# 1.3 Subtract Whole Numbers

The topics covered in this section are:

## 1.3.1 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.

#### Example 1

Translate from math notation to words:

• $8-1$
• $26-14$
Solution
• We read this as eight minus one. The result is the difference of eight and one.
• We read this as twenty-six minus fourteen. The result is the difference of twenty-six and fourteen.

## 1.3.2 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, $7-3$.

### MANIPULATIVE MATHEMATICS

Doing the Manipulative Mathematics activity Model Subtraction of Whole Numbers will help you develop a better understanding of subtracting whole numbers.

#### Example 2

Model the subtraction: $8-2$.

Solution

#### Example 3

Model the subtraction: $13-8$.

Solution

As we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens.

#### Example 4

Model the subtraction: $43-26$.

Solution

Because $43-26$ means $43$ take away $26$, we begin by modeling the $43$.

Now, we need to take away $26$, which is $2$ tens and $6$ ones. We cannot take away $6$ ones from $3$ ones. So, we exchange $1$ ten for $10$ ones.

Now we can take away $2$ tens and $6$ ones.

Count the number of blocks remaining. There is $1$ ten and $7$ ones, which is $17$.

## 1.3.3 Subtract Whole Numbers

Addition and subtraction are inverse operations. Addition undoes subtraction, and subtraction undoes addition. We know $7-3=4$ and $4+3=7$. 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.

 $7-3=4$ because $4+3=7$ $13-8=5$ because $5+8=13$ $43-26=17$ because $17+26=43$

#### Example 5

• $9-7$
• $8-3$
Solution

Part 1

Part 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 6

Subtract then check by adding: $89-61$.

Solution

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

1. Write the numbers so each place value lines up vertically.
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.
3. Continue subtracting each place value from right to left, borrowing if needed.

#### Example 7

Subtract: $43-26$.

Solution

#### Example 8

Subtract then check by adding: $207-64$.

Solution

#### Example 9

Subtract then check by adding: $910-586$.

Solution

#### Example 10

Subtract then check by adding: $2,162-479$.

Solution

## 1.3.4 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 below.

 Operation Word Phrase Example Expression Subtraction minusdifferencedecreased byless thansubtracted from $5$ minus $1$the difference of $9$ and $4$$7 decreased by 3$$5$ less than $8$$1 subtracted from 6 5-1$$9-4$$7-3$$8-5$$6-1$

#### Example 11

Translate and then simplify:

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

Part 1
The word difference tells us to subtract the two numbers. The numbers stay in the same order as in the phrase.

Part 2.
The words subtract from tells us to take the second number away from the first. We must be careful to get the order correct.

## 1.3.5 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 12

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.

#### Example 13

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.