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SSAT Middle Level Math : How to multiply fractions

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Example Questions

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Example Question #521 : Fractions

Raise to the fourth power.

Possible Answers:

-4,096

-65,536

4,096

65,536

Correct answer:

4,096

Explanation:

To raise a negative number to an even-numbered power, raise its absolute value to that power:

$(-8)^{4}= 8^{4} = 8 \times 8 \times 8 \times 8 = 4,096$

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Example Question #341 : Arithmetic

Evaluate:

$15 - \left ( \frac{2}{3} \times 3 - \frac{4}{3}\right )$

Possible Answers:

$42\frac{2}{3}$

$11\frac{2}{3}$

$14 \frac{1}{3}$

$13\frac{8}{9}$

Correct answer:

$14 \frac{1}{3}$

Explanation:

By the order of operations, carry out the operations in parentheses first; since there is a multiplication and a subtraction present, carry them out in that order. Finally, carry out the remaining subtraction:

$15 - \left ( \frac{2}{3} \times 3 - \frac{4}{3}\right )$

$= 15 - \left ( 2- \frac{4}{3}\right )$

$= 15 - \frac{2}{3}$

$= 14 \frac{1}{3}$

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Example Question #1 : Multiplicative Inverse Property

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

Possible Answers:

$\frac{6}{7} \times \frac{7}{6} = 1$

$\frac{6}{7} \times 1 = \frac{6}{7}$

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

$\frac{6}{7} \times\left ( \frac{1}{4} \times \frac{3}{8} \right ) =\left ( \frac{6}{7} \times\frac{1}{4} \right ) \times \frac{3}{8}$

$\frac{6}{7} \times\frac{1}{4} = \frac{1}{4} \times \frac{6}{7}$

Correct answer:

$\frac{6}{7} \times \frac{7}{6} = 1$

Explanation:

The inverse property of multiplication states that for every real number, a number exists, called the multiplicative inverse, such that the number and its inverse have product 1. Of the statements given, only

$\frac{6}{7} \times \frac{7}{6} = 1$

demonstrates this property.

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Example Question #51 : Fractions

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

Possible Answers:

$\frac{16} {81}$

$\frac{81}{16}$

$\frac{16}{81}$

$- \frac{16}{81}$

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 #341 : Concepts

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

Possible Answers:

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

$\frac{243} {32}$

$-\frac{243} {32}$

$\frac{32}{243}$

$-\frac{32}{243}$

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 #1011 : Numbers And Operations

Raise to the fifth power.

Possible Answers:

-16,807

16,807

cannot be raised to the fifth power.

78,125

-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 #1012 : Numbers And Operations

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

Possible Answers:

$\$629.92$

$\$62.99$

$\$1,016$

$\$10,160$

The correct answer is not given among the other choices.

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 #54 : Fractions

Evaluate:

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

Possible Answers:

-1.3

6.5

22.5

- 3.7

36.3

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 #61 : Fractions

Evaluate:

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

Possible Answers:

6.5

22.5

36.3

- 3.7

-1.3

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 #1 : Multiplicative Identity Property

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

Possible Answers:

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

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

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

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

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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SSAT Middle Level Math : How to multiply fractions

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #521 : Fractions

Example Question #341 : Arithmetic

Example Question #1 : Multiplicative Inverse Property

Example Question #51 : Fractions

Example Question #341 : Concepts

Example Question #1011 : Numbers And Operations

Example Question #1012 : Numbers And Operations

Example Question #54 : Fractions

Example Question #61 : Fractions

Example Question #1 : Multiplicative Identity Property

All SSAT Middle Level Math Resources

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