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SSAT Middle Level Math : Numbers and Operations

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

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Example Questions

Example Question #12 : How To Find Percentage

Assorted 1

What percent of the above figures are circles?

Possible Answers:

$40 \%$

$25 \%$

$75 \%$

$50 \%$

Correct answer:

$50 \%$

Explanation:

There are twelve figures, six of which are circles. This is

$\frac{6}{12} \times 100 \% = \frac{600}{12} \% = 50 \%$

of the figures.

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Example Question #16 : How To Find Percentage

is $\frac{1}{2} \%$ of .

is 2.5 % of .

What percent of is ?

Possible Answers:

$20 \%$

$5 \%$

$1 \frac{1}{4} \%$

$500 \%$

Correct answer:

$500 \%$

Explanation:

For the sake of simplicity, since this reasoning is independent of the actual value of , we will assume that C = 100 . Then is $\frac{1}{2} \%$ of 100, or simply $\frac{1}{2} = 0.5$ , and is 2.5% of 100, or simply 2.5. To find out what percent is of , evaluate:

$\frac{B}{A} \cdot 100 \% = \frac{2.5}{0.5} \cdot 100 \% = 5 \cdot 100 \% = 500 \%$

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Example Question #53 : Percentage

is 20% of and $\frac{1}{4} \%$ of .

What percent of is ?

Possible Answers:

$80 \%$

$8,000 \%$

$5 \%$

$1 \frac{1}{4} \%$

Correct answer:

$1 \frac{1}{4} \%$

Explanation:

20% of a number is $\frac{20}{100} = \frac{1}{5}$ of that number, so $S = \frac{1}{5} T$ . Equivalently,

$5 \cdot S =5 \cdot \frac{1}{5} T$

5S = T

$\frac{1}{4} \%$ of a number is $\frac{\frac{1}{4}}{100} = \frac{1}{4} \div 100 = \frac{1}{4} \times \frac{1}{100} = \frac{1}{4 00}$ of that number, so $S = \frac{1}{400 } U$ . Equivalently,

$400 \cdot S =400 \cdot \frac{1}{400 } U$

400 S = U

To find out what percent is of , evaluate:

$\frac{T}{U}\cdot 100 \% = \frac{5S}{400S} \cdot 100 \% = \frac{5}{400} \cdot 100 \% = \frac{500}{400} \% = \frac{5}{4} \% = 1 \frac{1}{4} \%$

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Example Question #1393 : Numbers And Operations

is 40% of . is 72% of .

What percent of is ?

Possible Answers:

$55 \frac{5}{9} \%$

$32 \%$

$112 \%$

$180 \%$

Correct answer:

$55 \frac{5}{9} \%$

Explanation:

is 40 % of , or $K = \frac{40}{100} L$ ; is 72% of , or $M = \frac{72}{100} L$ .

To find out what percent is of , evaluate:

$\frac{K}{M} \cdot 100 \%$

$= \frac{ \frac{40}{100} L }{ \frac{72}{100} L} \cdot 100 \%$

$= \frac{ \frac{40}{100} }{ \frac{72}{100} } \cdot 100 \%$

$= \frac{40 }{ 72} \cdot 100 \%$

$= \frac{5}{9} \cdot 100 \%$

$= \frac{500}{9} \%$

$= 55 \frac{5}{9} \%$ .

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Example Question #1 : Distributive Property

$3\times(4+\frac{1}{3})= ?$

Possible Answers:

$15+\frac{2}{3}$

$12+\frac{1}{3}$

Correct answer:

Explanation:

Using the distributive property we get: $(3\times4)+(3\times \frac{1}{3})=12+1=13$

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Example Question #2 : Distributive Property

Which of the following expressions is equivalent to the expression -6 (-3x+7) ?

Possible Answers:

18x -7

18x - 42

18x +7

18x +42

-18x - 42

Correct answer:

18x - 42

Explanation:

By the distributive property of multiplication over addition,

$-6 (-3x+7) = -6 \cdot (-3x) +(-6)\cdot 7 = 18x + (-42)= 18x - 42$

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Example Question #3 : Distributive Property

Which of the following expressions is equivalent to the expression 8 (-2x+7) ?

Possible Answers:

-16x+7

-16x+56

16x+7

-16x-56

16x-7

Correct answer:

-16x+56

Explanation:

By the distributive property of multiplication over addition,

$8 (-2x+7) = 8 (-2x)+8\cdot 7 = -16x + 56$

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Example Question #4 : How To Find The Distributive Property

Simplify the expression: 11y - 3y + 4y

Possible Answers:

-132y

18y

12y

-132y^3

Correct answer:

12y

Explanation:

Apply the distributive property:

11y - 3y + 4y

$= \left (11 - 3 + 4 \right ) y$

$= \left (8 + 4 \right ) y$

=12 y

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Example Question #3 : How To Find The Distributive Property

Simplify the expression: 7 (y+5)

Possible Answers:

7y+35

7y+12

7y+5

y+12

y+35

Correct answer:

7y+35

Explanation:

Apply the distributive property:

7 (y+5)

$= 7 \cdot y+7 \cdot5$

= 7 y+35

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Example Question #4 : How To Find The Distributive Property

Which of the following is an example of an application of the distributive property?

Possible Answers:

$13 \times (54 + 14) = 13 \times 54 + 13 \times 14$

$13 + (54 \times 14) = (54 \times 14) + 13$

$13 \times (54 \times 14) = \left (13 \times 54 \right ) \times 14$

$13 + (54 \times 14) = 13 +(14 \times 54)$

$1 \times (54 \times 14) =54 \times 14$

Correct answer:

$13 \times (54 + 14) = 13 \times 54 + 13 \times 14$

Explanation:

According to the distributive property, for any values of a,b,c ,

$a (b + c) = a \cdot b + a \cdot c$

If we set a=13,b=54,c=14 , this become the statement

$13 \times (54 + 14) = 13 \times 54 + 13 \times 14$ ,

so this is the correct choice.

All of the other statements are true for different reasons:

$13 \times (54 \times 14) = \left (13 \times 54 \right ) \times 14$ is true because of the associative property of multiplication.

$13 + (54 \times 14) = 13 +(14 \times 54)$ is true because of the commutative property of multiplication.

$13 + (54 \times 14) = (54 \times 14) + 13$ is true because of the commutative property of addition.

$1 \times (54 \times 14) =54 \times 14$ is true because of the identity property of multiplication.

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SSAT Middle Level Math : Numbers and Operations

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #12 : How To Find Percentage

Example Question #16 : How To Find Percentage

Example Question #53 : Percentage

Example Question #1393 : Numbers And Operations

Example Question #1 : Distributive Property

Example Question #2 : Distributive Property

Example Question #3 : Distributive Property

Example Question #4 : How To Find The Distributive Property

Example Question #3 : How To Find The Distributive Property

Example Question #4 : How To Find The Distributive Property

All SSAT Middle Level Math Resources

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