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1.6: Subtract Whole Numbers (Part 2)

Last updated

May 2, 2022
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- 1.5: Subtract Whole Numbers (Part 1)
- 1.7: Multiply Whole Numbers (Part 1)

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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 $\PageIndex{1}$ .

Table $\PageIndex{1}$
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

Example $\PageIndex{11}$ : translate

Translate and then simplify:

the difference of $13$ and $8$
subtract $24$ from $43$

Solution

The word difference tells us to subtract the two numbers. The numbers stay in the same order as in the phrase.

	the difference of 13 and 8
Translate.	13 - 8
Simplify.	5

The words subtract from tells us to take the second number away from the first. We must be careful to get the order correct.

	subtract 24 from 43
Translate.	43 - 24
Simplify.	19

Exercise $\PageIndex{21}$

Translate and simplify:

the difference of $14$ and $9$
subtract $21$ from $37$

Answer a: $14-9=5$
Answer b: $37-21=16$

Exercise $\PageIndex{22}$

Translate and simplify:

$11$ decreased by $6$
$18$ less than $67$

Answer a: $11-6=5$
Answer b: $67-18=49$

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 $\PageIndex{12}$ : difference

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?

Solution

We are asked to find the difference between the morning temperature and the noon temperature.

Write a phrase.	the difference of 73 and 27
Translate to math notation. Difference tells us to subtract.	73 - 27
Then we do the subtraction.	$CNX_BMath_Figure_01_03_032.png$
Write a sentence to answer the question.	The difference in temperatures was 46 degrees Fahrenheit.

Exercise $\PageIndex{23}$

The high temperature on June $1^{st}$ in Boston was $77$ degrees Fahrenheit, and the low temperature was $58$ degrees Fahrenheit. What was the difference between the high and low temperatures?

Answer: The difference is $19$ degrees Fahrenheit.

Exercise $\PageIndex{24}$

The weather forecast for June $2^{nd}$ 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?

Answer: The difference is $17$ degrees Fahrenheit.

Example $\PageIndex{13}$ : difference

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?

Solution

We are asked to find the difference between the regular price and the sale price.

Write a phrase	the difference between 588 and 399
Translate to math notation	588 - 399
Subtract	$CNX_BMath_Figure_01_03_033.png$
Write a sentence to answer the question	The difference between the regular price and the sale price is $189.

Exercise $\PageIndex{25}$

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?

Answer: The difference is $$149$ .

Exercise $\PageIndex{26}$

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?

Answer: The difference is $$136$ .

Access Additional Online Resources

Key Concepts

Operation	Notation	Expression	Read as	Result
Subtraction			seven minus three	the difference of

Subtract whole numbers
- Write the numbers so each place value lines up vertically.
- 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.
- Continue subtracting each place value from right to left, borrowing if needed.
- Check by adding.

Glossary

difference: The difference is the result of subtracting two or more numbers.

Practice Makes Perfect

Use Subtraction Notation

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

15 - 9
18 - 16
42 - 35
83 - 64
675 - 350
790 - 525

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

5 - 2
8 - 4
6 - 3
7 - 5
18 - 5
19 - 8
17 - 8
17 - 9
35 - 13
32 - 11
61 - 47
55 - 36

Subtract Whole Numbers

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

9 - 4
9 - 3
8 - 0
2 - 0
38 - 16
45 - 21
85 - 52
99 - 47
493 - 370
268 - 106
5,946 - 4,625
7,775 - 3,251
75 - 47
63 - 59
461 - 239
486 - 257
525 - 179
542 - 288
6,318 - 2,799
8,153 - 3,978
2,150 - 964
4,245 - 899
43,650 - 8,982
35,162 - 7,885

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

The difference of 10 and 3
The difference of 12 and 8
The difference of 15 and 4
The difference of 18 and 7
Subtract 6 from 9
Subtract 8 from 9
Subtract 28 from 75
Subtract 59 from 81
45 decreased by 20
37 decreased by 24
92 decreased by 67
75 decreased by 49
12 less than 16
15 less than 19
38 less than 61
47 less than 62

Mixed Practice

In the following exercises, simplify.

76−47
91 − 53
256 − 184
305 − 262
719 + 341
647 + 528
2,015 − 1,993
2,020 − 1,984

In the following exercises, translate and simplify.

Seventy-five more than thirty-five
Sixty more than ninety-three
13 less than 41
28 less than 36
The difference of 100 and 76
The difference of 1,000 and 945

Subtract Whole Numbers in Applications

In the following exercises, solve.

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?
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?
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?
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?
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?
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?
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?
Banking Mason had $1,125 in his checking account. He spent $892. How much money does he have left?

Everyday Math

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?
Test Scores Sara needs 350 points to pass her course. She scored 75, 50, 70, and 80 on her first four tests. How many more points does Sara need to pass the course?

Writing Exercises

Explain how subtraction and addition are related.
How does knowing addition facts help you to subtract numbers?

Self Check

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

$CNX_BMath_Figure_AppB_004.jpg$

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

Contributors and Attributions

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.

Translate Word Phrases to Math Notation

Example \PageIndex{11}\PageIndex{11}: translate

Exercise \PageIndex{21}\PageIndex{21}

Exercise \PageIndex{22}\PageIndex{22}

Subtract Whole Numbers in Applications

Example \PageIndex{12}\PageIndex{12}: difference

Exercise \PageIndex{23}\PageIndex{23}

Exercise \PageIndex{24}\PageIndex{24}

Example \PageIndex{13}\PageIndex{13}: difference

Exercise \PageIndex{25}\PageIndex{25}

Exercise \PageIndex{26}\PageIndex{26}

Access Additional Online Resources

Key Concepts

Glossary

Practice Makes Perfect

Use Subtraction Notation

Model Subtraction of Whole Numbers

Subtract Whole Numbers

Translate Word Phrases to Algebraic Expressions

Mixed Practice

Subtract Whole Numbers in Applications

Everyday Math

Writing Exercises

Self Check

Contributors and Attributions

Support Center

How can we help?

Example $\PageIndex{11}$ : translate

Exercise $\PageIndex{21}$

Exercise $\PageIndex{22}$

Example $\PageIndex{12}$ : difference

Exercise $\PageIndex{23}$

Exercise $\PageIndex{24}$

Example $\PageIndex{13}$ : difference

Exercise $\PageIndex{25}$

Exercise $\PageIndex{26}$