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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #521 : Concepts

Two line segments have lengths of $2\frac{3}{4} inches$ and $2\frac{5}{6} inches.$ What is the total measurement of these two line segments?

Possible Answers:

$4\frac{2}{3} inches$

$5\frac{7}{12} inches$

$4\frac{11}{12} inches$

$4\frac{3}{4} inches$

Correct answer:

$5\frac{7}{12} inches$

Explanation:

$2\frac{3}{4} +2\frac{5}{6}$

Convert all mixed numbers to improper fractions.

$2\frac{3}{4} = \frac{(4\times 2)+3}{4} = \frac{11}{4}$

$2\frac{5}{6} = \frac{(6\times 2)+5}{6} = \frac{17}{6}$

$\frac{11}{4} +\frac{17}{6}$

Because the denominators are not the same, find the LCD of 4 and 6.

Multiples of 4 are 4,8,12, 16.

Multiples of 6 are 6 and 12.

The LCM or the LCD of 4 and 6 is 12. Then, create equivalent fractions.

$\frac{11}{4} = \frac{33}{12}$ Both numerator and denominator were multiplied by 3.

$\frac{17}{6} =\frac{34}{12}$ Both numerator and denominator were multiplied by 2.

$\frac{33}{12} +\frac{34}{12} = \frac{33+34}{12} =\frac{67}{12}$

$\frac{67}{12} = 5\frac{7}{12}$

The sum of the two line segments is $5\frac{7}{12} inches.$

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Example Question #521 : Arithmetic

What is a fraction form of .036?

Possible Answers:

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

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

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

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

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 #522 : Arithmetic

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

Possible Answers:

$\dpi{100} 8$

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

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

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

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 #1 : Percentages

What is 32% of 2,000?

Possible Answers:

1,600

640

800

160

Correct answer:

640

Explanation:

Taking 32% of a number is the same as multiplying that number by 0.32. We therefore take the product:

$0.32 \cdot 2,000 = 640$

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Example Question #2 : Percentages

Which of the following operations is equivalent to taking of a number?

Possible Answers:

Dividing the number by

Moving the decimal point one place to the left, then doubling the result

Dividing the number by

Moving the decimal point one place to the left, then tripling the result

Correct answer:

Dividing the number by

Explanation:

Let's just pick a number at random, for example 100 .

of this number is , which is 100 divided by .

We can also work by simplifying the fractional form of . A percent can be written as the number divided by 100 .

$=\frac{25}{100}$

We can simplify this fraction: $\frac{25}{100}=\frac{5}{20}=\frac{1}{4}$ .

Either way, we get the same answer.

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Example Question #3 : Percentages

What percent of 12,000 is 3,300?

Possible Answers:

28.5%

25%

27.5%

24.5%

26%

Correct answer:

27.5%

Explanation:

To find out what percent a part is of a whole , evaluate the expression

$\frac{P}{W} \cdot 100 = \frac{3,300}{12,000} \cdot 100 = 27.5$

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Example Question #1 : How To Find The Part From The Whole With Percentage

is $12.5\%$ of what number?

Possible Answers:

530

480

500

520

420

Correct answer:

520

Explanation:

If is $12.5\%$ of a number, , then we can set up an equation. First, we convert $12.5\%$ to a decimal, 0.125 . Then, we can formulate the equation below.

65 = 0.125N

Solve for by dividing both sides of the equation by 0.125 .

$\frac{0.125N}{0.125}=\frac{65}{0.125}$

N = 520

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Example Question #1 : How To Find The Part From The Whole With Percentage

Which is larger?

a. 10% of 90

b. 5% of 160

c. 20% of 50

d. 30% of 40

Possible Answers:

Correct answer:

Explanation:

First find the percentage amount for each choice by multiplying the number by the percentage amount

a. $90\ast .10=9$

b. $160\ast .5=8$

c. $50\ast .20=10$

d. $40 \ast .30= 12$

Then compare the amounts to find the largest.

The answer is (d) 12.

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Example Question #1121 : Hspt Mathematics

75 is 60% of what number?

Possible Answers:

125

150

105

Correct answer:

125

Explanation:

Set up the proportion statement and solve for by cross-multiplying:

$\frac{75}{N}= \frac{60}{100}$

$N \cdot 60 = 75 \cdot 100 = 7,500$

$N \cdot 60 \div 60 = 7,500\div 60$

N = 125

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Example Question #2 : How To Find The Part From The Whole With Percentage

What is 120% of 120?

Possible Answers:

150

124

125

144

140

Correct answer:

144

Explanation:

Rewrite 120% as a decimal by writing 120 with a decimal point, then shifting it two spaces left:

$120.0\% = 1.20 = 1.2$

Multiply this by 120:

$120 \times 1.2 = 144$

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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #521 : Concepts

Example Question #521 : Arithmetic

Example Question #522 : Arithmetic

Example Question #1 : Percentages

Example Question #2 : Percentages

Example Question #3 : Percentages

Example Question #1 : How To Find The Part From The Whole With Percentage

Example Question #1 : How To Find The Part From The Whole With Percentage

Example Question #1121 : Hspt Mathematics

Example Question #2 : How To Find The Part From The Whole With Percentage

All HSPT Math Resources

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