
1.3: Subtract Whole Numbers (Part 2)

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 1.34.

Table 1.34

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 1.36:

Translate and then simplify: (a) the difference of 13 and 8 (b) subtract 24 from 43

Solution

(a) 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

(b) 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 1.71:

Translate and simplify: (a) the difference of 14 and 9 (b) subtract 21 from 37.

Exercise 1.72:

Translate and simplify: (a) 11 decreased by 6 (b) 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?

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. Write a sentence to answer the question. The difference in temperatures was 46 degrees Fahrenheit.

Exercise 1.73:

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

Exercise 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?

Solution

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

Everyday Math

1. 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?
2. 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

1. Explain how subtraction and addition are related.