237

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

Use subtraction notation
Model subtraction of whole numbers
Subtract whole numbers
Translate word phrases to math notation
Subtract whole numbers in applications
Be Prepared 1.3
Before you get started, take this readiness quiz.

Model 3+4
using base-ten blocks.
If you missed this problem, review Example 1.12.

Be Prepared 1.4
Add: 324+586.

If you missed this problem, review Example 1.20.

Use Subtraction Notation
Suppose there are seven bananas in a bowl. Elana uses three of them to make a smoothie. How many bananas are left in the bowl? To answer the question, we subtract three from seven. When we subtract, we take one number away from another to find the difference. The notation we use to subtract 3
from 7
is

7−3

We read 7−3
as seven minus three and the result is the difference of seven and three.

Subtraction Notation
To describe subtraction, we can use symbols and words.

Operation Notation Expression Read as Result
Subtraction −
7−3
seven minus three the difference of 7
and 3

Example 1.26
Translate from math notation to words: ⓐ 8−1
ⓑ 26−14
.

Try It 1.51
Translate from math notation to words:

ⓐ 12−4

ⓑ 29−11

Try It 1.52
Translate from math notation to words:

ⓐ 11−2

ⓑ 29−12

Model Subtraction of Whole Numbers
A model can help us visualize the process of subtraction much as it did with addition. Again, we will use base-10
blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, 7−3.

We start by modeling the first number, 7. CNX_BMath_Figure_01_03_018_img-02.png
Now take away the second number, 3. We’ll circle 3 blocks to show that we are taking them away. CNX_BMath_Figure_01_03_018_img-03.png
Count the number of blocks remaining. CNX_BMath_Figure_01_03_018_img-04.png
There are 4 ones blocks left. We have shown that 7−3=4
.
Example 1.27
Model the subtraction: 8−2.

Try It 1.53
Model: 9−6.

Try It 1.54
Model: 6−1.

Example 1.28
Model the subtraction: 13−8.

Try It 1.55
Model the subtraction: 12−7.

Try It 1.56
Model the subtraction: 14−8.

Example 1.29
Model the subtraction: 43−26.

Try It 1.57
Model the subtraction: 42−27.

Try It 1.58
Model the subtraction: 45−29.

Subtract Whole Numbers
Addition and subtraction are inverse operations. Addition undoes subtraction, and subtraction undoes addition.

We know 7−3=4
because 4+3=7.
Knowing all the addition number facts will help with subtraction. Then we can check subtraction by adding. In the examples above, our subtractions can be checked by addition.

7−3=413−8=543−26=17becausebecausebecause4+3=75+8=1317+26=43

Example 1.30
Subtract and then check by adding:

ⓐ 9−7

ⓑ 8−3.

Try It 1.59
Subtract and then check by adding:

7−0

Try It 1.60
Subtract and then check by adding:

6−2

To subtract numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition. Align the digits by place value, and then subtract each column starting with the ones and then working to the left.

Example 1.31
Subtract and then check by adding: 89−61.

Try It 1.61
Subtract and then check by adding: 86−54.

Try It 1.62
Subtract and then check by adding: 99−74.

When we modeled subtracting 26
from 43,
we exchanged 1
ten for 10
ones. When we do this without the model, we say we borrow 1
from the tens place and add 10
to the ones place.

How To
Find the difference of whole numbers.
Step 1. Write the numbers so each place value lines up vertically.
Step 2. Subtract the digits in each place value. Work from right to left starting with the ones place. If the digit on top is less than the digit below, borrow as needed.
Step 3. Continue subtracting each place value from right to left, borrowing if needed.
Step 4. Check by adding.
Example 1.32
Subtract: 43−26.

Try It 1.63
Subtract and then check by adding: 93−58.

Try It 1.64
Subtract and then check by adding: 81−39.

Example 1.33
Subtract and then check by adding: 207−64.

Try It 1.65
Subtract and then check by adding: 439−52.

Try It 1.66
Subtract and then check by adding: 318−75.

Example 1.34
Subtract and then check by adding: 910−586.

Try It 1.67
Subtract and then check by adding: 832−376.

Try It 1.68
Subtract and then check by adding: 847−578.

Example 1.35
Subtract and then check by adding: 2,162−479.

Try It 1.69
Subtract and then check by adding: 4,585−697.

Try It 1.70
Subtract and then check by adding: 5,637−899.

Translate Word Phrases to Math Notation
As with addition, word phrases can tell us to operate on two numbers using subtraction. To translate from a word phrase to math notation, we look for key words that indicate subtraction. Some of the words that indicate subtraction are listed in Table 1.3.

Operation Word Phrase Example Expression
Subtraction minus 5
minus 1
5−1

difference the difference of 9
and 4
9−4

decreased by 7
decreased by 3
7−3

less than 5
less than 8
8−5

subtracted from 1
subtracted from 6
6−1

Table 1.3
Example 1.36
Translate and then simplify:

ⓐ the difference of 13
and 8

ⓑ subtract 24
from 43

Try It 1.71
Translate and simplify:

ⓐ the difference of 14
and 9

ⓑ subtract 21
from 37

Try It 1.72
Translate and simplify:

ⓐ 11
decreased by 6

ⓑ 18
less than 67

Subtract Whole Numbers in Applications
To solve applications with subtraction, we will use the same plan that we used with addition. First, we need to determine what we are asked to find. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question, using the appropriate units.

Example 1.37
The temperature in Chicago one morning was 73
degrees Fahrenheit. A cold front arrived and by noon the temperature was 27
degrees Fahrenheit. What was the difference between the temperature in the morning and the temperature at noon?

Try It 1.73
The high temperature on June1st
in Boston was 77
degrees Fahrenheit, and the low temperature was 58
degrees Fahrenheit. What was the difference between the high and low temperatures?

Try It 1.74
The weather forecast for June 2
in St Louis predicts a high temperature of 90
degrees Fahrenheit and a low of 73
degrees Fahrenheit. What is the difference between the predicted high and low temperatures?

Example 1.38
A washing machine is on sale for $399.
Its regular price is $588.
What is the difference between the regular price and the sale price?

Try It 1.75
A television set is on sale for $499.
Its regular price is $648.
What is the difference between the regular price and the sale price?

Try It 1.76
A patio set is on sale for $149.
Its regular price is $285.
What is the difference between the regular price and the sale price?

Media
ACCESS ADDITIONAL ONLINE RESOURCES
Model subtraction of two-digit whole numbers
Model subtraction of three-digit whole numbers
Subtract Whole Numbers
Section 1.3 Exercises
Practice Makes Perfect
Use Subtraction Notation

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

141. 15−9

142. 18−16

143. 42−35

144. 83−64

145. 675−350

146. 790−525

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

147. 5−2

148. 8−4

149. 6−3

150. 7−5

151. 18−5

152. 19−8

153. 17−8

154. 17−9

155. 35−13

156. 32−11

157. 61−47

158. 55−36

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.

159. 9−4

160. 9−3

161. 8−0

162. 2−0

163. 38−16

164. 45−21

165. 85−52

166. 99−47

167. 493−370

168. 268−106

169. 5,946−4,625

170. 7,775−3,251

171. 75−47

172. 63−59

173. 461−239

174. 486−257

175. 525−179

176. 542−288

177. 6,318−2,799

178. 8,153−3,978

179. 2,150−964

180. 4,245−899

181. 43,650−8,982

182. 35,162−7,885

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

183. The difference of 10
and 3

184. The difference of 12
and 8

185. The difference of 15
and 4

186. The difference of 18
and 7

187. Subtract 6
from 9

188. Subtract 8
from 9

189. Subtract 28
from 75

190. Subtract 59
from 81

191. 45
decreased by 20

192. 37
decreased by 24

193. 92
decreased by 67

194. 75
decreased by 49

195. 12
less than 16

196. 15
less than 19

197. 38
less than 61

198. 47
less than 62

Mixed Practice

In the following exercises, simplify.

199. 76−47

200. 91−53

201. 256−184

202. 305−262

203. 719+341

204. 647+528

205. 2,015−1,993

206. 2,020−1,984

In the following exercises, translate and simplify.

207. Seventy-five more than thirty-five
208. Sixty more than ninety-three
209. 13
less than 41

210. 28
less than 36

211. The difference of 100
and 76

212. The difference of 1,000
and 945

Subtract Whole Numbers in Applications

In the following exercises, solve.

213. Temperature The high temperature on June 2
in Las Vegas was 80
degrees and the low temperature was 63
degrees. What was the difference between the high and low temperatures?
214. Temperature The high temperature on June 1
in Phoenix was 97
degrees and the low was 73
degrees. What was the difference between the high and low temperatures?
215. Class size Olivia’s third grade class has 35
children. Last year, her second grade class had 22
children. What is the difference between the number of children in Olivia’s third grade class and her second grade class?
216. Class size There are 82
students in the school band and 46
in the school orchestra. What is the difference between the number of students in the band and the orchestra?
217. Shopping A mountain bike is on sale for $399.
Its regular price is $650.
What is the difference between the regular price and the sale price?
218. Shopping A mattress set is on sale for $755.
Its regular price is $1,600.
What is the difference between the regular price and the sale price?
219. Savings John wants to buy a laptop that costs $840.
He has $685
in his savings account. How much more does he need to save in order to buy the laptop?
220. Banking Mason had $1,125
in his checking account. He spent $892.
How much money does he have left?
Everyday Math
221. Road trip Noah was driving from Philadelphia to Cincinnati, a distance of 502
miles. He drove 115
miles, stopped for gas, and then drove another 230
miles before lunch. How many more miles did he have to travel?
222. Test Scores Sara needs 350
points to pass her course. She scored 75,50,70,and80
on her first four tests. How many more points does Sara need to pass the course?
Writing Exercises
223. Explain how subtraction and addition are related.
224. How does knowing addition facts help you to subtract numbers?
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?