Adding Whole Numbers in Applications
Learning Outcomes
- Translate word phrases into mathematical notation representing addition
- Solve application problems by translating word phrases into mathematical expressions
Translate Word Phrases to Math Notation
Earlier in this section, we translated math notation into words. Now we’ll reverse the process. We’ll translate word phrases into math notation. Some of the word phrases that indicate addition are listed in the table below.Operation | Words | Example | Expression |
---|---|---|---|
Addition | plus sum increased by more than total of added to | [latex]1[/latex] plus [latex]2[/latex] the sum of [latex]3[/latex] and [latex]4[/latex] [latex-display]5[/latex] increased by [latex]6[/latex-display] [latex-display]8[/latex] more than [latex]7[/latex-display] the total of [latex]9[/latex] and [latex]5[/latex] [latex]6[/latex] added to [latex]4[/latex] | [latex]1+2[/latex] [latex-display]3+4[/latex-display] [latex-display]5+6[/latex-display] [latex-display]7+8[/latex-display] [latex-display]9+5[/latex-display] [latex]4+6[/latex] |
example
Translate and simplify: the sum of [latex]19[/latex] and [latex]23[/latex]. Solution The word sum tells us to add. The words of [latex]19[/latex] and [latex]23[/latex] tell us the addends.The sum of [latex]19[/latex] and [latex]23[/latex] | |
Translate. | [latex]19+23[/latex] |
Add. | [latex]42[/latex] |
The sum of [latex]19[/latex] and [latex]23[/latex] is [latex]42[/latex]. |
example
Translate and simplify: [latex]28[/latex] increased by [latex]31[/latex].Answer: Solution The words increased by tell us to add. The numbers given are the addends.
[latex]28[/latex] increased by [latex]31[/latex]. | |
Translate. | [latex]28+31[/latex] |
Add. | [latex]59[/latex] |
So [latex]28[/latex] increased by [latex]31[/latex] is [latex]59[/latex]. |
try it
Translate and simplify: [latex]29[/latex] increased by [latex]76[/latex].Answer: Translate: [latex]29+76[/latex]; Simplify [latex]105[/latex]
Translate and simplify: [latex]37[/latex] increased by [latex]69[/latex].Answer: Translate[latex]37+69[/latex]; Simplify[latex]106[/latex]
Add Whole Numbers in Applications
Now that we have practiced adding whole numbers, let’s use what we’ve learned to solve real-world problems. We’ll start by outlining a plan. First, we need to read the problem to determine what we are looking for. Then we write a word phrase that gives the information to find it. Next we translate the word phrase into math notation and then simplify. Finally, we write a sentence to answer the question.example
Hao earned grades of [latex]87,93,68,95,\text{and }89[/latex] on the five tests of the semester. What is the total number of points he earned on the five tests?Answer: Solution We are asked to find the total number of points on the tests.
Write a phrase. | the sum of points on the tests |
Translate to math notation. | [latex]87+93+68+95+89[/latex] |
Then we simplify by adding. | |
Since there are several numbers, we will write them vertically. | [latex]\begin{array}{}\\ \\ \\ \stackrel{3}{8}7\hfill \\ 93\hfill \\ 68\hfill \\ 95\hfill \\ \underset{\text{____}}{+89}\hfill \\ 432\hfill \end{array}[/latex] |
Write a sentence to answer the question. | Hao earned a total of 432 points. |
example
Find the perimeter of the patio shown.Answer: Solution
We are asked to find the perimeter. | |
Write a phrase. | the sum of the sides |
Translate to math notation. | [latex]4+6+2+3+2+9[/latex] |
Simplify by adding. | [latex]26[/latex] |
Write a sentence to answer the question. | |
We added feet, so the sum is [latex]26[/latex] feet. | The perimeter of the patio is [latex]26[/latex] feet. |
Licenses & Attributions
CC licensed content, Shared previously
- Ex: Find the Perimeter of an L-shaped Polygon Involving Whole Numbers. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- The Language of Addition. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- Question ID: 143207, 143227. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.
- Question ID: 7964. Authored by: James Sousa. 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].