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HSPT Math : HSPT Mathematics

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Example Questions

Example Question #971 : Hspt Mathematics

$\frac{3}{7}$ is the square root of what number?

Possible Answers:

$\frac{9}{49}$

$\frac{3}{14}$

$\frac{6}{7}$

$\frac{9}{7}$

Correct answer:

$\frac{9}{49}$

Explanation:

The square root of a number is the number which, when squared - multiplied by itself - yields that number as its result. Therefore, $\frac{3}{7}$ is the square root of

$\frac{3}{7} \times \frac{3}{7} = \frac{3 \times 3 }{7 \times 7} = \frac{9}{49}$

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Example Question #84 : Fractions

Define an operation $\bigstar$ on the real numbers as follows:

$a \bigstar b = \frac{a-1}{b-2}$

Which of the following is an undefined quantity?

Possible Answers:

$3 \bigstar 2$

$1 \bigstar 4$

$2 \bigstar 1$

$3 \bigstar 0$

Correct answer:

$3 \bigstar 2$

Explanation:

$a \bigstar b = \frac{a-1}{b-2}$ ; since the divisor in a division expression cannot be equal to 0, it cannot hold that

b - 2 =0 , or

b= 2 .

In other words, $a \bigstar b$ is undefined if and only if b= 2 .

The only choice in which this holds is $3 \bigstar 2$ .

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Example Question #972 : Hspt Mathematics

Which of the following is the square root of 0.36?

Possible Answers:

$\frac{3}{5}$

$\frac{9}{50}$

$\frac{3}{50}$

$\frac{18}{25}$

Correct answer:

$\frac{3}{5}$

Explanation:

$0.36 = \frac{36}{100} = \frac{36 \div 4}{100 \div 4} = \frac{9}{25}$

The square root of 0.36 is therefore the square root of $\frac{9}{25}$ . The square root of a fraction whose numerator and denominator are both perfect squares can be found as follows:

$\sqrt{\frac{9}{25} } = \frac{\sqrt{9}}{\sqrt{25}} = \frac{3}{5}$

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Example Question #973 : Hspt Mathematics

Solve:

$\frac{4}{5}*\frac{8}{7}$

Possible Answers:

$\frac{32}{35}$

$\frac{5}{6}$

$\frac{34}{35}$

$\frac{6}{7}$

Correct answer:

$\frac{32}{35}$

Explanation:

To multiple fractions, you just multiply the numerators together and the denominators together.

This gives you

4*8=32 as a numerator

and

5*7=35 as a denominator.

Your final answer would be $\frac{32}{35}$ .

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Example Question #91 : Fractions

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

Which of the following is true of ?

Possible Answers:

45 < A < 46

43 < A < 44

42 < A < 43

44 < A < 45

Correct answer:

42 < A < 43

Explanation:

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

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

$= \frac{15}{2} \times \frac{17}{3}$

$= \frac{255}{6}$

Since $255 \div 6 = 42 \textup{ R }3$ ,

$42 < \frac{255}{6} < 43$

The correct choice is

42 < A < 43 .

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Example Question #92 : Fractions

$A = -1 \frac{1}{3 }$

Which of the following is the greatest number?

Possible Answers:

-3 - A

$-3 \cdot A$

$-3 \div A$

-3+A

Correct answer:

$-3 \cdot A$

Explanation:

$-3+ A = -3 +\left ( -1\frac{1}{3} \right ) = - \left ( 3+ 1\frac{1}{3} \right ) = - 4 \frac{1}{3}$ ,

$-3 - A = -3 - \left ( -1 \frac{1}{3}\right ) = -3+ 1 \frac{1}{3} = - \left ( 3- 1 \frac{1}{3} \right )=- 1 \frac{2}{3}$

$-3 \cdot A= -3 \cdot \left ( -\frac{4}{3} \right ) = 3 \cdot \frac{4}{3} = 4$

$-3 \div A = -3 \div \left ( -\frac{4}{3} \right ) = 3 \div \frac{4}{3} = 3 \cdot \frac{3}{4} = \frac{9}{4} = 2 \frac{1}{4}$ .

The correct response is $-3 \cdot A$ .

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Example Question #973 : Hspt Mathematics

Solve this problem:

$\frac{2}{9}*\frac{3}{7}$

Possible Answers:

$\frac{1}{10}$

$\frac{2}{21}$

$\frac{14}{27}$

$\frac{5}{16}$

Correct answer:

$\frac{2}{21}$

Explanation:

To multiple fractions, you just have to multiple across.

First multiple the numerators

(2*3=6) .

Then do the same for the denominators

(9*7=63) .

This means the final answer after simplifying is

$\frac{6}{63}=\frac{2\cdot 3}{21\cdot 3}=\frac{2}{21}$ .

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Example Question #94 : Fractions

$\frac{7}{8} \div \frac{3}{4}$

Possible Answers:

$1\frac{1}{6}$

$1\frac{1}{2}$

$\frac{3}{7}$

$\frac{21}{32}$

Correct answer:

$1\frac{1}{6}$

Explanation:

$\frac{7}{8} \div \frac{3}{4}$

To divide a fraction, multiply by it's multiplicative inverse, or reciprocal.

The multiplicative inverse or the reciprocal is for the fraction that comes after the division sign. The division sign will then change to a multiplication sign.

The multiplicative inverse or the reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$ .

$\frac{7}{8\ }\times \frac{4}{3} = \frac{28}{24}$

$\frac{28}{24} = 1 \frac{4}{24}$

Reduce to simplest form by dividing the numerator and the denominator by the Greatest Common Factor of 4 and 24, which is 4.

$4\div4 =1$

$24\div4=6$

$1\frac{4}{24} = 1\frac{1}{6}$

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Example Question #93 : Fractions

$\frac{3}{4} \div 6$

Possible Answers:

$\frac{1}{8}$

$2\frac{1}{2}$

$4\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{8}$

Explanation:

$\frac{3}{4} \div 6$

To divide a fraction, multiply by it's multiplicative inverse, or reciprocal.

The multiplicative inverse or the reciprocal is for the fraction that comes after the division sign. The division sign will then change to a multiplication sign.

The multiplicative inverse or the reciprocal of $\frac{6}{1}$ is $\frac{1}{6}$ .

$\frac{3}{4} \times \frac{1}{6} = \frac{3}{24}$

Reduce to simplest form by dividing the numerator and the denominator by the Greatest Common Factor of 3 and 24, which is 3.

$\frac{3}{24} = \frac{1}{8}$

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Example Question #96 : Fractions

$-\frac{3}{8} \div \frac{9}{10}$

Possible Answers:

$-\frac{5}{12}$

$\frac{27}{80}$

$\frac{5}{12}$

$-\frac{27}{80}$

Correct answer:

$-\frac{5}{12}$

Explanation:

$-\frac{3}{8} \div \frac{9}{10}$

To divide fractions, take the multiplicative inverse or reciprocal of the fraction that comes after the division sign and then change the division sign to a multiplication sign and multiply.

The multiplicative inverse of $\frac{9}{10} = \frac{10}{9}$ .

$-\frac{3}{8} \times \frac{10}{9 } = -\frac{30}{72}$ (A negative times a positive is a negative.)

Reduce to simplest form by dividing the numerator and the denominator by the Greatest Common Factor of 30 and 72, which is 6.

$-\frac{30\div 6}{72\div 6} = -\frac{5}{12}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #971 : Hspt Mathematics

Example Question #84 : Fractions

Example Question #972 : Hspt Mathematics

Example Question #973 : Hspt Mathematics

Example Question #91 : Fractions

Example Question #92 : Fractions

Example Question #973 : Hspt Mathematics

Example Question #94 : Fractions

Example Question #93 : Fractions

Example Question #96 : Fractions

All HSPT Math Resources

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