex{13}\): translate and simplify

    Translate and simplify: \(28\) increased by \(31\).

    Solution

    The words increased by tell us to add. The numbers given are the addends.

    28 increased by 31.
    Translate. 28 + 31
    Add. 59
    So 28 increased by 31 is 59.

    Exercise \(\PageIndex{25}\)

    Translate and simplify: \(29\) increased by \(76\).

    Answer

    Translate: \(29+76\); Simplify: \(105\)

    Exercise \(\PageIndex{26}\)

    Translate and simplify: \(37\) increased by \(69\).

    Answer

    Translate: \(37+69\); Simplify: \(106\)

    Add Whole Numbers in Applications

    Now that we have practiced adding whole numbers, let’s use what we’ve learned to solve real-world problems. We’ll start by outlining a plan. First, we need to read the problem to determine what we are looking for. Then we write a word phrase that gives the information to find it. Next we translate the word phrase into math notation and then simplify. Finally, we write a sentence to answer the question.

    Example \(\PageIndex{14}\): add whole numbers

    Hao earned grades of \(87, 93, 68, 95,\) and \(89\) on the five tests of the semester. What is the total number of points he earned on the five tests?

    Solution

    We are asked to find the total number of points on the tests.

    Write a phrase. the sum of points on the tests
    Translate to math notation. 87 + 93 + 68 + 95 + 89
    Then we simplify by adding
    Since there are several numbers, we will write them vertically.
    Write a sentence to answer the question. Hao earned a total of 432 points.

    Notice that we added points, so the sum is \(432\) points. It is important to include the appropriate units in all answers to applications problems.

    Exercise \(\PageIndex{27}\)

    Mark is training for a bicycle race. Last week he rode \(18\) miles on Monday, \(15\) miles on Wednesday, \(26\) miles on Friday, \(49\) miles on Saturday, and \(32\) miles on Sunday. What is the total number of miles he rode last week?

    Answer

    He rode \(140\) miles.

    Exercise \(\PageIndex{28}\)

    Lincoln Middle School has three grades. The number of students in each grade is \(230, 165,\) and \(325\). What is the total number of students?

    Answer

    The total number is \(720\) students.

    Some application problems involve shapes. For example, a person might need to know the distance around a garden to put up a fence or around a picture to frame it. The perimeter is the distance around a geometric figure. The perimeter of a figure is the sum of the lengths of its sides.

    Example \(\PageIndex{15}\): perimeter

    Find the perimeter of the patio shown.

    This is an image of a perimeter of a patio. There are six sides. The far left side is labeled 4 feet, the top side is labeled 9 feet, the right side is short and labeled 2 feet, then extends across to the left and is labeled 3 feet. From here, the side extends down and is labeled 2 feet. Finally, the base is labeled 6 feet.

    Figure \(\PageIndex{3}\)

    Solution

    We are asked to find the perimeter.
    Write a phrase. the sum of the sides
    Translate to math notation. 4 + 6 + 2 + 3 + 2 + 9
    Simplify by adding. 26
    Write a sentence to answer the question.
    We added feet, so the sum is 26 feet. The perimeter of the patio is 26 feet.

    Exercise \(\PageIndex{29}\)

    Find the perimeter of each figure. All lengths are in inches.

    This image includes 8 sides. Side one on the left is labeled 4 inches, side 2 on the top is labeled 9 inches, side 3 on the right is labeled 4 inches, side 4 is labeled 3 inches, side 5 is labeled 2 inches, side 6 is labeled 3 inches, side 7 is labeled 2 inches, and side 8 is labeled 3 inches.

    Figure \(\PageIndex{4}\)

    Answer

    The perimeter is \(30\) inches.

    Exercise \(\PageIndex{30}\)

    Find the perimeter of each figure. All lengths are in inches.

    This image includes 8 sides. Moving in a clockwise direction, the first side is labeled 2 inches, side 2 is labeled 12 inches, side 3 is labeled 6 inches, side 4 is labeled 4 inches, side 5 is labeled 2 inches, side 6 is labeled 4 inches, side 7 is labeled 2 inches and side 8 is labeled 4 inches.

    Figure \(\PageIndex{5}\)

    Answer

    The perimeter is \(36\) inches.

    Key Concepts

    • Addition Notation To describe addition, we can use symbols and words.
      Operation Notation Expression Read as Result
      Addition three plus four the sum of
    • Identity Property of Addition
      • The sum of any number \(
    • Commutative Property of Addition
      • Changing the order of the addends \(
    • Add whole numbers.
      • Write the numbers so each place value lines up vertically.
      • 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.
      • Continue adding each place value from right to left, adding each place value and carrying if needed.

    Glossary

    sum

    The sum is the result of adding two or more numbers.

    Practice Makes Perfect

    Use Addition Notation

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

    1. 5 + 2
    2. 6 + 3
    3. 13 + 18
    4. 15 + 16
    5. 214 + 642
    6. 438 + 113

    Model Addition of Whole Numbers

    In the following exercises, model the addition

    1. 2 + 4
    2. 5 + 3
    3. 8 + 4
    4. 5 + 9
    5. 14 + 75
    6. 15 + 63
    7. 16 + 25
    8. 14 + 27

    Add Whole Numbers

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

    1. An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The first column has the values “+; 0; 1; 2; 3; 4; 5; 6; 7; 8; 9”. The second column has the values “0; 0; 1; null; 3; 4; 5; 6; null; 8; 9”. The third column has the values “1; 1; 2; 3; null; 5; 6; 7; null; 9; 10”. The fourth column has the values “2; 2; 3; 4; 5; null; 7; 8; 9; null; 11”. The fifth column has the values “3; null; 4; 5; null; null; 8; null; 10; 11; null”. The sixth column has the values “4; 4; null; 6;7; 8; null; 10; null; null; 13”. The seventh column has the values “5; 5; null; null; 8; 9; null; null; 12; null; 14”. The eighth column has the values “6; 6; 7; 8; null; null; 11; null; null; 14; null”. The ninth column has the values “7; 7; 8; null; 10; 11; null; 13; null; null; null”. The tenth column has the values “8; null; 9; null; null; 12; 13; null; 15; 16; 17”. The eleventh column has the values “9; 9; null; 11; 12; null; null; 15; 16; null; null”.
    2. An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The first column has the values “+; 0; 1; 2; 3; 4; 5; 6; 7; 8; 9”. The second column has the values “0; 0; 1; 2; null; 4; 5; null; 7; 8; null”. The third column has the values “1; 1; 2; null; 4; 5; 6; null; 8; 9; null”. The fourth column has the values “2; 2; 3; 4; null; 6; null; 8; null; 10; 11”. The fifth column has the values “3; 3; null; null; 6; 7; 8; 9; 10; null; 12”. The sixth column has the values “4; 4; 5; 6; null; null; 9; null; null; 12; 13”. The seventh column has the values “5; null; 6; 7; null; null; null; null; 12; null; null”. The eighth column has the values “6; 6; null; null; 9; 10; 11; 12; null; 14; null”. The ninth column has the values “7; null; 8; 9; null; 11; 12; 13; null; null; 16”. The tenth column has the values “8; 8; null; 10; 11; null; 13; null; 15; 16; null”. The eleventh column has the values “9; 9; 10; null; null; 13; null; 15; 16; 17; null”.
    3. An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values “+; 6; 7; 8; 9”. The first row has the values “+; 3; 4; 5; 6; 7; 8; 9”.
    4. An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first row has the values “+; 6; 7; 8; 9”. The first column has the values “+; 3; 4; 5; 6; 7; 8; 9”.
    5. An image of a table with 6 columns and 6 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first row has the values “+; 5; 6; 7; 8; 9”. The first column has the values “+; 5; 6; 7; 8; 9”.
    6. An image of a table with 5 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or first column are all null. The first row has the values “+; 6; 7; 8; 9”. The first column has the values “+; 6; 7; 8; 9”.

    In the following exercises, add.

    1. (a) 0 + 13 (b) 13 + 0
    2. (a) 0 + 5,280 (b) 5,280 + 0
    3. (a) 8 + 3 (b) 3 + 8
    4. (a) 7 + 5 (b) 5 + 7
    5. 45 + 33
    6. 37 + 22
    7. 71 + 28
    8. 43 + 53
    9. 26 + 59
    10. 38 + 17
    11. 64 + 78
    12. 82 + 39
    13. 168 + 325
    14. 247 + 149
    15. 584 + 277
    16. 175 + 648
    17. 832 + 199
    18. 775 + 369
    19. 6,358 + 492
    20. 9,184 + 578
    21. 3,740 + 18,593
    22. 6,118 + 15,990
    23. 485,012 + 649,848
    24. 368,911 + 587,289
    25. 24,731 + 592 + 3,868
    26. 28,925 + 817 + 4,593
    27. 8,015 + 76,946 + 16,570
    28. 6,291 + 54,107 + 28,635

    Translate Word Phrases to Math Notation

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

    1. the sum of 13 and 18
    2. the sum of 12 and 19
    3. the sum of 90 and 65
    4. the sum of 70 and 38
    5. 33 increased by 49
    6. 68 increased by 25
    7. 250 more than 599
    8. 115 more than 286
    9. the total of 628 and 77
    10. the total of 593 and 79
    11. 1,482 added to 915
    12. 2,719 added to 682

    Add Whole Numbers in Applications

    In the following exercises, solve the problem.

    1. 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?
    2. 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?
    3. 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?
    4. 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?
    5. 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?
    6. 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?
    7. 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?
    8. 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?

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

    1. An image of a triangle with side lengths of 14 inches, 12 inches, and 18 inches.
    2. An image of a right triangle with base of 12 centimeters, height of 5 centimeters, and diagonal hypotenuse of 13 centimeters.
    3. A rectangle 21 meters wide and 7 meters tall.
    4. A rectangle 19 feet wide and and 14 feet tall.
    5. 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.
    6. A trapezoid with horizontal top length of 24 meters, the side lengths are 17 meters and are diagonal, and the horizontal bottom length is 29 meters.
    7. 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.
    8. This is an image with 6 straight sides. Starting from the top left of the figure, the first line runs right for 25 inches. From the end of this line, the second line runs down for 10 inches. Then the third line runs left from this point for 14 inches. The fourth line runs up 7 inches. The fifth line runs left for 11 inches. The sixth line runs up, connecting it at a corner with start of the first line.

    Everyday Math

    1. 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?
    2. 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?
    3. 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?
    4. 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?

    Writing Exercises

    1. 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?
    2. How have you used models to help you learn the addition facts?

    Self Check

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

    .

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

    Contributors

    • Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (formerly of Santa Ana College). This content produced by OpenStax and is licensed under a Creative Commons Attribution License 4.0 license.