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	$1$ plus $2$ the sum of $3$ and $4$ $5[/latex] increased by [latex]6$ $8[/latex] more than [latex]7$ the total of $9$ and $5$ $6$ added to $4$	$1+2$ $3+4$ $5+6$ $7+8$ $9+5$ $4+6$

example

Translate and simplify: the sum of

19

and

23

. Solution The word sum tells us to add. The words of

19

and

23

tell us the addends.

	The sum of $19$ and $23$
Translate.	$19+23$
Add.	$42$
	The sum of $19$ and $23$ is $42$ .

example

Translate and simplify:

28

increased by

31

Answer: Solution The words increased by tell us to add. The numbers given are the addends.

	$28$ increased by $31$ .
Translate.	$28+31$
Add.	$59$
	So $28$ increased by $31$ is $59$ .

try it

Translate and simplify:

29

increased by

76

Answer: Translate: $29+76$ ; Simplify $105$

Translate and simplify:

37

increased by

69

Answer: Translate $37+69$ ; Simplify $106$

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

87,93,68,95,\text{and }89

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.	$87+93+68+95+89$
Then we simplify by adding.
Since there are several numbers, we will write them vertically.	$\begin{array}{}\\ \\ \\ \stackrel{3}{8}7\hfill \\ 93\hfill \\ 68\hfill \\ 95\hfill \\ \underset{\text{____}}{+89}\hfill \\ 432\hfill \end{array}$
Write a sentence to answer the question.	Hao earned a total of 432 points.

Notice that we added points, so the sum is

432

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.

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.	$4+6+2+3+2+9$
Simplify by adding.	$26$
Write a sentence to answer the question.
We added feet, so the sum is $26$ feet.	The perimeter of the patio is $26$ feet.

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

Adding Whole Numbers in Applications

Learning Outcomes

Translate Word Phrases to Math Notation

example

example

try it

Add Whole Numbers in Applications

example

example

Licenses & Attributions

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Study Guides > Prealgebra

Adding Whole Numbers in Applications

Learning Outcomes

Translate Word Phrases to Math Notation

example

example

try it

Add Whole Numbers in Applications

example

example

Licenses & Attributions

CC licensed content, Shared previously

CC licensed content, Specific attribution