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HSPT Math : Concepts

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Example Questions

Example Question #1016 : Numbers And Operations

Evaluate:

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

Possible Answers:

-1.3

22.5

36.3

- 3.7

6.5

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 #3 : Multiplicative Identity Property

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

Possible Answers:

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

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

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

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

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

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 #351 : Arithmetic

is larger than 0. Which of the following could be equal to $3 \times Z$ ?

II. $2\frac{2}{7}$

III.

Possible Answers:

I, II and III

III only

II only

I only

I and II

Correct answer:

I, II and III

Explanation:

All of the answers can be divided by 3 to yield an answer larger than zero. In fact, any positive number would be a viable answer.

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Example Question #352 : Arithmetic

Express the quotient as a fraction in lowest terms:

$5 \frac{3}{5} \div 4 \frac{1}{5}$

Possible Answers:

$1 \frac{1}{3}$

$\frac{4}{5}$

$1 \frac{1}{4}$

$\frac{3}{4}$

$1 \frac{3}{4}$

Correct answer:

$1 \frac{1}{3}$

Explanation:

Rewrite the mixed fractions as improper fractions, change to a multiplication by inverting the second, cross-cancel, and multiply across:

$5 \frac{3}{5} \div 4 \frac{1}{5} = \frac{28}{5 } \div \frac{21}{5 } = \frac{28}{5 } \cdot \frac{5}{21 }= \frac{4}{1 } \cdot \frac{1}{3 }= \frac{4}{3 }$

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Example Question #353 : Arithmetic

Express the quotient as a fraction in lowest terms:

$4 \frac{1}{5} \div 5 \frac{3}{5}$

Possible Answers:

$1 \frac{1}{3}$

$1 \frac{1}{4}$

$\frac{6}{7}$

$\frac{5}{7}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

Rewrite the mixed fractions as improper fractions, change to a multiplication by inverting the second, cross-cancel, and multiply across:

$4 \frac{1}{5} \div 5 \frac{3}{5} = \frac{21}{5} \div \frac{28}{5} = \frac{21}{5} \cdot \frac{5}{28} = \frac{3}{1} \cdot \frac{1}{4} = \frac{3}{4}$

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Example Question #354 : Arithmetic

Evaluate:

$\frac{12}{5} \div \frac{4}{25}$

Possible Answers:

$\frac{8}{25}$

$\frac{3}{5}$

$\frac{1}{15}$

$\frac{5}{3}$

Correct answer:

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{12}{5} \div \frac{4}{25} = \frac{12}{5} \times \frac{25}{4} = \frac{3}{1} \times \frac{5}{1} = \frac{15}{1} = 15$

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Example Question #355 : Arithmetic

Evaluate:

$\frac{4}{25} \div \frac{12}{5}$

Possible Answers:

$\frac{1}{15}$

$\frac{3}{5}$

$\frac{5}{3}$

$\frac{8}{25}$

Correct answer:

$\frac{1}{15}$

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{4}{25} \div \frac{12}{5} = \frac{4}{25} \times \frac{5}{12} = \frac{1}{5} \times \frac{1}{3} = \frac{1}{15}$

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Example Question #356 : Arithmetic

Evaluate:

$\frac{5}{8} \div \frac{25}{16}$

Possible Answers:

$\frac{2}{5}$

$\frac{5}{4}$

$\frac{1}{10}$

$\frac{4}{5}$

$\frac{5}{2}$

Correct answer:

$\frac{2}{5}$

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{5}{8} \div \frac{25}{16} = \frac{5}{8} \times \frac{16}{25} = \frac{1}{1} \times \frac{2}{5} = \frac{2}{5}$

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Example Question #357 : Arithmetic

Evaluate:

$\frac{8}{5} \div \frac{24}{35}$

Possible Answers:

$\frac{8}{3}$

$\frac{3}{8}$

$\frac{1}{21}$

$\frac{3}{7}$

$\frac{7}{3}$

Correct answer:

$\frac{7}{3}$

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{8}{5} \div \frac{24}{35} = \frac{8}{5} \times \frac{35}{24} = \frac{1}{1} \times \frac{7}{3} =\frac{7}{3}$

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Example Question #358 : Arithmetic

Evaluate:

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

Possible Answers:

$\frac{1}{4}$

$\frac{1}{36}$

Correct answer:

Explanation:

$3 \div \frac{1}{12} = \frac{3}{1} \div \frac{1}{12} = \frac{3}{1}\times \frac{12}{1} = 3 \times 12 = 36$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1016 : Numbers And Operations

Example Question #3 : Multiplicative Identity Property

Example Question #351 : Arithmetic

Example Question #352 : Arithmetic

Example Question #353 : Arithmetic

Example Question #354 : Arithmetic

Example Question #355 : Arithmetic

Example Question #356 : Arithmetic

Example Question #357 : Arithmetic

Example Question #358 : Arithmetic

All HSPT Math Resources

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