ISEE Middle Level Math : How to subtract variables

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

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Example Questions

Example Question #2257 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Subtract the following:

\displaystyle 7b-4b

Possible Answers:

\displaystyle 4b

\displaystyle 3b^2

\displaystyle 6b

\displaystyle 3

\displaystyle 3b

Correct answer:

\displaystyle 3b

Explanation:

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

\displaystyle 7b-4b

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

\displaystyle 7 \text{ books} - 4 \text{ books}

We can read this as:  We have borrowed 7 books from the library.  We return 4 of those books to the library.  How many books do we have left?  We have 3 books.  So,

\displaystyle 7 \text{ books} - 4 \text{ books} = 3 \text{ books}

 

We can subtract variables the same way.  We get

\displaystyle 7b-4b=3b

Example Question #41 : How To Subtract Variables

Simplify the following:

\displaystyle 10c-4c

Possible Answers:

\displaystyle 6c^2

\displaystyle 5c

\displaystyle 4c

\displaystyle 6c

\displaystyle 6

Correct answer:

\displaystyle 6c

Explanation:

When subtracting variables, we can look at the variables as objects.  So, in the problem

\displaystyle 10c-4c

we can think of the variable as crackers.  So, we can write the problem like this:

\displaystyle 10\text{ crackers} - 4\text{ crackers}

Now, we can read the problem like this:  We have a plate with 10 crackers.  We go and eat 4 of the crackers.  How many crackers are left on the plate?  There are 6 crackers.  So,

\displaystyle 10\text{ crackers} - 4\text{ crackers} = 6\text{ crackers}

 

We can subtract variables the same way:

\displaystyle 10c-4c = 6c

Example Question #41 : How To Subtract Variables

Subtract the following:

\displaystyle 10b - 2b

Possible Answers:

\displaystyle 8b^2

\displaystyle 102b

\displaystyle 102

\displaystyle 8

\displaystyle 8b

Correct answer:

\displaystyle 8b

Explanation:

When subtracting variables, we can look at the variables like objects.  So, in the problem

\displaystyle 10b - 2b

we can think of the variable b as brownies.  So, we can write the problem like this:

\displaystyle 10 \text{ brownies} - 2 \text{ brownies}

We can read it like this:  You see there is a plate that contains 10 brownies.  You love brownies, so you eat 2 of them.  How many brownies are left on the plate?  There are 8 brownies left.

\displaystyle 10 \text{ brownies} - 2 \text{ brownies} = 8 \text{ brownies}

We can subtract variables the same way.

\displaystyle 10b - 2b = 8b

Example Question #141 : Operations

Subtract the following:

\displaystyle 10c-4c

Possible Answers:

\displaystyle 6

\displaystyle 104

\displaystyle 7c

\displaystyle 6c

\displaystyle 6c^2

Correct answer:

\displaystyle 6c

Explanation:

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

\displaystyle 10c-4c

we can think of the variable c as cookies.  So, we can write it like this:

\displaystyle 10 \text{ cookies} - 4 \text{ cookies}

We can read it like this:  There is a plate with 10 cookies on it.  They smell delicious, so we decide to eat 4 cookies.  How many cookies are left on the plate?  There are 6 cookies left on the plate.

\displaystyle 10 \text{ cookies} - 4 \text{ cookies} = 6 \text{ pretzels}

 

We can subtract variables the same way:

\displaystyle 10c-4c = 6c

Example Question #91 : Algebra

Simplify:

\displaystyle 53x - (21x - 33y) + 32y

Possible Answers:

\displaystyle 33x - y

\displaystyle 32xy

\displaystyle 33x +y

\displaystyle 88xy

Correct answer:

Explanation:

Begin by distributing the subtraction through the group:

\displaystyle 53x - 21x - (-33y) + 32y

Next, change the double negative to a positive:

 \displaystyle 32x + 65y

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