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HSPT Math : Arithmetic

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Example Questions

Example Question #311 : Concepts

$\dpi{100} 9\div \frac{1}{7}=$

Possible Answers:

$\dpi{100} \frac{7}{9}$

$\dpi{100} \frac{9}{7}$

$\dpi{100} 1$

$\dpi{100} 63$

Correct answer:

$\dpi{100} 63$

Explanation:

We never actually divide fractions. When given a division problem, you multiply by the reciprocal of the 2nd fraction.

So, $\dpi{100} 9\div \frac{1}{7}$ becomes $\dpi{100} 9\times \frac{7}{1}$ .

This is the same as $\dpi{100} 9\times7=63$

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Example Question #312 : Concepts

Divide: $0.17 \div 32$

Possible Answers:

0.001882

0.53125

0.0053125

0.01882

0.053125

Correct answer:

0.0053125

Explanation:

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

$0.17 \div 32 = 0.0053125$

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Example Question #313 : Concepts

Solve:

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

Possible Answers:

$\frac{4}{9}$

$\frac{9}{4}$

$\frac{1}{4}$

Correct answer:

$\frac{9}{4}$

Explanation:

$\frac{3}{4}\div\frac{1}{3}=\frac{3}{4}\times\frac{3}{1}=\frac{9}{4}$

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Example Question #314 : Concepts

Simplify: $\frac{\frac{2}{7}}{\frac{9}{14}}$

Possible Answers:

$\frac{5}{14}$

$\frac{9}{49}$

$\frac{4}{9}$

$\frac{2}{9}$

$\frac{13}{14}$

Correct answer:

$\frac{4}{9}$

Explanation:

Rewrite this as a division, dividing the numerator by the denominator:

$\frac{\frac{2}{7}}{\frac{9}{14}} = \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \times \frac{14}{9}= \frac{2}{1} \times \frac{2}{9}=\frac{2 \times 2}{1 \times 9}= \frac{4}{9}$

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Example Question #315 : Concepts

Simplify:

$\frac{\frac{2}{5}}{\frac{7}{10}}$

Possible Answers:

$\frac{7}{25}$

$\frac{7}{4}$

$\frac{25}{7}$

$\frac{4}{7}$

$\frac{11}{10}$

Correct answer:

$\frac{4}{7}$

Explanation:

Rewrite as a division, then solve:

$\frac{\frac{2}{5}}{\frac{7}{10}} = \frac{2}{5} \div \frac{7}{10} = \frac{2}{5} \times \frac{10}{7} = \frac{2}{1} \times \frac{2}{7} = \frac{4}{7}$

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Example Question #316 : Concepts

Simplify:

$\frac{ 2 \frac{1}{5}}{7 \frac{1}{3}}$

Possible Answers:

$\frac{4}{15}$

$\frac{1}{30}$

$3\frac{1}{3}$

$\frac{3}{10}$

Correct answer:

$\frac{3}{10}$

Explanation:

Rewrite as a division, then solve:

$\frac{ 2 \frac{1}{5}}{7 \frac{1}{3}}$

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

$= \frac{1+ 2 \times 5}{5} \div \frac{1+ 7 \times 3}{3}$

$= \frac{11}{5} \div \frac{22}{3}$

$= \frac{11}{5} \times \frac{3}{22}$

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

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Example Question #317 : Concepts

Evaluate:

$\sqrt{3}\div \frac{3}{4}$

Possible Answers:

$\sqrt{3}$

$\frac{3\sqrt{3}}{4}$

$4\sqrt{3}$

$\frac{4\sqrt{3}}{3}$

$\frac{4}{3}$

Correct answer:

$\frac{4\sqrt{3}}{3}$

Explanation:

To divide any number by a fraction, we can multiply that number by the reciprocal of the fraction. That means:

$\frac{a}{b}\div \frac{c}{d} = \frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}$

So we have:

$\sqrt{3}\div \frac{3}{4}= \frac{\sqrt{3}}{1}\times \frac{4}{3}$

$=\frac{4\sqrt{3}}{3}$

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Example Question #318 : Concepts

Simplify:

$\frac{2+\frac{5}{6}}{2-\frac{5}{6}}$

Possible Answers:

$\frac{5}{6}$

$\frac{17}{6}$

$\frac{17}{7}$

$\frac{7}{17}$

Correct answer:

$\frac{17}{7}$

Explanation:

Multiply each term by 6:

$\frac{2+\frac{5}{6}}{2-\frac{5}{6}} = \frac{12+5}{12-5}$

$=\frac{17}{7}$

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Example Question #319 : Concepts

Evaluate:

$8\frac{1}{3}\div \frac{1}{6}$

Possible Answers:

$\frac{50}{3}$

$\frac{50}{6}$

Correct answer:

Explanation:

A mixed number represents the sum of an integer and a fraction. In order to evaluate this problem first we need to change the mixed number ( $8\frac{1}{3}$ ) to an improper fraction. Improper fractions are fractions whose numerator is greater than the denominator. So we can write:

$8\frac{1}{3}=\frac{8\times 3+1}{3}=\frac{25}{3}$

Now we should evaluate $\frac{25}{3}\div \frac{1}{6}$ and we have:

$\frac{25}{3}\div \frac{1}{6}=\frac{25}{3}\times \frac{6}{1}=50$

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Example Question #320 : Concepts

Simplify:

$\frac{\frac{4}{x}}{(\frac{1}{x}-4x)}$

Possible Answers:

$\frac{4}{(1-4x^2)}$

$\frac{1}{(1-x^2)}$

$\frac{1}{(1+4x^2)}$

$\frac{4}{(1+4x^2)}$

$\frac{1}{(1-4x^2)}$

Correct answer:

$\frac{4}{(1-4x^2)}$

Explanation:

We can first find a common denominator for the expression in the numerator, which is . This gives us:

$\frac{\frac{4}{x}}{\left(\frac{1}{x}-\frac{4x^2}{x}\right)}=\frac{\frac{4}{x}}{\left(\frac{1-4x^2}{x}\right)}$

$=\frac{4}{x}\times \left(\frac{x}{1-4x^2}\right)$

$=\frac{4}{(1-4x^2)}$

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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #311 : Concepts

Example Question #312 : Concepts

Example Question #313 : Concepts

Example Question #314 : Concepts

Example Question #315 : Concepts

Example Question #316 : Concepts

Example Question #317 : Concepts

Example Question #318 : Concepts

Example Question #319 : Concepts

Example Question #320 : Concepts

All HSPT Math Resources

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