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HSPT Math : Arithmetic

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Example Questions

Example Question #331 : Arithmetic

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

Possible Answers:

$\frac{1}{2}$

$5\frac{1}{2}$

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 #332 : Arithmetic

Simplify the expression.

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

Possible Answers:

$\frac{5}{16}$

$\frac{1}{8}$

$\frac{5}{12}$

$\frac{3}{16}$

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 #333 : Arithmetic

Express the product in simplest form:

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

Possible Answers:

$1\frac{6}{7}$

$2\frac{8}{35}$

$2 \frac{2}{5}$

$2 \frac{2}{7}$

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 #334 : Arithmetic

Evaluate:

$5.96 + 3.2 \times 1.5$

Possible Answers:

64.4

9.76

6.44

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 #335 : Arithmetic

Evaluate:

$6.5 + 1.4 \times 1.6$

Possible Answers:

12.64

6.724

28.9

2.89

8.74

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 #336 : Arithmetic

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

Possible Answers:

$\frac{1}{10}$

$\frac{5}{18}$

$\frac{3}{5}$

$\frac{3}{11}$

$\frac{1}{2}$

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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Example Question #1003 : Numbers And Operations

Multiply:

$0.58 \times 8.3$

Possible Answers:

4.814

4.2164

0.4814

0.42164

4.6574

Correct answer:

4.814

Explanation:

First, multiply the numbers, ignoring the decimal points:

$58 \times 83 = 4814$

Since the two factors in the original product have three digits to the right of the decimal points between them, position the decimal point in the product such that three digits are at its right. The result, therefore, is

4.814

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Example Question #6 : How To Multiply Fractions

Multiply: $6.73 \times 0.006$

Possible Answers:

0.04308

0.4038

0.04038

0.438

0.0438

Correct answer:

0.04038

Explanation:

First, remove the decimal points, multiplying as follows:

$673 \times 6 = 4 038$

Between them, the two factors have five digits to the right of their decimal points, so position the decimal point in the product so that there are five digits to the right. This will require placing a zero in front as a placeholder, so the final result is

$6.73 \times 0.006 = 0.04038$

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Example Question #337 : Arithmetic

Find $\frac{3}{5}\cdot \frac{7}{9}$ .

Possible Answers:

$\frac{7}{5}$

$\frac{15}{7}$

$\frac{3}{5}$

$\frac{7}{15}$

Correct answer:

$\frac{7}{15}$

Explanation:

To find the product of two fractions, multiply the numerators together and then multiply the denominators together.

$\frac{3}{5}\cdot \frac{7}{9}=\frac{21}{45}$ , which can be reduced to $\frac{7}{15}$ .

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Example Question #338 : Arithmetic

Find $\frac{5}{7}\cdot \frac{3}{4}=$ .

Possible Answers:

$\frac{2}{3}$

$\frac{15}{28}$

$\frac{20}{21}$

$\frac{5}{7}$

Correct answer:

$\frac{15}{28}$

Explanation:

To find the product of two fractions, multiply the numerators together and then multiply the denominators together.

$\frac{5}{7}\cdot \frac{3}{4}=\frac{15}{28}$

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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #331 : Arithmetic

Example Question #332 : Arithmetic

Example Question #333 : Arithmetic

Example Question #334 : Arithmetic

Example Question #335 : Arithmetic

Example Question #336 : Arithmetic

Example Question #1003 : Numbers And Operations

Example Question #6 : How To Multiply Fractions

Example Question #337 : Arithmetic

Example Question #338 : Arithmetic

All HSPT Math Resources

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