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HSPT Math : How to add and subtract fractions

Study concepts, example questions & explanations for HSPT Math

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

Example Questions

Example Question #31 : Problem Solving

$2\frac{3}{4} -6\frac{2}{3}$

Possible Answers:

$-3\frac{11}{12}$

$-9\frac{5}{8}$

$3\frac{11}{12}$

$9\frac{5}{8}$

Correct answer:

$-3\frac{11}{12}$

Explanation:

$2\frac{3}{4} -6\frac{2}{3}$

First, convert all mixed numbers to improper fractions.

$2\frac{3}{4} = \frac{(4\times 2)+3}{4} =\frac{11}{4}$

$6\frac{2}{3} = \frac{(3\times 6)+2}{3} = \frac{20}{3}$

Because the denominators are not alike, the fractions have to be converted to equivalent fractions with the same denominator. This is done by finding the LCM which becomes the Least Common Denominator. The LCD of 4 and 3 is 12.

$\frac{11}{4} = \frac{33}{12}$ Both the numerator and the denominator were multiplied by 3.

$\frac{20}{3} = \frac{80}{12}$ Both the numerator and the denominator were multiplied by 4.

$\frac{33}{12} - \frac{80}{12} = \frac{33-80}{12} = -\frac{47}{12}$

The answer is negative because the method to solving would be to subtract and take the sign of the higher number.

$-\frac{47}{12} = -3\frac{11}{12}$

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Example Question #32 : Problem Solving

$-2\frac{2}{5} + (-3\frac{1}{3})$

Possible Answers:

$-5\frac{11}{15}$

$-6\frac{1}{5}$

$-6\frac{2}{15}$

$6\frac{1}{5}$

Correct answer:

$-5\frac{11}{15}$

Explanation:

$-2\frac{2}{5} + (-3\frac{1}{3})$

First, convert all mixed numbers to improper fractions.

$-2\frac{2}{5} = -\frac{(5\times 2)+2}{5} = -\frac{12}{5}$

$-3\frac{1}{3} = -\frac{(3\times 3)+1}{3} = -\frac{10}{3}$

Because the denominators are different, find the LCM Of 3 and 5. This becomes the LCD or least common denominator.

The LCD of 5 and 3 is 15.

Create equivalent fractions with 15 as the denominator.

$-\frac{12}{5} = -\frac{36}{15}$ Both numerator and denominator were multiplied by 3.

$-\frac{10}{3} = -\frac{50}{15}$ Both numerator and denominator were multiplied by 5.

$-\frac{36}{15} + -\frac{50}{15} = \frac{-36+-50}{15}$ When adding two negative integers, the result is negative.

$-\frac{86}{15} = -5\frac{11}{15}$

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Example Question #33 : Problem Solving

$\frac{9}{4}-\frac{3}{2}=?$

Possible Answers:

$\frac{3}{4}$

$\frac{15}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

To add or subtract fractions, you need a common denominator.

You can multiple the second fraction by two to get a common denominator of four.

$\frac{3}{2}\times\frac{2}{2}=\frac{6}{4}$

Then you just subtract the numerators to get

$\frac{9}{4}-\frac{6}{4}=\frac{3}{4}$ .

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HSPT Math : How to add and subtract fractions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #31 : Problem Solving

Example Question #32 : Problem Solving

Example Question #33 : Problem Solving

All HSPT Math Resources

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