We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

TEXT
Unlock Solution Steps
Sign in to
Symbolab
Get full access to all Solution Steps for any math problem
By continuing, you agree to our Terms of Use
and have read our Privacy Policy

Study Guides > Prealgebra

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]

  In the video below we present more examples of how to translate from words to expressions. https://youtu.be/sFbNgjxdf1A

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.

  Notice that we added points, so the sum is [latex]432[/latex] points. It is important to include the appropriate units in all answers to applications problems.   Some application problems involve shapes. For example, a person might need to know the distance around a garden to put up a fence or around a picture to frame it. The perimeter is the distance around a geometric figure. The perimeter of a figure is the sum of the lengths of its sides.

example

Find the perimeter of the patio shown. This is an image of a perimeter of a patio. There are six sides. The far left side is labeled 4 feet, the top side is labeled 9 feet, the right side is short and labeled 2 feet, then extends across to the left and is labeled 3 feet. From here, the side extends down and is labeled 2 feet. Finally, the base is labeled 6 feet.

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.

    The video below helps with finding the perimeter of an L-shaped Polygon involving hole numbers. https://youtu.be/0HfnFXm7zHI

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