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HSPT Math : Concepts

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Example Questions

Example Question #501 : Concepts

Add the following fractions:

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

Possible Answers:

$\frac{7}{15}$

$\frac{11}{15}$

$\frac{5}{15}$

$\frac{1}{3}$

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 #502 : Concepts

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

Possible Answers:

0.375

0.154

0.325

0.24

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 #503 : Concepts

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

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

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 #504 : Concepts

Solve:

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

Possible Answers:

$\frac{5}{3}$

$\frac{11}{6}$

$\frac{4}{3}$

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 #505 : Concepts

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 #506 : Concepts

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

Possible Answers:

$1\frac{2}{3}$

$\frac{3}{4}$

$\frac{2}{3}$

$1\frac{1}{3}$

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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Example Question #507 : Concepts

$\frac{4}{5} - (-\frac{3}{5})$

Possible Answers:

$-\frac{1}{5}$

$\frac{1}{5}$

$1\frac{2}{5}$

$-1\frac{2}{5}$

Correct answer:

$1\frac{2}{5}$

Explanation:

$\frac{4}{5} - (-\frac{3}{5})$

When subtracting a negative, the subtraction and negative sign become an addition sign.

$\frac{4}{5} - (-\frac{3}{5}) = \frac{4}{5} + \frac{3}{5}$

$\frac{4}{5} + \frac{3}{5} = \frac{7}{5}$

$\frac{7}{5}$ is an improper fraction because the numerator is greater than the denominator. Therefore, it needs to be simplified. This is done by dividing the numerator by the denominator.

$7\div 5 = 1 \frac{2}{5}$

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Example Question #508 : Concepts

Find a-b if

$a = 6\frac{1}{3}$ and

$b=-1\frac{1}{3}$

Possible Answers:

$-7\frac{2}{3}$

$7\frac{2}{3}$

Correct answer:

$7\frac{2}{3}$

Explanation:

Find a-b if

$a = 6\frac{1}{3}$ and

$b=-1\frac{1}{3}$

$6\frac{1}{3} - (-1\frac{1}{3}) = 6\frac{1}{3} + 1\frac{1}{3}$

When subtracting a negative, the sign becomes a plus sign which indicates addition.

$6\frac{1}{3} + 1\frac{1}{3} = (6+1) + \frac{1+1}{3}$

$7\frac{2}{3}$

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Example Question #509 : Concepts

$8\frac{1}{10 } - 3\frac{7}{10}$

Possible Answers:

$5\frac{2}{5}$

$4\frac{3}{5}$

$5\frac{3}{5}$

$4\frac{2}{5}$

Correct answer:

$4\frac{2}{5}$

Explanation:

$8\frac{1}{10 } - 3\frac{7}{10}$

Because the numerator of the second mixed number (7) is greater than the numerator of the first mixed number (1) and the operation is subtraction, convert both mixed numbers into improper fractions.

$8\frac{1}{10} = \frac{(10\times 8)+1}{10} = \frac{81}{10}$

$3\frac{7}{10 } = \frac{(10\times 3)+7}{10} = \frac{37}{10}$

$\frac{81}{10} -\frac{37}{10} =\frac{81-37}{10}$

$\frac{44}{10} = 4\frac{4}{10} = 4\frac{2}{5}$

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Example Question #510 : Concepts

Find a + b if

a = 5/12 and

$b = -1\frac{1}{12}$

Possible Answers:

$-\frac{2}{3}$

$1\frac{1}{2}$

$1\frac{1}{3}$

$-\frac{3}{4}$

Correct answer:

$-\frac{2}{3}$

Explanation:

Find a + b if

a = 5/12 and

$b = -1\frac{1}{12}$

$\frac{5}{12} + (-1\frac{1}{12})$

Convert the mixed number to an improper fraction.

$\frac{5}{12} + (-\frac{13}{12}) =$

$\frac{5+ (-13)}{12} = \frac{-8}{12}$

Reduce to simplest form by dividing the numerator and the denominator by the GCF or the Greatest Common Factor which is 4.

$\frac{-8\div 4}{12\div 4} = -\frac{2}{3}$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #501 : Concepts

Example Question #502 : Concepts

Example Question #503 : Concepts

Example Question #504 : Concepts

Example Question #505 : Concepts

Example Question #506 : Concepts

Example Question #507 : Concepts

Example Question #508 : Concepts

Example Question #509 : Concepts

Example Question #510 : Concepts

All HSPT Math Resources

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