1.2 Add whole numbers (Page 4/6)

Prealgebra Page 4 / 6

Operation	Words	Example	Expression
Addition	plus sum increased by more than total of added to	$1$ plus $2$ the sum of $3$ and $4$ $5$ increased by $6$ $8$ more than $7$ the total of $9$ and $5$ $6$ added to $4$	$1 + 2$ $3 + 4$ $5 + 6$ $7 + 8$ $9 + 5$ $4 + 6$

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 $42.$

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Translate and simplify: the sum of $17$ and $26 .$

Translate: $17 + 26$ ; Simplify: $43$

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Translate and simplify: the sum of $28$ and $14 .$

Translate: $28 + 14$ ; Simplify: $42$

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Translate and simplify: $28$ increased by $31 .$

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 $59.$

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Translate and simplify: $29$ increased by $76 .$

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

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Translate and simplify: $37$ increased by $69 .$

Translate 37 + 69; Simplify 106

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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.

Hao earned grades of $87, 93, 68, 95, and 89$ on the five tests of the semester. What is the total number of points he earned on the five tests?

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.	$\begin{matrix} \overset{3}{8} 7 \\ 93 \\ 68 \\ 95 \\ \underset{____}{+ 89} \\ 432 \end{matrix}$
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.

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Mark is training for a bicycle race. Last week he rode $18$ miles on Monday, $15$ miles on Wednesday, $26$ miles on Friday, $49$ miles on Saturday, and $32$ miles on Sunday. What is the total number of miles he rode last week?

He rode 140 miles.

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Lincoln Middle School has three grades. The number of students in each grade is $230, 165, and 325 .$ What is the total number of students?

The total number is 720 students.

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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.

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.

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.

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Find the perimeter of each figure. All lengths are in inches.

This image includes 8 sides. Side one on the left is labeled 4 inches, side 2 on the top is labeled 9 inches, side 3 on the right is labeled 4 inches, side 4 is labeled 3 inches, side 5 is labeled 2 inches, side 6 is labeled 3 inches, side 7 is labeled 2 inches, and side 8 is labeled 3 inches.

The perimeter is 30 inches.

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Find the perimeter of each figure. All lengths are in inches.

This image includes 8 sides. Moving in a clockwise direction, the first side is labeled 2 inches, side 2 is labeled 12 inches, side 3 is labeled 6 inches, side 4 is labeled 4 inches, side 5 is labeled 2 inches, side 6 is labeled 4 inches, side 7 is labeled 2 inches and side 8 is labeled 4 inches.

The perimeter is 36 inches.

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Source: OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9

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