GED Math : Numbers and Operations

Study concepts, example questions & explanations for GED Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #11 : Order Of Operations

Evaluate:

Do not use a calculator.

Possible Answers:

Correct answer:

Explanation:

In the order of operations, multiplications and divisions have equal rank and, collectively, are carried out from left to right, as follows:

Example Question #341 : Numbers And Operations

Which of the following operations might yield a negative result?

Possible Answers:

Dividing the square of a positive number by a positive number.

Subtracting the square of a positive number from a positive number.

Multiplying the square of a positive number by a positive number.

Adding the square of a positive number to a positive number.

Correct answer:

Subtracting the square of a positive number from a positive number.

Explanation:

The square of a positive number, as the product of two positive factors, must be positive.

Adding the square of a positive number to a positive number is adding two positive numbers; the sum must be positive. The same happens when multiplying and dividing; in both cases, both numbers are positive and the result must be positive.

Subtracting the square of a positive number from a positive number can yield a negative result. For example:

Example Question #342 : Numbers And Operations

In order to calculate 

what step must you take first?

Possible Answers:

Subtracting two hundred from two hundred fifty

Adding six and four

Dividing two hundred by six

Squaring four

Correct answer:

Adding six and four

Explanation:

By the order of operations, the operation(s) within grouping symbols - here, the addition of six and four - must be carried out first.

Example Question #343 : Numbers And Operations

Jeff went to the casino with $1,000 in his pocket. He lost $400 of it playing blackjack, won $900 playing craps, then left the casino. How much money did he leave with?

Do not use a calculator.

Possible Answers:

Correct answer:

Explanation:

A loss is a subtraction; a win is an addition. Jeff leaves the casino with

.

Example Question #344 : Numbers And Operations

Suppose the values of all of the variables in the expression 

are known. In order to evaluate this expression, what would be the first step?

Possible Answers:

Addition

Subtraction

Multiplication

Division

Correct answer:

Division

Explanation:

In the absence of grouping symbols, the first operations that should be carried out are exponentiations, of which there are none here. 

The next operations to be carried out are the multiplications and divisions, from left to right. The division is to the left, so it is executed first.

Example Question #345 : Numbers And Operations

Define an operation  on the real numbers as follows:

 for all real .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Substitute 7 for  and 8 for :

By order of operations, square, then add, then subtract.

Example Question #346 : Numbers And Operations

Solve:  

Possible Answers:

Correct answer:

Explanation:

Simplify the parentheses first.  Notice that there is an exponent in the first parentheses.

The expression becomes:  

Simplify the terms inside the parentheses by subtraction.

Multiply the terms.

The answer is:  

Example Question #16 : Order Of Operations

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Evaluate the terms of the inner parentheses.

The inner parentheses become:

Replace the terms.

The answer is:  

Example Question #17 : Order Of Operations

Solve:  

Possible Answers:

Correct answer:

Explanation:

Simplify by distributing the coefficient through the binomial.

Distribute the negative through the second binomial.

Combine the terms.

The answer is:  

Example Question #18 : Order Of Operations

Evaluate for :

Possible Answers:

Correct answer:

Explanation:

Substitute 12 for ; the expression becomes 

By the order of operations, multiplication precedes addition and subtraction, so  multiply first:

Addition and subtraction are worked from left to right, so add next, then subtract:

 

Learning Tools by Varsity Tutors