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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 #1411 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Evaluate:

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

Possible Answers:

$4\sqrt{3}$

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

$\sqrt{3}$

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

$\frac{4}{3}$

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 #11 : How To Divide Fractions

Simplify:

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

Possible Answers:

$\frac{17}{7}$

$\frac{5}{6}$

$\frac{7}{17}$

$\frac{17}{6}$

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 #1413 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Evaluate:

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

Possible Answers:

$\frac{50}{6}$

$\frac{50}{3}$

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 #1414 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Simplify:

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

Possible Answers:

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

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

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

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

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

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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Example Question #321 : Arithmetic

Which of the following is the reciprocal of $-1 \frac {4}{5}$ ?

Possible Answers:

$\frac {5}{9}$

$-\frac {5}{9}$

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

$1 \frac {4}{5}$

Correct answer:

$-\frac {5}{9}$

Explanation:

First, rewrite this as an improper fraction:

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

The reciprocal of an improper fraction can be found by switching its numerator and denominator, retaining the negative sign, so the reciprocal is $-\frac {5}{9}$ .

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Example Question #322 : Arithmetic

Which of the following is the reciprocal of 2.8?

Possible Answers:

$\frac{5}{14}$

$2 \frac{4}{5}$

$\frac{2}{7}$

$-2 \frac{4}{5}$

Correct answer:

$\frac{5}{14}$

Explanation:

First, rewrite this as an improper fraction:

$2.8 = \frac{28}{10} = \frac{28\div 2}{10\div 2} = \frac{14}{5}$

The reciprocal of an improper fraction can be found by switching its numerator and denominator, so the reciprocal is $\frac{5}{14}$ .

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Example Question #323 : Arithmetic

Solve:

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

Possible Answers:

$\frac{3}{2}$

$\frac{1}{2}$

$\frac{15}{7}$

$\frac{3}{35}$

Correct answer:

$\frac{15}{7}$

Explanation:

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

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Example Question #324 : Arithmetic

Which of the following is the reciprocal of 31.25?

Possible Answers:

0.032

0.036

0.024

0.028

Correct answer:

0.032

Explanation:

Rewrite 31.25 as a fraction:

$31.25 = \frac{3,125}{100} = \frac{3,125\div 25}{100\div 25} = \frac{125}{4}$

Exchange the positions of the numerator and the denominator to get $\frac{4}{125}$ . Now divide 4 by 125:

$\frac{4}{125} = 4 \div 125 = 0.032$

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Example Question #325 : Arithmetic

Solve:

$\frac{9}{10}\div \frac{3}{5}=$

Possible Answers:

$\frac{3}{2}$

$\frac{5}{6}$

$\small \frac{6}{5}$

$\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

$\small \frac{9}{10}\div \frac{3}{5}=\frac{9}{10}\times\frac{5}{3}=\frac{45}{30}=\frac{3}{2}$

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Example Question #23 : How To Divide Fractions

$\frac{7}{49}\div \frac{2}{14}=$

Possible Answers:

$\frac{2}{94}$

196

$1\frac{3}{4}$

Correct answer:

Explanation:

Change division to multiplication by flipping the second fraction. Then, simplify and perform the multiplication.

$\frac{7}{49}\div \frac{2}{14}=$

$\frac{7}{49}\times \frac{14}{2}= \frac{1}{7}\times \frac{7}{1}=\frac{7}{7}=1$

The answer is 1.

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1411 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #11 : How To Divide Fractions

Example Question #1413 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1414 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #321 : Arithmetic

Example Question #322 : Arithmetic

Example Question #323 : Arithmetic

Example Question #324 : Arithmetic

Example Question #325 : Arithmetic

Example Question #23 : How To Divide Fractions

All HSPT Math Resources

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