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HSPT Math : Arithmetic

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Example Questions

Example Question #491 : Arithmetic

Which of the following statements demonstrates the inverse property of addition?

Possible Answers:

2.5 + 0 = 2.5

None of the examples in the other responses demonstrates the inverse property of addition.

2.5+5= 5+2.5

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

2.5+ (-2.5) = 0

Correct answer:

2.5+ (-2.5) = 0

Explanation:

The inverse property of addition states that for every real number, a number exists, called the additive inverse, such that the number and its inverse have sum 0. Of the statements given, only

2.5+ (-2.5) = 0

demonstrates this property, so it is the correct choice.

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Example Question #11 : How To Add Fractions

Which of the following statements demonstrates the identity property of addition?

Possible Answers:

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

2.5 + 0 = 2.5

2.5+5= 5+2.5

None of the examples in the other responses demonstrates the identity property of addition.

2.5+ (-2.5) = 0

Correct answer:

2.5 + 0 = 2.5

Explanation:

The identity property of addition states that there is a number 0, called the additive identity, that can be added to any number to yield that number as the sum. Of the four statements,

2.5 + 0 = 2.5

demonstrates this property.

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Example Question #492 : Arithmetic

Which of the following is the sum of two-thirds and one-fifth?

Possible Answers:

$\frac{3}{8}$

$\frac{11}{15}$

$\frac{13}{10}$

$\frac{13}{15}$

$\frac{11}{12}$

Correct answer:

$\frac{13}{15}$

Explanation:

Since GCF (3,5) = 15 , rewrite each fraction as its equivalent in fifteenths and add the numerators:

$\frac{2}{3 } + \frac{1}{5} = \frac{2 \times 5}{3 \times 5 } + \frac{3 \times 1}{3 \times 5} = \frac{10}{15 } + \frac{3 }{15} = \frac{10+3}{15 } = \frac{13}{15 }$

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Example Question #1 : Decimals

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$

Possible Answers:

11.125

11.25

11.3125

11.625

11.1875

Correct answer:

11.3125

Explanation:

To get the decimal from a fraction, divide the numerator by the denominator

$\frac{1}{8}=0.125$

$5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$

5.125+6.1875=11.3125

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Example Question #493 : Arithmetic

Solve: $\frac{7}{4}-\frac{2}{7}$

Possible Answers:

$-\frac{5}{3}$

$\frac{1}{2}$

$\frac{5}{28}$

$\frac{41}{28}$

$\frac{3}{2}$

Correct answer:

$\frac{41}{28}$

Explanation:

The numerators of a fraction cannot be added or subtracted if their denominators are different.

Find the least common denominator, or LCD, by multiplying the denominators together.

$4\times 7=28$

Both fractions share the common denominator 28. The numerator must multiply with what was multiplied by their denominator to get the LCD. Rewrite the fractions.

$\frac{7}{4}-\frac{2}{7} = \frac{7\times 7}{4\times 7}-\frac{2\times 4}{7\times 4} = \frac{49}{28}-\frac{8}{28}$

Subtract the numerators. Remember, the denominator does not change when we add or subtract fractions.

$\frac{49}{28}-\frac{8}{28}= \frac{41}{28}$

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Example Question #494 : Arithmetic

Simplify: $\frac{1}{4}-\frac{2}{3}$

Possible Answers:

$\frac{1}{7}$

$\frac{5}{12}$

$-\frac{5}{12}$

$-\frac{1}{7}$

Correct answer:

$-\frac{5}{12}$

Explanation:

The denominators must be like before the numerators can be subtracted.

Find the least common denominator, which is 12.

Remember, when creating common denominators you must multiply the numerator by the same number that you multiplied the denominator by to get the common denominator.

$\frac{1}4{} \ast\frac{3}{3}=\frac{3}{12}$ and $\frac{2}{3}\ast\frac{4}{4}=\frac{8}{12}$

$\frac{3}{12}-\frac{8}{12} = -\frac{5}{12}$

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Example Question #495 : Arithmetic

Add: $\frac{a}{b}+\frac{c}{b}$

Possible Answers:

$\frac{ac}{b}$

$\frac{a+c}{b}$

$\frac{ac}{2b}$

$\frac{a+c}{2b}$

$\frac{2a+2c}{b}$

Correct answer:

$\frac{a+c}{b}$

Explanation:

Since the denominator is alike, combine the numerators. Do not add the denominators.

$\frac{a}{b}+\frac{c}{b} = \frac{a+c}{b}$

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Example Question #496 : Arithmetic

Add: $\frac{1}{3}+ \frac{4}{3}$

Possible Answers:

$\frac{5}{6}$

$\frac{4}{15}$

$\frac{5}{3}$

Correct answer:

$\frac{5}{3}$

Explanation:

The denominators of the fractions are alike. This means we can add the numerators. The denominator will stay the same.

$\frac{1}{3}+ \frac{4}{3}=\frac{5}{3}$

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Example Question #497 : Arithmetic

Subtract: $\frac{7}{4}- \frac{7}{2}$

Possible Answers:

$\frac{7}{2}$

$-\frac{7}{2}$

$-\frac{7}{4}$

$\frac{7}{4}$

Correct answer:

$-\frac{7}{4}$

Explanation:

First, find the common denominator. The common denominator is four.

Rewrite the fractions.

$\frac{7}{4}- \frac{7}{2}= \frac{7}{4}- \frac{14}{4} = -\frac{7}{4}$

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Example Question #498 : Arithmetic

Evaluate: $\frac{3}{11}-\frac{1}{33}$

Possible Answers:

$\frac{1}{3}$

$\frac{2}{33}$

$\frac{8}{33}$

$-\frac{3}{2}$

Correct answer:

$\frac{8}{33}$

Explanation:

Find the common denominator. The common denominator is since goes into three times.

Rewrite the fraction.

$\frac{3}{11}-\frac{1}{33} = \frac{9}{33}-\frac{1}{33}=\frac{8}{33}$

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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #491 : Arithmetic

Example Question #11 : How To Add Fractions

Example Question #492 : Arithmetic

Example Question #1 : Decimals

Example Question #493 : Arithmetic

Example Question #494 : Arithmetic

Example Question #495 : Arithmetic

Example Question #496 : Arithmetic

Example Question #497 : Arithmetic

Example Question #498 : Arithmetic

All HSPT Math Resources

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