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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 [latex]3[/latex] from [latex]7[/latex] is

[latex]7 - 3[/latex]

We read [latex]7 - 3[/latex] 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 [latex]-[/latex] [latex]7 - 3[/latex] seven minus three the difference of [latex]7[/latex] and [latex]3[/latex]
 

example

Translate from math notation to words: 1. [latex]8 - 1[/latex] 2. [latex]26 - 14[/latex] . 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 [latex]\text{base - 10}[/latex] blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, [latex]7 - 3[/latex].
We start by modeling the first number,[latex]7[/latex]. CNX_BMath_Figure_01_03_018_img-02.png
Now take away the second number,[latex]3[/latex]. We'll circle [latex]3[/latex] 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 [latex]4[/latex] ones blocks left. We have shown that [latex]7 - 3=4[/latex] .
 

example

Model the subtraction: [latex]8 - 2[/latex].

Answer: Solution

[latex]8 - 2[/latex] means the difference of[latex]8[/latex] and[latex]2[/latex].
Model the first,[latex]8[/latex]. CNX_BMath_Figure_01_03_019_img-02.png
Take away the second number, [latex]2[/latex]. 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 [latex]6[/latex] ones blocks left. We have shown that [latex]8 - 2=6[/latex] .

 

try it

Model: [latex]9 - 6[/latex].

Answer: No Alt Text

Model: [latex]6 - 1[/latex].

Answer: No Alt Text

 

example

Model the subtraction: [latex]13 - 8[/latex].

Answer: Solution

Model the first number, [latex]13[/latex]. We use[latex]1[/latex] ten and [latex]3[/latex] ones. CNX_BMath_Figure_01_03_020_img-02.png
Take away the second number, [latex]8[/latex]. However, there are not [latex]8[/latex] ones, so we will exchange the [latex]1[/latex] ten for [latex]10[/latex] ones. CNX_BMath_Figure_01_03_020_img-03.png
Now we can take away [latex]8[/latex] 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 [latex]13 - 8=5[/latex] .

  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: [latex]12 - 7[/latex].

Answer: No Alt Text

Model the subtraction: [latex]14 - 8[/latex].

Answer: No Alt Text

 

example

Model the subtraction: [latex]43 - 26[/latex].

Answer: Solution Because [latex]43 - 26[/latex] means [latex]43[/latex] take away [latex]26[/latex], we begin by modeling the [latex]43[/latex]. 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 [latex]26[/latex], which is [latex]2[/latex] tens and [latex]6[/latex] ones. We cannot take away [latex]6[/latex] ones from [latex]3[/latex] ones. So, we exchange [latex]1[/latex] ten for [latex]10[/latex] 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 [latex]2[/latex] tens and [latex]6[/latex] 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 [latex]1[/latex] ten and [latex]7[/latex] ones, which is [latex]17[/latex]. [latex-display]43 - 26=17[/latex-display]

 

try it

Model the subtraction: [latex]42 - 27[/latex].

Answer: No Alt Text

Model the subtraction: [latex]45 - 29[/latex].

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

Licenses & Attributions

CC licensed content, Shared previously

  • Model Subtraction of Two Digit Whole Numbers Using Base Ten Blocks. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • The Language of Subtraction. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • Question ID: 143245. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.

CC licensed content, Specific attribution