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- 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.
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]. | |
Now take away the second number,[latex]3[/latex]. We'll circle [latex]3[/latex] blocks to show that we are taking them away. | |
Count the number of blocks remaining. | |
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]. | |
Take away the second number, [latex]2[/latex]. | |
Count the number of blocks remaining. | |
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:
Model: [latex]6 - 1[/latex].Answer:
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. | |
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. | |
Now we can take away [latex]8[/latex] ones. | |
Count the blocks remaining. | |
There are five ones left. | We have shown that [latex]13 - 8=5[/latex] . |
try it
Model the subtraction: [latex]12 - 7[/latex].Answer:
Model the subtraction: [latex]14 - 8[/latex].Answer:
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]. 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. Now we can take away [latex]2[/latex] tens and [latex]6[/latex] ones. 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:
Model the subtraction: [latex]45 - 29[/latex].Answer:
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
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].