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HSPT Math : HSPT Mathematics

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Example Questions

Example Question #1091 : Hspt Mathematics

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

Possible Answers:

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

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

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

$\frac{ac}{2b}$

$\frac{ac}{b}$

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 #1092 : Hspt Mathematics

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

Possible Answers:

$\frac{5}{3}$

$\frac{5}{6}$

$\frac{4}{15}$

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 #1093 : Hspt Mathematics

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

Possible Answers:

$\frac{7}{4}$

$-\frac{7}{2}$

$-\frac{7}{4}$

$\frac{7}{2}$

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 #1094 : Hspt Mathematics

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

Possible Answers:

$-\frac{3}{2}$

$\frac{2}{33}$

$\frac{8}{33}$

$\frac{1}{3}$

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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Example Question #1095 : Hspt Mathematics

Add the following fractions:

$\frac{3}{5}+\frac{2}{15}$

Possible Answers:

$\frac{5}{15}$

$\frac{1}{3}$

$\frac{11}{15}$

$\frac{7}{15}$

Correct answer:

$\frac{11}{15}$

Explanation:

To solve, simply find a common denominator and add.

Multiply the first fraction by $\frac{3}{3}$ to get 15 as the common denomintor and then add the numerators.

Thus,

$\frac{3}{5}*\frac{3}{3}+\frac{2}{15}=\frac{9}{15}+\frac{2}{15}=\frac{11}{15}$

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Example Question #212 : Fractions

Which of the following is equal to the sum of $\frac{1}{8}$ and $\frac{1}{5}$ ?

Possible Answers:

0.24

0.154

0.375

0.325

Correct answer:

0.325

Explanation:

The easiest way is to convert each fraction to a decimal first, then add. $\frac{1}{8}$ can be converted to a decimal by dividing 1 by 8; $\frac{1}{5}$ can be converted similarly:

Division \

Add:

$\begin{matrix} 0.125\\ \underline{0.200}\\ 0.325 \end{matrix}$

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Example Question #502 : Arithmetic

$A = -4 \frac{1}{2}$

$B = 1 \frac{1}{3}$

Which of the following is the least of the four?

Possible Answers:

A + B

$A \cdot B$

$A \div B$

A -B

Correct answer:

$A \cdot B$

Explanation:

$-1\frac{1}{3} < 1 \frac{1}{3}$

$-4 \frac{1}{2} - 1\frac{1}{3 } < -4 \frac{1}{2}+ 1\frac{1}{3 }$

A-B < A+B

so A + B can be eliminated as the least of the four.

$1 \frac{1}{3}$ , which is equal to $\frac{4}{3}$ , has as its reciprocal $\frac{3}{4}$ , and:

$1 \frac{1}{3} > 1 > \frac{3}{4}$

$-4 \frac{1}{2} \cdot 1 \frac{1}{3} < -4 \frac{1}{2} \cdot \frac{3}{4}$

$-4 \frac{1}{2} \cdot 1 \frac{1}{3} < -4 \frac{1}{2} \div 1 \frac{1}{3}$

$A \cdot B<A \div B$

so $A \div B$ can be eliminated as the least of the four.

To find the least of the four, we only need to compare $A \cdot B$ and A-B :

$A \cdot B =-4 \frac{1}{2} \cdot 1 \frac{1}{3}$

$=- \frac{4 \cdot 2+ 1}{2} \cdot \frac{1 \cdot 3 + 1}{3}$

$=- \frac{9}{2} \cdot \frac{4}{3} = - \frac{36}{6} = -6$

$A - B =-4 \frac{1}{2}- 1 \frac{1}{3}$

$=-4 \frac{1}{2} + \left (- 1 \frac{1}{3} \right )$

$=-4 \frac{3}{6} + \left (- 1 \frac{2}{6} \right )$

$=-5\frac{5}{6}$

$A \cdot B < A - B$ ;

$A \cdot B$ is the least of the four and is the correct choice.

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Example Question #213 : Fractions

Solve:

$\frac{3}{2}+\frac{1}{3}$

Possible Answers:

$\frac{5}{3}$

$\frac{4}{3}$

$\frac{11}{6}$

Correct answer:

$\frac{11}{6}$

Explanation:

To add fractions, they must have a common denominator.

Both and have as a multiple.

You must multiple the first fraction by to get $\frac{9}{6}$ and the second by to get $\frac{2}{6}$ .

Then you just add the two numerators 9+2=11 to get $\frac{11}{6}$ .

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Example Question #1096 : Hspt Mathematics

The lowest common denominator for and is . True or false?

Possible Answers:

True

False

Correct answer:

False

Explanation:

Since is an actual factor of , you can just use as your common denominator which is less than .

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Example Question #1097 : Hspt Mathematics

$\frac{5}{9} + \frac{7}{9} =$

Possible Answers:

$1\frac{1}{3}$

$\frac{3}{4}$

$1\frac{2}{3}$

$\frac{2}{3}$

Correct answer:

$1\frac{1}{3}$

Explanation:

$\frac{5}{9} + \frac{7}{9} =$

These two fractions are like fractions, because they have the same denominator.

Just add the numerators and write the sum over the denominator. Then simplify.

$\frac{5}{9} + \frac{7}{9} = \frac{12}{9}$

$\frac{12}{9} = 1\frac{3}{9} = 1\frac{1}{3}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1091 : Hspt Mathematics

Example Question #1092 : Hspt Mathematics

Example Question #1093 : Hspt Mathematics

Example Question #1094 : Hspt Mathematics

Example Question #1095 : Hspt Mathematics

Example Question #212 : Fractions

Example Question #502 : Arithmetic

Example Question #213 : Fractions

Example Question #1096 : Hspt Mathematics

Example Question #1097 : Hspt Mathematics

All HSPT Math Resources

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