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 #551 : Numbers And Operations

Solve for 

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to have all the variables on one side that isn't . Lucky for us our only other variable, , is on the other side of the equation.

Our next step then is to make sure  is naked, meaning that there is nothing attached to our variable in order to solve it. We can see that our  is encased in a square root, so we will need to get it out of there first.

In order to get rid of the square root, we will need to square the entire equation. The square and square root will cancel each other, releasing the .

We can now stop, as there is nothing else we can do to this equation because  is the lowest we can go.

Our answer is 

Example Question #552 : Numbers And Operations

Solve for 

Possible Answers:

Correct answer:

Explanation:

In order to solve for , our first priority is to get all the variables to one side so that  is by itself. And luckily for us the problem already has all of the variables to to the other side.

Our next step then is to make sure  is naked, meaning that there is nothing attached to the . We can see that our  is not naked and is within a square root.

In order to get rid of the square root, we must square both sides of the equation The square root and square will cancel each other out, freeing the .

Since the right side of the equation needs to be squared, we have to foil  in order to properly distribute the square.

 can be also written as 

Foil the equation.

 and  can be classified as the same as it would be like writing  and , so we can combine the two.

Let's bring back our  since there is nothing more we can do to this equation.

Our answer is 

Example Question #553 : Numbers And Operations

Solve for 

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to move all of the variables on its side over to the other side. We can see that our  is being squared. In order to get rid of that square, we will need to square root the whole equation, as the square and square root will cancel out.

 

Because this is a square root of , our  is like saying we have  's. A square root can divide to the power of  by , which leaves us with . The square root will also disappear for the  because it has divided it.

We cannot go any further into this equation as there are no like variables to put together.

Our answer is 

Example Question #554 : Numbers And Operations

Solve for 

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to move all the variables beside it to the other side of the equation. Luckily for us  is all by itself.

Our next step then is to make sure  is naked, meaning nothing it attached to it. We can see though that our  is being squared, so we need to get rid of that in order to proceed.

In order to get rid of the square, we must square root the whole equation. The square root and square will cancel each other out.

Since we don't have any variables that are the same, this is as far as we can go.

Our answer is 

Example Question #32 : Square Roots And Radicals

Simplify:

Possible Answers:

Correct answer:

Explanation:

Start by simplifying each radical.

The radicals all simplify down into multiples of . You can add them together.

Example Question #1 : Patterns And Sequences

What is the next number in the series?

Possible Answers:

39

Correct answer:

Explanation:

To pattern uses the formula .

 

Example Question #1 : Patterns And Sequences

What is the next number in the sequence?

Possible Answers:

Correct answer:

Explanation:

The pattern follows this equation:

Example Question #1 : Patterns And Sequences

What property of arithmetic is symbolized below?

If , then 

Possible Answers:

Symmetric

Commutative 

Associative

Reflexive

Correct answer:

Symmetric

Explanation:

The symbols show that if one number is equal to another,  the equality holds no matter the order of the two. This is the symmetric property of equality.

Example Question #161 : Numbers

What property of arithmetic is symbolized below?

Possible Answers:

Reflexive

Identity

Transitive

Commutative

Correct answer:

Reflexive

Explanation:

The symbols express the idea that any number is equal to itself. This is the reflexive property of equality.

Example Question #3 : Patterns And Sequences

What property of arithmetic is symbolized below?

Possible Answers:

Transitive

Associative

Commutative

Symmetric

Correct answer:

Associative

Explanation:

The symbols express the idea that if three numbers are added, the same sum results regardless of which numbers are added first. This is the associative property of addition.

Learning Tools by Varsity Tutors