1.2 Add Whole Numbers

PreAlgebra 2e 1 Whole Numbers 1.2 Add Whole Numbers

Learning Objectives

By the end of this section, you will be able to:

Use addition notation
Model addition of whole numbers
Add whole numbers without models
Translate word phrases to math notation
Add whole numbers in applications

Use Addition Notation

A college student has a part-time job. Last week he worked 3 hours on Monday and 4 hours on Friday. To find the total number of hours he worked last week, he added 3 and 4.

The operation of addition combines numbers to get a sum. The notation we use to find the sum of 3 and 4 is:

3+4

We read this as three plus four and the result is the sum of three and four. The numbers 3 and 4 are called the addends. A math statement that includes numbers and operations is called an expression.

Model Addition of Whole Numbers

Addition is really just counting. We will model addition with base-10 blocks. Remember, a block represents 1 and a rod represents 10. Let’s start by modeling the addition expression we just considered,

3+4.

Each addend is less than 10, so we can use ones blocks.

Add Whole Numbers Without Models

Now that we have used models to add numbers, we can move on to adding without models. Before we do that, make sure you know all the one digit addition facts. You will need to use these number facts when you add larger numbers.

Imagine filling in Table 1.1 by adding each row number along the left side to each column number across the top. Make sure that you get each sum shown. If you have trouble, model it. It is important that you memorize any number facts you do not already know so that you can quickly and reliably use the number facts when you add larger numbers.

+	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

Table1.1

Did you notice what happens when you add zero to a number? The sum of any number and zero is the number itself. We call this the Identity Property of Addition. Zero is called the additive identity.

An image containing two groups of items. The left group includes 1 horizontal rod with 10 blocks and 7 individual blocks 2 horizontal rods with 10 blocks each and 6 individual blocks. The label to the left of this group of items is “17 + 26 =”. The right group contains two items. Four horizontal rods containing 10 blocks each. Then, 3 individual blocks. The label for this group is “17 + 26 = 43”.

Figure 1.10

When we add the ones, 7+6, we get 13 ones. Because we have more than 10 ones, we can exchange 10 of the ones for 11 ten. Now we have 4 tens and 3 ones. Without using the model, we show this as a small red 11 above the digits in the tens place.

When the sum in a place value column is greater than 9, we carry over to the next column to the left. Carrying is the same as regrouping by exchanging. For example, 10 ones for 1 ten or 10 tens for 1 hundred.

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.

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

Model Addition of Whole Numbers

In the following exercises, model the addition.65.

2+42+466.

5+35+367.

8+48+468.

5+95+969.

14+7514+7570.

15+6315+6371.

16+2516+2572.

14+2714+27

Add Whole Numbers

In the following exercises, fill in the missing values in each chart.73.

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”.

74.

75.

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”.

76.

77.

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”.

78.

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.79.

ⓐ 0+130+13
ⓑ 13+013+0

80.

ⓐ 0+5,2800+5,280
ⓑ 5,280+05,280+0

81.

ⓐ 8+38+3
ⓑ 3+83+8

82.

ⓐ 7+57+5
ⓑ 5+75+7

45+33
37+22
71+28
43+53
26+59
38+17
64+78
92+39
168+325
247+149
584+277
175+648
832+199
775+369
6,358+492
9,184+578
3,740+18,593
6,118+15,990
485,012+619,848
368,911+857,289
24,731+592+3,868
28,925+817+4,593
8,015+76,946+16,570
6,291+54,107+28,635

Translate Word Phrases to Math Notation

the sum of 13 and 18
the sum of 12 and 19
the sum of 90 and 65
the sum of 70 and 38
33 increased by 49
68 increased by 25
250 more than 599
115 more than 286
the total of 628 and 77
the total of 593 and 79
1,482 added to 915
2,719 added to 682

Add Whole Numbers in Applications

In the following exercises, solve the problem.119.

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?
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?
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?
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?
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?
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?
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?
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.

127.