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HSPT Math : Concepts

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Example Questions

Example Question #381 : Arithmetic

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

Which of the following is true of ?

Possible Answers:

44 < A < 45

42 < A < 43

45 < A < 46

43 < A < 44

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 #976 : Hspt Mathematics

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

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 #92 : Fractions

Solve this problem:

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

Possible Answers:

$\frac{1}{10}$

$\frac{5}{16}$

$\frac{2}{21}$

$\frac{14}{27}$

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 #383 : Arithmetic

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

Possible Answers:

$\frac{3}{7}$

$\frac{21}{32}$

$1\frac{1}{6}$

$1\frac{1}{2}$

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 #979 : Hspt Mathematics

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

Possible Answers:

$2\frac{1}{2}$

$\frac{1}{8}$

$\frac{1}{2}$

$4\frac{1}{2}$

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 #384 : Arithmetic

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

Possible Answers:

$\frac{5}{12}$

$-\frac{5}{12}$

$-\frac{27}{80}$

$\frac{27}{80}$

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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Example Question #385 : Arithmetic

$-3\frac{1}{4} \div 8\frac{2}{3}$

Possible Answers:

$-1\frac{3}{8}$

$-\frac{3}{8}$

$1\frac{3}{8}$

$\frac{3}{8}$

Correct answer:

$-\frac{3}{8}$

Explanation:

$-3\frac{1}{4} \div 8\frac{2}{3}$

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

Change all mixed numbers to improper fractions:

$-3\frac{1}{4}=-\frac{(4\times3 )+1}{4} = -\frac{13}{4}$

$8\frac{2}{3} =\frac{(3\times 8)+2}{3} = \frac{26}{3}$

The multiplicative inverse or reciprocal of $\frac{26}{3} = \frac{3}{26}$

$-\frac{13}{4} \times \frac{3}{26} = -\frac{39}{104}$ 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 39 and 104, which is 12.

$-\frac{39\div 3}{104\div 3} = -\frac{3}{8}$

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Example Question #386 : Arithmetic

Evaluate $x\div y$ if $x = -\frac{5}{12}$ and $y = \frac{5}{8}$

Possible Answers:

$\frac{2}{3}$

$-\frac{2}{3}$

$\frac{3}{8}$

$-\frac{5}{8}$

Correct answer:

$-\frac{2}{3}$

Explanation:

$-\frac{5}{12} \div\frac{5}{8}$

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

The multiplicative inverse or the reciprocal of $\frac{5}{8 } =\frac{8}{5}$ .

$-\frac{5}{12} \times \frac{8}{5} = -\frac{40}{60}$ A negative time a positive is a negative.

Reduce to simplest form by dividing the numerator and the denominator by the Greatest Common Factor of 40 and 60, which is 20.

$-\frac{40\div 20}{60\div 20} =-\frac{2}{3}$

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Example Question #387 : Arithmetic

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

Possible Answers:

$3\frac{4}{5}$

$3\frac{1}{3}$

$3\frac{1}{5}$

$3\frac{1}{2}$

Correct answer:

$3\frac{1}{3}$

Explanation:

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

Convert both the whole number and the mixed number to improper fractions.

$5 = \frac{5}{1}$

$1\frac{1}{2} = \frac{(2\times 1)+1}{2} = \frac{3}{2}$

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

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

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

$\frac{10}{3} = 3\frac{1}{3}$

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Example Question #984 : Hspt Mathematics

Mary is making banners. She bought a roll of material that is 20 feet. Each small banner is 6 inches in length. How many banners can she make with the material that she bought?

Possible Answers:

banners

120 banners

banners

Correct answer:

banners

Explanation:

Since there are 12 inches in a foot and the banners are 6 inches, that would be $\frac{1}{2}$ of a foot.

To solve this problem, divide the total number of feet, which is 20, by $\frac{1}{2}$ .

$\frac{20}{1} \div \frac{1}{2}$

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

The multiplicative inverse or the reciprocal of $\frac{1}{2} = \frac{2}{1}$ .

$\frac{20}{1} \times\frac{2}{1} = \frac{40}{1} = 40$

Mary will be able to make banners with the material that she had purchased.

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #381 : Arithmetic

Example Question #976 : Hspt Mathematics

Example Question #92 : Fractions

Example Question #383 : Arithmetic

Example Question #979 : Hspt Mathematics

Example Question #384 : Arithmetic

Example Question #385 : Arithmetic

Example Question #386 : Arithmetic

Example Question #387 : Arithmetic

Example Question #984 : Hspt Mathematics

All HSPT Math Resources

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