Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #21 : Operations And Properties

Evaluate:

Possible Answers:

Correct answer:

Explanation:

You must use the order of operations to solve this. First evaluate the parentheses, then evaulate the multiplication and division, and finally you can evaulate the addition and subtraction.

 

Example Question #22 : Operations And Properties

Evaluate:

Possible Answers:

Correct answer:

Explanation:

Example Question #23 : Operations And Properties

What is the solution to the following equation?

 

Possible Answers:

Correct answer:

Explanation:

An operation is a symbol used to indicate a logical process used to solve an equation. For example, in the equation , the operation is represented by the "", and it indicates the two values associated with it must be added. 

The order in which operations are preformed begins with operations within parentheses, followed by any exponents, then multiplication, division, addition, and finally subtraction. 

For the equation , the first step is to multiply the values joined by the multiplication symbol, six and four. as the operation of multiplication comes before the operation of addition. This results in the simplified equation of

The second operation is to add the values from left to right, so  simplifies to , which simplifies to our answer, 

Example Question #24 : Operations And Properties

Simplify:

Possible Answers:

26

28

24

36

22

Correct answer:

24

Explanation:

In order to simplify this expression, you need to remember the order of operations. In short, this can be represented by the acronym PEMDAS. When solving an expression, first begin by simplifying anything in parentheses (P), then exponents (E), then multiplication and division (M and D), then addition and subtraction (A and D). Remember when doing this to read the equation from left to right.

In this case, we must perform the multiplication before the addtion:

The answer is 24.

Example Question #25 : Operations And Properties

Solve using order of operations.

Possible Answers:

Correct answer:

Explanation:

PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Parentheses:

The expression now looks like this:

Square 10:

Multiply the last two terms:

Finally divide to finish:

 

Example Question #26 : Operations And Properties

If you are asked to evaluate 

,

what should you do first?

Possible Answers:

Add 40 and 15

Add 20 and 25

Subtract 40 from 25

Subtract 20 from 10

Subtract 5 from 15

Correct answer:

Subtract 20 from 10

Explanation:

In the order of operations, additions and subtractions have equal rank and, collectively, are carried out from left to right. The first operation carried out is therefore the leftmost of the operations - the subtraction of 20 from 10.

Example Question #27 : Operations And Properties

If you are asked to evaluate 

,

what should you do first?

Possible Answers:

Divide 10,000 by 20

Multiply 40 by 15

Multiply 20 by 25

Divide 15 by 2

Divide 25 by 40

Correct answer:

Divide 10,000 by 20

Explanation:

In the order of operations, multiplications and divisions have equal rank and, collectively, are carried out from left to right. The first operation carried out is therefore the leftmost of the operations - 10,000 divided by 20.

Example Question #28 : Operations And Properties

Simplify:

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, one must follow the mathematical order of operations. The correct order of mathematical operations consists of the following pattern: parenthesis, exponents, multiplication and division, and finally, addition and subtraction. One should work beginning with the innermost nested parentheses and complete the correct operations from left to right. 

Remember, subtracting a negative is the same as adding a positive number, and adding a negative is like subtracting a positive.

Example Question #29 : Operations And Properties

Simplify:

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, one must follow the mathematical order of operations. The correct order of mathematical operations consists of the following pattern: parenthesis, exponents, multiplication and division, and finally, addition and subtraction. One should work beginning with the innermost nested parentheses and complete the correct operations from left to right. 

Remember, subtracting a negative is the same as adding a positive number, and adding a negative is like subtracting a positive.

Example Question #30 : Operations And Properties

Simplify:

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, one must follow the mathematical order of operations. The correct order of mathematical operations consists of the following pattern: parenthesis, exponents, multiplication and division, and finally, addition and subtraction. One should work beginning with the innermost nested parentheses and complete the correct operations from left to right. 

Remember, subtracting a negative is the same as adding a positive number, and adding a negative is like subtracting a positive.

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