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Study Guides > Prealgebra

Notation and Modeling Subtraction of Whole Numbers

Learning Outcomes

  • Use symbols and words to represent subtraction
  • Translate subtractions from math notation to words
  • Use base-10 blocks to model subtraction
 

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 33 from 77 is

7−37 - 3

We read 7−37 - 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 −- 7−37 - 3 seven minus three the difference of 77 and 33
 

example

Translate from math notation to words: 1. 8−18 - 1 2. 26−1426 - 14 . Solution
  1. We read this as eight minus one. The result is the difference of eight and one.
  2. We read this as twenty-six minus fourteen. The result is the difference of twenty-six and fourteen.
    The video below provides more examples of how to translate subtraction word phrases. https://youtu.be/vtnAdQHCt5s

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\text{base - 10} blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, 7−37 - 3.
We start by modeling the first number,77. CNX_BMath_Figure_01_03_018_img-02.png
Now take away the second number,33. We'll circle 33 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 44 ones blocks left. We have shown that 7−3=47 - 3=4 .
 

example

Model the subtraction: 8−28 - 2.

Answer: Solution

8−28 - 2 means the difference of88 and22.
Model the first,88. CNX_BMath_Figure_01_03_019_img-02.png
Take away the second number, 22. 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 66 ones blocks left. We have shown that 8−2=68 - 2=6 .

 

try it

Model: 9−69 - 6.

Answer: No Alt Text

Model: 6−16 - 1.

Answer: No Alt Text

 

example

Model the subtraction: 13−813 - 8.

Answer: Solution

Model the first number, 1313. We use11 ten and 33 ones. CNX_BMath_Figure_01_03_020_img-02.png
Take away the second number, 88. However, there are not 88 ones, so we will exchange the 11 ten for 1010 ones. CNX_BMath_Figure_01_03_020_img-03.png
Now we can take away 88 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=513 - 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.

try it

Model the subtraction: 12−712 - 7.

Answer: No Alt Text

Model the subtraction: 14−814 - 8.

Answer: No Alt Text

 

example

Model the subtraction: 43−2643 - 26.

Answer: Solution Because 43−2643 - 26 means 4343 take away 2626, we begin by modeling the 4343. An image containing two items. The first item is 4 horizontal rods containing 10 blocks each. The second item is 3 individual blocks. Now, we need to take away 2626, which is 22 tens and 66 ones. We cannot take away 66 ones from 33 ones. So, we exchange 11 ten for 1010 ones. This figure contains two groups. The first group on the left includes 3 rows of blue base 10 blocks and 1 red row of 10 blocks. This is labeled 4 tens. Alongside the first row of ten blocks are 3 individual blocks. This is labeled 3 ones. An arrow points to the right to the second group in which there are three rows of 10 base blocks labeled 3 tens. Next to this is a row of 3 blue individual blocks and two rows each with five individual blocks in red. This is labeled 13 ones. Now we can take away 22 tens and 66 ones. This image includes one row of base ten blocks at the top of the image; Next to it are seven individual blocks. Below this, is a group of two rows of base ten blocks, and two rows of 3 individual blocks with a circle around all. The arrow points to the right and shows one row of ten blocks and seven individual blocks underneath. Count the number of blocks remaining. There is 11 ten and 77 ones, which is 1717. 43−26=1743 - 26=17

 

try it

Model the subtraction: 42−2742 - 27.

Answer: No Alt Text

Model the subtraction: 45−2945 - 29.

Answer: No Alt Text

  Watch the video below to see more examples of using base 10 blocks to model subtraction. https://youtu.be/FQI0IgA-7fI

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