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HSPT Math : Concepts

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 #146 : Percentage

What is the decimal equivalent to $\frac{60}{300}$ ?

Possible Answers:

Correct answer:

Explanation:

Divide the numerator by the denominator: $60\div300=.20$

Answer:

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Example Question #261 : Concepts

Evaluate

$0.5\ast0.05\ast1.5$

Possible Answers:

0.025

0.375

3.75

0.0375

0.00375

Correct answer:

0.0375

Explanation:

First, $0.5\ast0.05=0.025$

Then, $0.025\ast1.5=0.0375$

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Example Question #262 : Concepts

Divide: $\frac{0.053}{0.11}$

Possible Answers:

5.5

$\frac{53}{110}$

5.3

5.1

$\frac{53}{11}$

Correct answer:

$\frac{53}{110}$

Explanation:

In order to solve the expression, simply move the decimal place to the right three units since the numerator has the placeholder three units to the left. Simplify.

$\frac{0.053}{0.11}=\frac{53}{110}$

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Example Question #857 : Hspt Mathematics

Multiply: $2.3 \times 2.3$

Possible Answers:

529

0.46

5.29

4.6

52.9

Correct answer:

5.29

Explanation:

Ignore the decimals for now and multiply by .

$23\times 23 = 529$

Since there is a decimal place one place from the right for both numbers, there will be a decimal place 2 places from the right.

The correct answer is: 5.29

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Example Question #158 : Decimals

Express the answer as a fraction: $0.25 \times 1.25$

Possible Answers:

$\frac{5}{16}$

$\frac{5}{8}$

$\frac{15}{8}$

$\frac{3}{2}$

$\frac{8}{11}$

Correct answer:

$\frac{5}{16}$

Explanation:

The decimals can be converted to improper fractions for convenience. Set each number over one, and move the decimal places two to the right. Reduce the fraction.

$\frac{0.25}{1} =\frac{25}{100}= \frac{1}{4}$

Knowing that 0.25 is similar to one-fourth, add one with one fourth in fraction and convert this to improper fraction.

$1.25 = 1+0.25 = 1+\frac{1}{4} = 1\frac{1}{4}$

To convert a fraction to an improper fraction, multiply the denominator with the whole number, and add the numerator. The denominator will not change.

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

Multiply the two fractions.

$\frac{1}{4}\times \frac{5}{4} = \frac{5}{16}$

The answer is: $\frac{5}{16}$

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Example Question #263 : Concepts

0.41 is the square root of what number?

Possible Answers:

0.1681

0.82

1.681

0.082

Correct answer:

0.1681

Explanation:

The square root of a number is the number which, when squared - multiplied by itself - yields that number as its result. Therefore, 0.41 is the square root of

$0.41 \times 0.41 = 0.1681$

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Example Question #861 : Hspt Mathematics

Which of the following is a true statement?

Possible Answers:

$0.45 <\sqrt{ \frac{9}{49 }} < 0.46$

$0.44 <\sqrt{ \frac{9}{49 }} < 0.45$

$0.43<\sqrt{ \frac{9}{49 }} < 0.44$

$0.42 <\sqrt{ \frac{9}{49 }} < 0.43$

Correct answer:

$0.42 <\sqrt{ \frac{9}{49 }} < 0.43$

Explanation:

The square root of a number is the number which, when squared - multiplied by itself - yields that number as the product. The square root of a fraction whose numerator and denominator are both perfect squares can be found as follows:

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

Divide 3 by 7:

Division

The number falls between 0.42 and 0.43.

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Example Question #862 : Hspt Mathematics

Which of the following is true of $\sqrt{73}$ ?

Possible Answers:

$8.5 < \sqrt{73} < 8.6$

$8.7 < \sqrt{73} < 8.8$

$8.4 < \sqrt{73} < 8.5$

$8.6 < \sqrt{73} < 8.7$

Correct answer:

$8.5 < \sqrt{73} < 8.6$

Explanation:

The principal square root of a number is the number that, when multiplied by itself, yields that number. To determine which of the four statements is true, we find the squares of the numbers 8.4, 8.5, 8.6, 8.7, and 8.8. If we do this, we find that

$8.5 ^{2}= 8.5 \times 8.5 = 72.25$

$8.6 ^{2}= 8.6 \times 8.6 = 73.96$

$8.5 ^{2} < 73 < 8.6 ^{2}$ ,

$8.5 < \sqrt{73} < 8.6$ .

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Example Question #861 : Hspt Mathematics

Which of the following is a true statement about the expression $8- \sqrt{58}$ ?

Possible Answers:

$0.3 < 8- \sqrt{58} < 0.4$

$0.4 < 8- \sqrt{58} < 0.5$

$0.5 < 8- \sqrt{58} < 0.6$

$0.2 < 8- \sqrt{58} < 0.3$

Correct answer:

$0.3 < 8- \sqrt{58} < 0.4$

Explanation:

If each of 0.2, 0.3, 0.4, 0.5, and 0.6 is subtracted from 8, the resulting differences are 7.8, 7.7, 7.6, 7.5, and 7.4, respectively. Therefore, we ask which of these two numbers $\sqrt{58}$ falls between and work from there.

$\sqrt{58}$ , the square root of 58, is the number which, when squared - multiplied by itself - yields the product 58. If each of the numbers are squared, we see that

$7.6 ^{2} = 7.6 \times 7.6 = 57.76$

$7.7 ^{2} = 7.7 \times 7.7 = 59.29$

$7.6 < \sqrt{58} < 7.7$

$-7.6 >- \sqrt{58} >- 7.7$

$-7.6+ 8 >- \sqrt{58} + 8 >- 7.7 + 8$

$0.4 > 8 - \sqrt{58} >0.3$ , or, equivalently,

$0.3 < 8- \sqrt{58} < 0.4$ .

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Example Question #162 : Decimals

Which of the following four expressions is the greatest?

Possible Answers:

1.2 + 1.3 + 1.4

$1.2 + 1.3 \times 1.4$

$1.2 \times 1.3 + 1.4$

$1.2 \times 1.3 \times 1.4$

Correct answer:

1.2 + 1.3 + 1.4

Explanation:

By order of operations, multiplication takes precedence over addition, and each is worked right to left. Keeping this in mind:

$1.2 \times 1.3 \times 1.4 = 1.56 \times 1.4 = 2.184$

$1.2 \times 1.3 + 1.4 = 1.56 + 1.4 = 2.96$

1.2 + 1.3 + 1.4 = 2.5 + 1.4 = 3.9

$1.2 + 1.3 \times 1.4 = 1.2 + 1.82 = 3.02$

The greatest of the four is 1.2 + 1.3 + 1.4 .

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #146 : Percentage

Example Question #261 : Concepts

Example Question #262 : Concepts

Example Question #857 : Hspt Mathematics

Example Question #158 : Decimals

Example Question #263 : Concepts

Example Question #861 : Hspt Mathematics

Example Question #862 : Hspt Mathematics

Example Question #861 : Hspt Mathematics

Example Question #162 : Decimals

All HSPT Math Resources

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