ISEE Middle Level Math : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #191 : Operations

Combine the following:

Possible Answers:

Correct answer:

Explanation:

To add variables, we will look at the variables like objects. So, in the problem

we can think of the variable a as airplanes.  So, we can write it like this:

We can think of the problem like this:  We are outside and we see 5 airplanes in the sky.  Throughout the day, we see 6 more airplanes.  How many airplanes do we see all day?  We see 11 airplanes.  So,

 

We add variables the same way.

Example Question #41 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

To add variables, we can think of the variables like objects.  So, in the problem

we can think of the variable s as snakes.  So, we can write it like this:

We can think of it like this:  We are at the zoo.  We see 2 snakes in a pit.  We walk a little more, and we see 8 more snakes.  How many snakes have we seen at the zoo?  We have seen 10 snakes.  So,

 

We add variables the same way:

Example Question #46 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

To add variables, we will look at the variables like they are objects.  So, in the problem

we can think of b as books.  So, we can write it like this:

We can think of the problem like this:  You have borrowed 2 books from the library.  You go back, and you borrow 7 more books.  How many total books have you borrowed?  You have borrowed a total of 9 books.  So,

 

We add variables the same way.  We get

Example Question #47 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

When combining variables, we can think of the variables as objects. So, in the problem

we can think of the variable m as movies.  So, we can write it like this:

We can read it like this:  We have 2 movies.  We go to the store, and we buy 3 more movies.  How many movies do we have now?  We have 5 movies.  So,

 

We add variables the same way.

Example Question #48 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

To add variables, we will look at the variables like they are objects. So, in the problem

we can think of the variable b as books.  So, we can write the problem as

So, we can read the problem like this:  We have borrowed 2 books from the library.  We go back to the library and borrow 5 more books.  How many total books have we borrowed from the library?  We have borrowed 7 books.  So,

 

We add variables the same way.

Example Question #49 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

To add variables, we will look at the variables like objects. 

So, in the problem

we can think of the variable p as potatoes.  So, we can write it like

We can read the problem like this:  We go to the store to buy 5 potatoes.  We realize we need more, so we buy 5 more potatoes.  How many potatoes did we buy in total?  We bought 10 potatoes.  So,

 

We can add variables the same way.

Example Question #50 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

When adding variables, we will look at the variables like objects.  So, in the problem

we can think of the variable p as pictures.  So, we can write it like this:

We can read it like this:  We have taken 9 pictures with our new camera.  We walk around for a while, and we take 6 more pictures.  How many pictures have we taken in total?  We have taken 15 pictures.  So,

 

We add variables the same way.  So,

Example Question #51 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

When adding variables, we will look at the variables like objects.  So, in the problem

we can think of p as pancakes.  So, we can write it like

We can read the problem like this:  We are eating breakfast.  We are very hungry, and we decided to eat 2 pancakes.  We are still hungry, so we eat 3 more pancakes.  How many pancakes have we eaten for breakfast? We have eaten 5 pancakes.

We can add variables the same way.

Example Question #52 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

To add variables, we will look at the variables like they are objects.  So, in the problem

we can think of the variable p as pretzels.  So, we can write it like

We can read the problem like this:  We eat 2 pretzels.  They are really good, so we eat 5 more pretzels.  How many pretzels have we eaten in total?  We have eaten 7 pretzels.

 

We can add variables the same way.  So,

Example Question #53 : How To Add Variables

Combine the following:

Possible Answers:

Correct answer:

Explanation:

When adding terms with variables, we can only combine the terms with like variables.  So, we get

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