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HSPT Math : Fractions

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #361 : Arithmetic

Evaluate:

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

Possible Answers:

$\frac{1}{3}$

$\frac{1}{108}$

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 #72 : Fractions

Evaluate:

$6.51 + 4.2 \div 14$

Possible Answers:

6.81

6.54

7.65

9.51

0.765

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 #73 : Fractions

Evaluate:

$80.8 + 6.4 \div 0.16$

Possible Answers:

120.8

480.8

54.5

84.8

545

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 #74 : Fractions

Evaluate:

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

Possible Answers:

$\frac{100}{27}$

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{27}{100}$

$\frac{21}{20}$

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 #13 : Fractions

Evaluate:

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

Possible Answers:

$\frac{3}{4}$

$1 \frac{1}{3}$

$\frac{2}{3}$

$1 \frac{1}{2}$

$1 \frac{2}{3}$

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 #75 : Fractions

Evaluate:

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

Possible Answers:

$\frac{3}{4}$

$\frac{2}{3}$

$1 \frac{2}{3}$

$1 \frac{1}{2}$

$1 \frac{1}{3}$

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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Example Question #362 : Arithmetic

Which of the following yields the largest number?

Possible Answers:

$\frac{1}{3}\div\frac{1}{6}$

$\frac{1}{3}+\frac{1}{6}$

$\frac{1}{3}\times\frac{1}{6}$

$\frac{1}{3}-\frac{1}{6}$

Correct answer:

$\frac{1}{3}\div\frac{1}{6}$

Explanation:

When dividing by a fraction between 0 and 1, the answer will always get larger. In this case it is larger than simply adding the two fractions together.

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Example Question #363 : Arithmetic

Divide: $1.2 \div 64$

Possible Answers:

0.1875

0.00768

0.01875

0.0768

0.001875

Correct answer:

0.01875

Explanation:

Simply use the long division process. The quotient will be:

$12 \div 64 = 0.01875$

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Example Question #17 : Fractions

Simplify:

$\frac{4\frac{1}{2} }{\frac{3}{10}}$

Possible Answers:

$\frac {1}{15}$

$\frac {5}{9}$

$1 \frac {4}{5}$

Correct answer:

Explanation:

Rewrite as a division and evaluate:

$\frac{4\frac{1}{2} }{\frac{3}{10}}$

$= 4\frac{1 }{2} \div \frac{3}{10}$

$= \frac{1 + 4 \times 2}{2} \div \frac{3}{10}$

$= \frac{9}{2} \div \frac{3}{10}= \frac{9}{2} \times \frac{10}{3}= \frac{3}{1} \times \frac{5}{1}= \frac{15}{1} = 15$

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Example Question #17 : Fractions

Simplify:

$\frac{5 \frac{1}{4}}{1 \frac{5}{9}}$

Possible Answers:

$\frac{6}{49}$

$3 \frac{3}{8}$

$\frac{8}{27}$

$8 \frac{1}{6}$

$5 \frac{9}{20}$

Correct answer:

$3 \frac{3}{8}$

Explanation:

Rewrite as a division, then solve:

$\frac{5 \frac{1}{4}}{1 \frac{5}{9}}$

$= 5 \frac{1}{4} \div 1 \frac{5}{9}$

$= \frac{1 + 5 \times 4}{4} \div \frac{5 + 1 \times 9}{9}$

$= \frac{21}{4} \div \frac{14}{9}$

$= \frac{21}{4} \times \frac{9}{14}$

$= \frac{3}{4} \times \frac{9}{2}$

$= \frac{3 \times 9}{4 \times 2} = \frac{27}{8} = 3 \frac{3}{8}$

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HSPT Math : Fractions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #361 : Arithmetic

Example Question #72 : Fractions

Example Question #73 : Fractions

Example Question #74 : Fractions

Example Question #13 : Fractions

Example Question #75 : Fractions

Example Question #362 : Arithmetic

Example Question #363 : Arithmetic

Example Question #17 : Fractions

Example Question #17 : Fractions

All HSPT Math Resources

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