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Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #121 : Order Of Operations

Solve the equation below:

8 + 4 * 6 - 12 =

Possible Answers:

Correct answer:

Explanation:

When solving an order of operations question use the GEMDAS method.

G = Grouping Symbols

E = Exponets

M/D = Multiplication OR Division from left to right.

A/S = Addition OR Subtraction from left to right.

8 + 4 * 6 - 12 =

4 * 6 = 24

8 + 24 - 12 =

32 - 12 =

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Example Question #122 : Order Of Operations

Solve using the order of operations:

$9 \cdot 3^2 + 12 \div 3$

Possible Answers:

Correct answer:

Explanation:

The order of operations is the order in which you must solve a problem. The order is defined as

PARENTHESES

EXPONENTS

MULTIPLICATION

DIVISION

ADDITION

SUBTRACTION

where we solve parentheses first, followed by exponents, and so on. Following the order of operations, we get

$9 \cdot 3^2 + 12 \div 3$

$9 \cdot 9 + 12 \div 3$

$81 + 12 \div 3$

81 + 4

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Example Question #121 : Order Of Operations

Solve using the order of operations:

$4(3^2 + 5^2) - 24 \div 2$

Possible Answers:

148

124

Correct answer:

124

Explanation:

The order of operations is a specific order in which you must solve a problem. It is defined as

PARENTHESES

EXPONENTS

MULTIPLICATION

DIVISION

ADDITION

SUBTRACTION

where you solve parentheses first, followed by exponents, and so on.

So, following this order, we get

$4(3^2 + 5^2) - 24 \div 2$

PARENTHESES

$4(9 + 25) - 24 \div 2$

$4(34) - 24 \div 2$

MULTIPLICATION

$136-24 \div 2$

DIVISION

SUBTRACTION

124

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Example Question #122 : Order Of Operations

What is the solution to the following problem?

$2(4-3)^{2}+14$

Possible Answers:

Correct answer:

Explanation:

This problem requires proper order of operations. Remember the acronym for the order of operations: PEMDAS. This acronym will help you to remember the proper order for solving problems:

Parentheses
Exponents
Multiplication and Division (whichever comes first as you read the problem from left to right)
Addition and Subtraction (whichever comes first as you read the problem from left to right)

Step 1: Parentheses

$2(4-3)^{2}+14$

$2(1)^{2}+14$

Step 2: Exponents

$2(1)^{2}+14=2(1\cdot 1)+14=2(1)+14$

Step 3: Multiplication

2(1)+14=2+14

Step 4: Addition

2+14=16

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Example Question #122 : Order Of Operations

Fifty friends are renting a restaurant venue for a graduation party. Rental of the venue requires a $\$315.00$ up-front deposit plus a $\$25.00$ per hour operation cost. The friends have booked the venue from 8:00$ AM to 5:00 $ PM . If the friends have agreed to split the cost evenly, how much money should each person expect to pay?

Possible Answers:

$\$6.80$

$\$10.80$

$\$6.30$

$\$31.30$

$\$9.80$

Correct answer:

$\$10.80$

Explanation:

First, let's write an equation that will calculate the cost for each person.

$\textup{Cost}=\frac{\$315+(\$25\times h\textup{ hours})}{50 \textup{ students}}$

We need to calculate the number of hours that the students plan to rent the venue from 8:00$ AM to 5:00 $ PM .

$\textup{8:00 AM to 12:00 PM=4 hours}$

$\textup{12:00 PM to 5:00 PM=5 hours}$

Let's add these values together to calculate our x-variable (i.e. the number of hours that the students will rent the venue).

$4+5=9\textup{ hours}$

Now, we can substitute in the number of hours that the students will rent the venue and calculate the cost that each student should expect to pay.

$\textup{Cost}=\frac{\$315+(\$25\times 9\textup{ hours})}{50 \textup{ students}}$

$\textup{Cost}=\frac{\$315+\$225}{50 \textup{ students}}$

$\textup{Cost}=\frac{\$540}{50 \textup{ students}}$

Last, we need to divide this total cost by the number of students.

$\textup{Cost}=\$10.80$

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Example Question #123 : Order Of Operations

Fahrenheit temperature can be converted to its Celsius equivalent using the following formula:

$^{\circ}\textup{C} = (^{\circ}\textup{F}-32)\times\frac{5}{9}$ .

Similarly, Celsius temperature can be converted to its Fahrenheit equivalent using another formula:

$^{\circ}\textup{F} = \frac{9}{5} ^{\circ}\textup{C} + 32$ .

A scientist knows that nickel melts at the following temperature:

$\textup{1,455} ^{\circ } \textup{C}$

In order to complete an experiment, the scientist needs to know this temperature in degrees Fahrenheit. What is the melting point of nickel in degrees Fahrenheit?

Possible Answers:

$791^\circ $F$

$1\textup,524^\circ $F$

$776^\circ $F$

$2\textup,651^\circ $F$

None of these

Correct answer:

$2\textup,651^\circ $F$

Explanation:

Since we are converting from Celsius to Fahrenheit, we need to use the following formula:

$^{\circ}\textup{F} = \frac{9}{5} ^{\circ}\textup{C} + 32$ .

Substitute the value for the melting point of nickel in degrees Celsius and solve.

$^{\circ}\textup{F} = \frac{9}{5} \cdot \textup{1,455} ^{\circ } \textup{C} + 32$

According to the order of operations, we need to perform the multiplication/division operations first.

$^{\circ}\textup{F} = \frac{9\times\textup{1,455} ^{\circ } \textup{C}}{5}+32$

$^{\circ}\textup{F} = \frac{\textup{13,095}}{5}+32$

Simplify.

$^{\circ}\textup{F} =\textup{2,619}+32$

Solve.

$^{\circ}\textup{F} = \textup{2,651}$

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Example Question #124 : Order Of Operations

Select the equation that reflects the phrase below.

First subtract and , then divide by .

Possible Answers:

$28-17\div3$

$28\div17-3$

$28-(7\div3)$

$(28-17)\div3$

$28\div3-17$

Correct answer:

$(28-17)\div3$

Explanation:

Because we want to subtract 28 and 17 first, we need to set that off into parentheses due to the order of operation rules. Remember: without parentheses, division would come before subtraction. The parentheses around (28 - 17) tells you that the subtraction comes first, then we can do the division by 3.

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Example Question #4 : Write And Interpret Simple Expressions That Record Calculations: Ccss.Math.Content.5.Oa.A.2

Select the equation that reflects the phrase below.

First add and , then multiply by .

Possible Answers:

$(8+9)\times2$

$(18+9)\times2$

$8+9\times2$

$2\times9+8$

$2\times8+9$

Correct answer:

$(8+9)\times2$

Explanation:

Because we want to add and first, we need to set that off into parentheses due to the order of operation rules. Then we can multiply by .

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Example Question #1 : Addition And Subtraction

Simplify the expression.

6x+7y-3x+2y

Possible Answers:

6x-4y

9xy-6xy

5y-3x

9y-3x

3x+9y

Correct answer:

3x+9y

Explanation:

6x+7y-3x+2y

Re-write the expression to group like terms together.

(6x-3x)+(7y+2y)

Simplify.

3x+9y

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Example Question #2 : Addition And Subtraction

What is $2x^{2}+3x^{2}$ simplified?

Possible Answers:

$5x^{4}$

$6x^{2}$

$5x^{2}$

$6x^{4}$

Correct answer:

$5x^{2}$

Explanation:

To simplify a problem like the example above we must combine the like-termed variables.

Like terms are the terms that share the same variable(s) to the same power. In this example the like term is $x^{2}$ .

To combine like terms the variable $x^{2}$ stays the same and you add the numbers in front.

Perform the necessary addition, 2+3=5 , to get $5x^{2}$ .

We have the simplified version of the equation, $5x^{2}$ .

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Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #121 : Order Of Operations

Example Question #122 : Order Of Operations

Example Question #121 : Order Of Operations

Example Question #122 : Order Of Operations

Example Question #122 : Order Of Operations

Example Question #123 : Order Of Operations

Example Question #124 : Order Of Operations

Example Question #4 : Write And Interpret Simple Expressions That Record Calculations: Ccss.Math.Content.5.Oa.A.2

Example Question #1 : Addition And Subtraction

Example Question #2 : Addition And Subtraction

All Pre-Algebra Resources

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