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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #951 : Hspt Mathematics

Evaluate:

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

Possible Answers:

$\frac{5}{3}$

$\frac{8}{25}$

$\frac{1}{15}$

$\frac{3}{5}$

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 #486 : Numbers And Operations

Evaluate:

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

Possible Answers:

$\frac{1}{10}$

$\frac{4}{5}$

$\frac{5}{2}$

$\frac{2}{5}$

$\frac{5}{4}$

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 #487 : Numbers And Operations

Evaluate:

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

Possible Answers:

$\frac{1}{21}$

$\frac{3}{8}$

$\frac{3}{7}$

$\frac{8}{3}$

$\frac{7}{3}$

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 #488 : Numbers And Operations

Evaluate:

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

Possible Answers:

$\frac{1}{36}$

$\frac{1}{4}$

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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Example Question #489 : Numbers And Operations

Evaluate:

$18 \div \frac{1}{6}$

Possible Answers:

$\frac{1}{3}$

108

$\frac{1}{108}$

Correct answer:

108

Explanation:

$18 \div \frac{1}{6} = \frac{18}{1} \div \frac{1}{6} = \frac{18}{1} \times \frac{6}{1} = 18 \times 6 = 108$

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Example Question #491 : Numbers And Operations

Evaluate:

$6.51 + 4.2 \div 14$

Possible Answers:

0.765

6.54

9.51

7.65

6.81

Correct answer:

6.81

Explanation:

By order of operations, divide first. Since the divisor is a whole number, divide as is:

$4.2 \div 14 = 0.3$

Add this quotient to 6.51.

$6.51 + 4.2 \div 14 = 6.51 + 0.3$

Add vertically, aligning the decimal points (appending a zero to 0.3):

6.51

$\underline{0.30}$

6.81

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Example Question #492 : Numbers And Operations

Evaluate:

$80.8 + 6.4 \div 0.16$

Possible Answers:

545

480.8

84.8

54.5

120.8

Correct answer:

120.8

Explanation:

By order of operations, divide first. Move the decimal point right two places in both dividend and divisor to make the divisor a whole number, and divide the resulting whole numbers:

$6.4 \div 0.16 = 640 \div 16 = 40$

Add this quotient to 80.8:

$80.8 + 6.4 \div 0.16 = 80.8 + 40$

Append a decimal point and a zero to 40, align the decimal points, and add:

80. 8

$\underline{40.0}$

120.8

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Example Question #493 : Numbers And Operations

Evaluate:

$\dpi{150} \frac{\frac{3}{5}}{\frac{9}{20}}$

Possible Answers:

$\frac{100}{27}$

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{21}{20}$

$\frac{27}{100}$

Correct answer:

$\frac{4}{3}$

Explanation:

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and multply across:

$\dpi{150} \frac{\frac{3}{5}}{\frac{9}{20}}$ $= \frac{3}{5} \div \frac{9}{20} = \frac{3}{5} \cdot \frac{20}{9} = \frac{1}{1} \cdot \frac{4}{3} = \frac{4}{3}$

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Example Question #494 : Numbers And Operations

Evaluate:

$\frac{7\frac{1}{2}}{5 }$

Possible Answers:

$\frac{2}{3}$

$1 \frac{2}{3}$

$1 \frac{1}{2}$

$1 \frac{1}{3}$

$\frac{3}{4}$

Correct answer:

$1 \frac{1}{2}$

Explanation:

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and multply across:

$\frac{7\frac{1}{2}}{5 } = 7\frac{1}{2} \div 5 = \frac{15} {2} \div \frac{5}{1} = \frac{15} {2} \cdot \frac{1} {5}=\frac{3} {2} \cdot \frac{1} {1} =\frac{3} {2}$

Since $3 \div 2 = 1 \textrm{ R }1$ ,

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

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Example Question #495 : Numbers And Operations

Evaluate:

$\frac{6}{4 \frac{1}{2}}$

Possible Answers:

$1 \frac{2}{3}$

$1 \frac{1}{3}$

$\frac{3}{4}$

$1 \frac{1}{2}$

$\frac{2}{3}$

Correct answer:

$1 \frac{1}{3}$

Explanation:

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and finally multiply across:

$\frac{6}{4 \frac{1}{2}} = 6 \div 4 \frac{1}{2} = \frac{6}{1}\div \frac{9}{2}= \frac{6}{1}\cdot \frac{2}{9} = \frac{2}{1}\cdot \frac{2}{3} = \frac{2\cdot 2}{1\cdot 3} = \frac{4}{3}$

Since $4 \div 3 = 1 \textrm{ R }3$ ,

$\frac{4}{3} = 1 \frac{1}{3}$ ,

which is the correct answer.

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #951 : Hspt Mathematics

Example Question #486 : Numbers And Operations

Example Question #487 : Numbers And Operations

Example Question #488 : Numbers And Operations

Example Question #489 : Numbers And Operations

Example Question #491 : Numbers And Operations

Example Question #492 : Numbers And Operations

Example Question #493 : Numbers And Operations

Example Question #494 : Numbers And Operations

Example Question #495 : Numbers And Operations

All HSPT Math Resources

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