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SSAT Middle Level Math : Fractions

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Example Questions

Example Question #1011 : Numbers And Operations

Raise $- \frac{3}{2}$ to the fourth power.

Possible Answers:

$\frac{16} {81}$

$- \frac{16}{81}$

$\frac{81}{16}$

$\frac{16}{81}$

Correct answer:

$\frac{81}{16}$

Explanation:

To raise a negative number to an even-numbered power, raise its absolute value to that power. Also, to raise a fraction to a power, raise its numerator and its denominator to that power. Combine these ideas as follows:

$\left (- \frac{3}{2} \right )^{4} = \left( \frac{3}{2}\right )^{4} = \frac{3^{4} }{2^{4} } = \frac{ 3 \times 3\times 3 \times 3 }{ 2 \times 2 \times 2 \times 2 } \right ) = \frac{81}{16}$

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Example Question #531 : Fractions

Raise $- \frac{2}{3}$ to the fifth power.

Possible Answers:

$-\frac{32}{243}$

$\frac{243} {32}$

$- \frac{2}{3}$ cannot be raised to the fifth power.

$-\frac{243} {32}$

$\frac{32}{243}$

Correct answer:

$-\frac{32}{243}$

Explanation:

To raise a negative number to an odd-numbered power, raise its absolute value to that power, then make the sign negative. Also, to raise a fraction to a power, raise its numerator and its denominator to that power. Combine these ideas as follows:

$\left (- \frac{2}{3} \right )^{5} = - \left ( \frac{2}{3} \right )^{5} = - \left ( \frac{2^{5} }{3^{5} } \right ) = - \left ( \frac{2\times 2 \times 2 \times 2 \times 2 }{3 \times 3 \times 3\times 3 \times 3 } \right ) = -\frac{32}{243}$

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Example Question #531 : Fractions

Raise to the fifth power.

Possible Answers:

cannot be raised to the fifth power.

78,125

16,807

-16,807

-78,125

Correct answer:

-16,807

Explanation:

To raise a negative number to an odd-numbered power, raise its absolute value to that power, then make the sign negative:

$\left ( -7\right )^{5} = - \left ( 7^{5}\right ) = -(7 \times 7 \times 7 \times 7 \times 7) = - 16,807$

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Example Question #532 : Fractions

One euro is worth approximately $1.27. For how much American money can a French tourist expect to exchange 800 euros?

Possible Answers:

The correct answer is not given among the other choices.

$\$62.99$

$\$629.92$

$\$1,016$

$\$10,160$

Correct answer:

$\$1,016$

Explanation:

One Euro is equivalent to $1.27, so multiply the number of euros - 800 - by this conversion factor.

$\$1.27 \times 800 = \$ 1,016$

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Example Question #532 : Fractions

Evaluate:

$\left (20 - 7.5 \right )\times 3 - 1.2$

Possible Answers:

6.5

-1.3

36.3

- 3.7

22.5

Correct answer:

36.3

Explanation:

By the order of operations, carry out the operation in parentheses, which is the leftmost subtraction, then the multiplication, then the rightmost subtraction:

$\left (20 - 7.5 \right )\times 3 - 1.2$

$= 12.5 \times 3 - 1.2$

= 37.5 - 1.2

= 36.3

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Example Question #1011 : Numbers And Operations

Evaluate:

$20 - 7.5 \times\left ( 3 - 1.2 \right )$

Possible Answers:

-1.3

22.5

6.5

- 3.7

36.3

Correct answer:

6.5

Explanation:

By the order of operations, carry out the operation in parentheses, which is the rightmost subtraction, then the multiplication, then the leftmost subtraction:

$20 - 7.5 \times\left ( 3 - 1.2 \right )$

$= 20 - 7.5 \times 1.8$

= 20 - 13.5

= 6.5

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Example Question #534 : Fractions

Which of the following statements demonstrates the identity property of multiplication?

Possible Answers:

$\frac{2}{3} \times \frac{5}{7} = \frac{5}{7} \times \frac{2}{3}$

$\frac{2}{3} \times \frac{3}{2} = 1$

$\left (\frac{2}{3} \times \frac{5}{7} \right ) \times \frac{6}{11} = \frac{2}{3} \times\left ( \frac{5}{7} \times \frac{6}{11} \right )$

$\frac{2}{3} \times 1 = \frac{2}{3}$

None of the examples in the other responses demonstrates the identity property of multiplication.

Correct answer:

$\frac{2}{3} \times 1 = \frac{2}{3}$

Explanation:

The identity property of multiplication states that there is a number 1, called the multiplicative identity, that can be multiplied by any number to obtain that number. Of the four statements,

$\frac{2}{3} \times 1 = \frac{2}{3}$

demonstrates this property.

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Example Question #13 : Concepts

Evaluate:

$20.1 \cdot (-20.3)$

Possible Answers:

-40.803

-480.3

-408.3

-408.03

-40.83

Correct answer:

-408.03

Explanation:

The product of two numbers of unlike sign is the (negative) opposite of the product of their absolute values.

$20.1 \cdot (-20.3) = - \left (20.1 \cdot 20.3 \right )$

There are a total of two digits to the right of the two decimal points. Therefore, the product can be calculated by multiplying 201 by 203, then placing the decimal point so that there are three digits at right.

$201 \cdot 203 = 40,803 \Rightarrow 20.1 \cdot 20.3 = 408.03$

Since we need to affix a negative symbol in front, the answer is -408.03

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Example Question #21 : How To Multiply Fractions

$\small \frac{6}{7}\times\frac{1}{2}$

Possible Answers:

$\small \frac{1}{2}$

$\small \frac{2}{7}$

$\small \frac{1}{5}$

$\small \frac{3}{7}$

$\small \frac{2}{3}$

Correct answer:

$\small \frac{3}{7}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{6}{7}\times\frac{1}{2}=\frac{6}{14}$

$\small \frac{6}{14}$ can be reduced by dividing both sides by $\small 2$

$\small \small \frac{6}{14}\div\frac{2}{2}=\frac{3}{7}$

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Example Question #2 : Multiply A Fraction Or Whole Number By A Fraction: Ccss.Math.Content.5.Nf.B.4

$\small \frac{1}{2}\times\frac{5}{11}$

Possible Answers:

$\small \frac{5}{22}$

$\small \frac{6}{11}$

$\small \frac{1}{4}$

$\small \frac{5}{7}$

$\small \frac{2}{3}$

Correct answer:

$\small \frac{5}{22}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{1}{2}\times\frac{5}{11}=\frac{5}{22}$

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SSAT Middle Level Math : Fractions

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #1011 : Numbers And Operations

Example Question #531 : Fractions

Example Question #531 : Fractions

Example Question #532 : Fractions

Example Question #532 : Fractions

Example Question #1011 : Numbers And Operations

Example Question #534 : Fractions

Example Question #13 : Concepts

Example Question #21 : How To Multiply Fractions

Example Question #2 : Multiply A Fraction Or Whole Number By A Fraction: Ccss.Math.Content.5.Nf.B.4

All SSAT Middle Level Math Resources

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