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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #112 : Order Of Operations

Solve:

$15^{2}-12^{2}+7$

Possible Answers:

112

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

For this problem, we solve the exponents before completing addition and subtraction to get our final answer of 88:

$15^{2}-12^{2}+7$

$225-12^{2}+7$

225-144+7

81+7=88

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Example Question #113 : Operations And Properties

Solve:

$6\cdot2+(7-2\cdot 3+11)$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

For this problem, we need to solve what is inside the parentheses first. In order to do this, solve the multiplication before the addition and subtraction. Complete the multiplication outside the parentheses, then solve the addition between that answer and the answer from the parentheses to get a final answer of 24:

$6\cdot2+(7-2\cdot 3+11)$

$6\cdot2+(7-6+11)$

$6\cdot2+(1+11)$

$6\cdot2+12$

12+12=24

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Example Question #119 : Operations

Solve:

$(12-3)\cdot (5+6)$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

For this problem, we need to solve the inside of each set of parentheses first. Once we get these answers, multiply them together to get the final answer of 99:

$(12-3)\cdot (5+6)$

$9\cdot (5+6)$

$9\cdot11=99$

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Example Question #111 : Operations And Properties

Solve the following using the order of operations.

$8 \cdot 4 + 12 \div 6-(9-4)$

Possible Answers:

Correct answer:

Explanation:

The order of operations is the order in which you must solve problems. The order is

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

where you start with parentheses and follow the order until you reach subtraction. So we will follow the order for this problem

$8 \cdot 4 + 12 \div 6-(9-4)$

Parentheses

$8 \cdot 4 + 12 \div 6-5$

Multiplication

$32 + 12 \div 6-5$

Division

32 + 2-5

Addition

34-5

Subtraction

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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 #121 : 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 #1131 : Pre Algebra

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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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #112 : Order Of Operations

Example Question #113 : Operations And Properties

Example Question #119 : Operations

Example Question #111 : Operations And Properties

Example Question #121 : Order Of Operations

Example Question #121 : Order Of Operations

Example Question #121 : Order Of Operations

Example Question #1131 : Pre Algebra

Example Question #122 : Order Of Operations

Example Question #123 : Order Of Operations

All Pre-Algebra Resources

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