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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #24 : Fractions

$12 \frac{4}{6} \div 4\frac{2}{4}=$

Possible Answers:

$2\frac{7}{9}$

$1\frac{2}{3}$

$2\frac{20}{27}$

$3\frac{1}{3}$

$2\frac{22}{27}$

Correct answer:

$2\frac{22}{27}$

Explanation:

First convert each fraction into an improper fraction.

$\frac{76}{6}\div \frac{18}{4}=$

Then flip the second fraction, reduce and multiply:

$\frac{76}{6}\ast \frac{4}{18}=$

The answer is $2\frac{22}{27}$ .

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Example Question #25 : Fractions

Divide:

$\frac{4}{9}\div \frac{2}{3}$

Possible Answers:

$\frac{4}{}9$

$\frac{1}{}3$

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{7}{}9$

Correct answer:

$\frac{2}{3}$

Explanation:

The first step in dividing fractions is to make the second fraction a reciprocal (flip it) and then rewrite the problem as a multiplication problem: $\left(\frac{4}{9}\times \frac{3}{2}\right)$ .

You can cross-reduce so that the problem now becomes $\left(\frac{2}{3}\times \frac{1}{1}\right)$ . Then, mulitply straight across so that your answer is $\frac{2}{3}$ .

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Example Question #329 : Concepts

What is the value of in this equation?

$\frac{9}{5}\div \frac{5}{7}=x$

Possible Answers:

$\frac{63}{25}$

$\frac{7}{9}$

$\frac{25}{63}$

$\frac{9}{7}$

Correct answer:

$\frac{63}{25}$

Explanation:

In order to solve $\frac{9}{5}\div \frac{5}{7}$ , the latter fraction must be inverted and then multiplied by the first fraction, as shown below:

$\frac{9}{5}\cdot \frac{7}{5} = \frac{63}{25}$

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Example Question #921 : Hspt Mathematics

$\frac{7}{16}*\frac{8}{3}=?$

Possible Answers:

$\frac{56}{19}$

$\frac{7}{6}$

$\frac{15}{19}$

$\frac{6}{7}$

Correct answer:

$\frac{7}{6}$

Explanation:

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.

So $\frac{(7*8)}{(16*3)}$

Then simplify the answer by dividing by the greatest common factor. $\frac{(56/8)}{(48/8)}$

After performing this the answer is $\frac{7}{6}$ .

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Example Question #922 : Hspt Mathematics

$\frac{11}{20}\div\frac{1}{10}=$

Possible Answers:

$5\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

$5\frac{1}{2}$

Explanation:

When dividing fractions, first find the reciprocal of the second fraction. Flip it so it becomes $\frac{10}{1}$ .

Then, multiply both fractions together to get $\frac{11}{2}$ .

Convert that into a mixed number and you get $5\frac{1}{2}$

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Example Question #923 : Hspt Mathematics

Simplify the expression.

$\left ( {\frac{1}{2} + \frac{1}{4}}\right ) * \left ({\frac{1}{2} - \frac{1}{4}}\right )$

Possible Answers:

$\frac{3}{16}$

$\frac{5}{16}$

$\frac{1}{8}$

$\frac{5}{12}$

Correct answer:

$\frac{3}{16}$

Explanation:

$\left ( {\frac{1}{2} + \frac{1}{4}}\right ) * \left ({\frac{1}{2} - \frac{1}{4}}\right )$

Start with the terms in parentheses, using the order of operations. Find the least common denominator.

$\left ( {\frac{1* 2}{2* 2} + \frac{1}{4}}\right ) *\left ({\frac{1* 2}{2*2} - \frac{1}{4}}\right )$

$\left ( {\frac{2}{4} + \frac{1}{4}}\right ) * \left ({\frac{ 2}{4} - \frac{1}{4}}\right )$

Add the fractions in parentheses.

$\left ( {\frac{2+1}{4} } \right ) * \left ({\frac{2-1}{4} } \right )$

Multiply the fractions and simplify.

${\frac{3}{4} } *{\frac{1}{4} } = \frac{3 * 1}{4 * 4} = \frac{3}{16}$

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Example Question #1661 : Ssat Middle Level Quantitative (Math)

Express the product in simplest form:

$\frac{5}{7} \cdot 1 \frac{1}{7} \cdot 2 \frac{4}{5}$

Possible Answers:

$2 \frac{2}{7}$

$2\frac{8}{35}$

$2 \frac{2}{5}$

$1\frac{6}{7}$

Correct answer:

$2 \frac{2}{7}$

Explanation:

Rewrite the mixed fractions as improper fractions, cross-cancel, and multiply across:

$\frac{5}{7} \cdot 1 \frac{1}{7} \cdot 2 \frac{4}{5} = \frac{5}{7} \cdot \frac{8}{7} \cdot \frac{14}{5}= \frac{1}{1} \cdot \frac{8}{7} \cdot \frac{2}{1}= \frac{16}{7}= 2\frac{2}{7}$

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Example Question #992 : Numbers And Operations

Evaluate:

$5.96 + 3.2 \times 1.5$

Possible Answers:

6.44

64.4

9.76

13.74

10.76

Correct answer:

10.76

Explanation:

By order of operations, multiply first:

$3.2 \times 1.5$

Multiply 32 by 15, and position the decimal point so that two digits are right of it:

$32 \times 15 = 480$

$3.2 \times 1.5 = 4.80 = 4.8$

Now add this product to 5.96:

$5.96 + 3.2 \times 1.5 = 5.96 + 4.8$

Append a zero to the 4.8, and align the decimal points:

5.96

$\underline{4.80}$

10.76

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Example Question #1662 : Ssat Middle Level Quantitative (Math)

Evaluate:

$6.5 + 1.4 \times 1.6$

Possible Answers:

28.9

8.74

2.89

6.724

12.64

Correct answer:

8.74

Explanation:

By order of operations, multiply first:

$1.4 \times 1.6$

Multiply 14 by 16, and position the decimal point so that two digits are right of it:

$14 \times 16 = 224$

$1.4 \times 1.6 = 2.24$

Now add this product to 6.5:

$6.5 + 1.4 \times 1.6 = 6.5 + 2.24$

Append a zero to the 6.5, and align the decimal points:

6.50

$\underline{2.24}$

8.74

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Example Question #924 : Hspt Mathematics

$\frac{3}{5} \times \frac{1}{6} =$

Possible Answers:

$\frac{3}{5}$

$\frac{1}{2}$

$\frac{1}{10}$

$\frac{3}{11}$

$\frac{5}{18}$

Correct answer:

$\frac{1}{10}$

Explanation:

When multiplying a fraction, simply multiply straight across - numerator times numerator, denominator times denominator. When you do that, you should get this answer:

$\tfrac{3}{5} \times \tfrac{1}{6} = \tfrac{3}{30}$

Do not forget to reduce. 3 and 30 can both be evenly divided by 3, which would give you $\tfrac{1}{10}$ as your answer.

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All HSPT Math Resources

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #24 : Fractions

Example Question #25 : Fractions

Example Question #329 : Concepts

Example Question #921 : Hspt Mathematics

Example Question #922 : Hspt Mathematics

Example Question #923 : Hspt Mathematics

Example Question #1661 : Ssat Middle Level Quantitative (Math)

Example Question #992 : Numbers And Operations

Example Question #1662 : Ssat Middle Level Quantitative (Math)

Example Question #924 : Hspt Mathematics

All HSPT Math Resources

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