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SSAT Middle Level Math : Variables

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Example Questions

Example Question #1 : Variables

Which of the following is NOT the same as

$z\times \frac{(2x+3y)}{3}$

Possible Answers:

$z\times(\frac{2x}{3}+y)$

$\frac{2zx+3zy}{3}$

$\frac{z}{3}\times(2x+3y)$

$\frac{2zx}{3}+zy$

$\frac{2zx +zy}{3}$

Correct answer:

$\frac{2zx +zy}{3}$

Explanation:

The answer shows that the 3 in front of the has been cancelled, but not removed from the denomitator for the .

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Example Question #2 : Variables

Simplify: -7 (3x - 11)

Possible Answers:

-21x + 77

-21x+11

-21x-11

21x-77

-21x-77

Correct answer:

-21x + 77

Explanation:

Apply the distributive property:

$-7 (3x - 11) = -7 \cdot 3x - \left (-7 \right ) \cdot 11 = -7 \cdot 3x + 7\cdot 11= -21x + 77$

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Example Question #3 : Variables

Simplify: -5 (-3x + 13)

Possible Answers:

-15x + 13

-15x - 65

-15x - 13

15x + 65

15x - 65

Correct answer:

15x - 65

Explanation:

Apply the distributive property:

$-5 (-3x + 13) = -5 (-3x) + \left (-5 \right ) \cdot 13= 5\cdot 3x - 5\cdot 13 = 15x -65$

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Example Question #4 : Variables

Simplify: $-6 \left ( 5x - 3y - 9 \right )$

Possible Answers:

-30x - 3y - 9

-30x + 3y + 9

-30x - 18y + 54

-30x + 18y + 54

-30x + 18y - 54

Correct answer:

-30x + 18y + 54

Explanation:

Apply the distributive property:

$-6 \left ( 5x - 3y - 9 \right )= -6 \cdot 5x - \left (-6 \right ) \cdot 3y - \left (-6 \right ) \cdot 9$

$= -6 \cdot 5x + 6 \cdot 3y + 6 \cdot 9$

= -30x + 18y + 54

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Example Question #5 : Variables

Simplify: $6 \left ( 5x - 3y + 7 \right )$

Possible Answers:

30x - 18y + 42

30x - 18y + 7

30x - 18y - 7

30x - 18y - 42

30x - 6y + 7

Correct answer:

30x - 18y + 42

Explanation:

Apply the distributive property:

$6 \left ( 5x - 3y + 7 \right ) = 6 \cdot 5x - 6 \cdot 3y + 6 \cdot 7=30x - 18y + 42$

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Example Question #6 : Operations

Shaun has twice as much money as Jessica. Jessica has one third as much money as Chris. Shaun has half as much money as Carmen. Who has the most money?

Possible Answers:

Shaun

Carmen

Both Shaun and Carmen

Jessica

Chris

Correct answer:

Carmen

Explanation:

In order to figure out who has the most money, we must organize the data we have. Since Shaun has more money than Jessica, let us use Jessica as our baseline. So, if the money that Jessica has is represented by , the money Shaun has will be because he has twice as much money as Jessica.

Jessica =

Shaun =

Next, we know that Jessica has one third as much money as Chris. In other words, Chris has three times as much money as Jessica. This can be represented by . We then learn that Shaun has half as much money as Carmen or, in other words, Carmen has two times the amount of money Shaun has. Since Shaun has dollars, that must mean Carmen has dollars because $2\times 2m = 4m$ . So, by comparing everyone side-by-side, we can see that Carmen has the most money as she has four times the amount of money that Jessica has.

Jessica =

Shaun =

Chris =

Carmen =

Carmen is the answer.

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Example Question #7 : Operations

Given x = 3 , y=6 , and z=3 , compute xyz .

Possible Answers:

Correct answer:

Explanation:

xyz refers to the product of the three variables: $3\cdot 6\cdot 3=54$ .

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Example Question #8 : Operations

Simplify:

$4m\cdot3m$

Possible Answers:

$6m^{2}$

$12m^{2}$

$12m^{3}$

24m

12m

Correct answer:

$12m^{2}$

Explanation:

To solve, you can use the commutative and associative properties of multiplication to group like-terms together.

$4m\cdot3m=4\times m\times 3\times m=4\times3\times m\times m$

The 4 and 3 should be first multiplied, resulting in 12.

$12\times m\times m$

Next should be multiplied by , giving us $m^{2}$ .

$12\times m^2$

12 times $m^{2}$ is equal to $12m^{2}$ .

Therefore, the correct answer is $12m^{2}$ .

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Example Question #6 : How To Multiply Variables

Simplify:

3a(2a+4)-7

Possible Answers:

$6a^{2}+12a$

$6a^{2}+12a-7$

6a+12a-7

$a^{2}+12a-7$

$6a^{2}+12-7a$

Correct answer:

$6a^{2}+12a-7$

Explanation:

When simplifying this expression, the first step is to apply the distributive property.

3a(2a+4)-7

$(3a\times2a)+(3a\times4)-7$

$6a^{2}+12a-7$

Next, we assert whether the expression can be reduced further. It cannot, as there are no like-terms to combine.

Therefore, the correct answer is $6a^{2}+12a-7$ .

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Example Question #5 : How To Multiply Variables

Suppose you know the values of all variables in the expression

$x \cdot\left ( y + b \right )^{2}$

and you want to evaluate the expression.

In which order will you carry out the operations?

Possible Answers:

Adding, squaring, multiplying

Squaring, multiplying, adding

Adding, multiplying, squaring

Multiplying, squaring, adding

Multiplying, adding, squaring

Correct answer:

Adding, squaring, multiplying

Explanation:

By the order of operations, the operation inside grouping symbols, which here is addition, takes precendence, followed by, in order, squaring and multiplication.

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SSAT Middle Level Math : Variables

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Variables

Example Question #2 : Variables

Example Question #3 : Variables

Example Question #4 : Variables

Example Question #5 : Variables

Example Question #6 : Operations

Example Question #7 : Operations

Example Question #8 : Operations

Example Question #6 : How To Multiply Variables

Example Question #5 : How To Multiply Variables

All SSAT Middle Level Math Resources

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