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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

Before you get started, take this readiness quiz.

  1. Model 3 + 4 using base-ten blocks.
    If you missed this problem, review Add Whole Numbers .
  2. Add: 324 + 586 .
    If you missed this problem, review Add Whole Numbers .

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

Translate from math notation to words: 8 1 26 14 .

Solution

  • The expression consists of a minus symbol connecting 8 and 1 . We read this as eight minus one or the difference of eight and one .
  • The expression consists of a minus symbol connecting 26 and 14 . We read this as twenty-six minus fourteen or the difference of twenty-six and fourteen .
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Translate from math notation to words:

  1. 12 4
  2. 29 11
  1. twelve minus four; the difference of twelve and four
  2. twenty-nine minus eleven; the difference of twenty-nine and eleven
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Translate from math notation to words:

  1. 11 2
  2. 29 12
  1. eleven minus two; the difference of eleven and two
  2. twenty-nine minus twelve; the difference of twenty-nine and twelve
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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 10 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 .
Doing the Manipulative Mathematics activity Model Subtraction of Whole Numbers will help you develop a better understanding of subtracting whole numbers.

Model the subtraction: 8 2 .

Solution

8 2 means the difference of 8 and 2.
Model the first, 8. CNX_BMath_Figure_01_03_019_img-02.png
Take away the second number, 2. CNX_BMath_Figure_01_03_019_img-03.png
Count the number of blocks remaining. CNX_BMath_Figure_01_03_019_img-04.png
There are 6 ones blocks left. We have shown that 8 2 = 6 .
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Model the subtraction: 13 8 .

Solution

Model the first number, 13. We use 1 ten and 3 ones. CNX_BMath_Figure_01_03_020_img-02.png
Take away the second number, 8. However, there are not 8 ones, so we will exchange the 1 ten for 10 ones. CNX_BMath_Figure_01_03_020_img-03.png
Now we can take away 8 ones. CNX_BMath_Figure_01_03_020_img-04.png
Count the blocks remaining. CNX_BMath_Figure_01_03_020_img-05.png
There are five ones left. We have shown that 13 8 = 5 .

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

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Model the subtraction: 12 7 .


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Model the subtraction: 14 8 .


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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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