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HSPT Math : HSPT Mathematics

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Example Questions

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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Example Question #981 : Hspt Mathematics

What is a fraction form of .036?

Possible Answers:

$\dpi{100} \frac{1}{36}$

$\dpi{100} \frac{9}{250}$

$\dpi{100} \frac{36}{100}$

$\dpi{100} \frac{1}{4}$

Correct answer:

$\dpi{100} \frac{9}{250}$

Explanation:

The fraction form of .036 is $\dpi{100} \frac{36}{1000}$ . None of our answers match this fraction, so we must reduce it. The easiest way to do so is to divide the top and bottom by 2.

$\dpi{100} \frac{36}{1000}=\frac{18}{500}$

We can divide by 2 again:

$\dpi{100} \frac{18}{500}=\frac{9}{250}$

This is one of our answers (and also the fraction in its most reduced form).

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Example Question #982 : Hspt Mathematics

$\dpi{100} 2\frac{1}{4}+5\frac{4}{5}=$

Possible Answers:

$\dpi{100} 7\frac{4}{5}$

$\dpi{100} 8\frac{1}{20}$

$\dpi{100} 8$

$\dpi{100} 7\frac{4}{9}$

Correct answer:

$\dpi{100} 8\frac{1}{20}$

Explanation:

First add the whole numbers.

$\dpi{100} 2+5=7$

Then add the fractions. In order to this, the fractions need to have a common denominator. The denominators are 4 and 5, so we need to find the least common multiple of 4 and 5. We can do this by finding all the multiples of the larger number (5) and try to divide each of them by 4.

5: No

10: No

15: No

20: Yes

So the least common multiple is 20. We can multiply $\dpi{100} 4\times 5$ to get 20, and $\dpi{100} 5\times 4$ to get 20.

$\dpi{100} \frac{1}{4}+\frac{4}{5}=\frac{5\times 1}{5\times 4}+\frac{4\times 4}{4\times 5}=\frac{5}{20}+\frac{16}{20}=\frac{21}{20}$

We convert $\dpi{100} \frac{21}{20}$ to $\dpi{100} 1\frac{1}{20}$ and add it to 7 to get $\dpi{100} 8\frac{1}{20}$ .

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Example Question #983 : Hspt Mathematics

What is $\frac{5}{12}-\frac{3}8{}=?$

Possible Answers:

$\frac{6}{8}$

$\frac{1}{24}$

$\frac{5}{6}$

$\frac{2}4{}$

Correct answer:

$\frac{1}{24}$

Explanation:

To subtract fractions we must first ensure that we have the same denominator which is the bottom part of the fraction.

To do this we must find the least common multiple of the denominators.

The least common multiple is the smallest number that multiples of both of the denominators multiply to. For example, for 2 and 6 it would be 6, for 2 and 5 it would be 10, for 3 and 8 it would be 24.

In this case the LCM is $8*3=24\:\:\:12*2=24$ .

We then multiply the numerator and denominator of the fractions by the numbers it takes to reach the LCM $\frac{5}{12}*\frac{2}{2}$ and $\frac{3}{8}*\frac{3}{3}$ to get the same denominator because anything divided by itself is one so the fractions maintain their same value as the numbers change into the format we need to determine the answer.

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction.

After doing this we then subtract the first numerator (top part of the fraction) from the second numerator and place the result over the new denominator

$\frac{10}{24}-\frac{9}{24}=\frac{1}{24}$

The final answer is $\frac{1}{24}$

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Example Question #984 : Hspt Mathematics

$\frac{4}{9}-\frac{1}{12}=$

Possible Answers:

$\frac{1}{4}$

$\frac{3}{9}$

$\frac{13}{36}$

Correct answer:

$\frac{13}{36}$

Explanation:

First, find a common denominator (36). Then, subtract the numerators.

The answer is $\frac{13}{36}$

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Example Question #1301 : Ssat Upper Level Quantitative (Math)

Find the arithmetic mean of the following five numbers.

$\frac{2}{5}, \frac{1}{5},\frac{1}{2},\frac{3}{10}, \frac{2}{5}$

Possible Answers:

$\frac{6}{25}$

$\frac{2}{5}$

$\frac{9}{25}$

$\frac{7}{25}$

$\frac{3}{5}$

Correct answer:

$\frac{9}{25}$

Explanation:

Add the numbers, then divide by or, equivalently, multiply by $\frac{1}{5}$ .

$\frac{\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}}{5}$

$\frac{1}{5} \left(\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}\right )$

Find the common denominator of the terms we are adding.

$\frac{1}{5} \left(\frac{4}{10}+ \frac{2}{10}+\frac{5}{10}+\frac{3}{10}+ \frac{4}{10}\right )$

$\frac{1}{5} \left(\frac{4+2+5+3+4}{10} \right)$

Multiply and simplify.

$\frac{1}{5} \left(\frac{18}{10} \right)= \frac{1}{5} \left(\frac{9}{5} \right) = \frac{9}{25}$

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Example Question #396 : Arithmetic

Add:

$\frac{1}{9}+\frac{7}{3}$

Possible Answers:

$\frac{8}{3}$

$\frac{20}{9}$

$\frac{22}{9}$

$\frac{22}{3}$

$\frac{2}{3}$

Correct answer:

$\frac{22}{9}$

Explanation:

Rewrite using the lowest comon denominator. Since LCM (9, 3) = 9 :

$\frac{1}{9}+\frac{7}{3}=\frac{1}{9}+\frac{7\times 3}{3\times 3}=\frac{1}{9}+\frac{21}{9}=\frac{1+21}{9}=\frac{22}{9}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #385 : Arithmetic

Example Question #386 : Arithmetic

Example Question #387 : Arithmetic

Example Question #984 : Hspt Mathematics

Example Question #981 : Hspt Mathematics

Example Question #982 : Hspt Mathematics

Example Question #983 : Hspt Mathematics

Example Question #984 : Hspt Mathematics

Example Question #1301 : Ssat Upper Level Quantitative (Math)

Example Question #396 : Arithmetic

All HSPT Math Resources

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