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Algebra II : Adding and Subtracting Fractions

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Example Question #90 : Fractions

Add the fractions: $\frac{3}{4}+\frac{8}{3}$

Possible Answers:

$\frac{38}{12}$

$\frac{31}{12}$

$\frac{21}{12}$

$\frac{41}{12}$

Correct answer:

$\frac{41}{12}$

Explanation:

Find the least common denominator to these fractions.

Multiply both denominators together.

$4\times3=12$

Convert the fractions using this denominator.

$\frac{3}{4}+\frac{8}{3} = \frac{9}{12}+\frac{32}{12} = \frac{41}{12}$

The answer is: $\frac{41}{12}$

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Example Question #61 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{2}{5}-\frac{1}{3}-\frac{3}{4}$

Possible Answers:

$-\frac{11}{60}$

$-\frac{30}{7}$

$-\frac{41}{60}$

$-\frac{15}{4}$

Correct answer:

$-\frac{41}{60}$

Explanation:

In order to subtract the fractions, we must find the least common denominator of the three fractions.

Multiply all three numbers together to find the common denominator.

$5 \times 3 \times 4=60$

Convert all the fractions to this denominator, and multiply the numerators with what was multiplied to the denominator to get the new numerator.

$\frac{2}{5}-\frac{1}{3}-\frac{3}{4}=\frac{2(3)(4)}{60}-\frac{1(5)(4)}{60}-\frac{3(3)(5)}{60}$

Simplify the numerators.

$=\frac{24}{60}-\frac{20}{60}-\frac{45}{60} = -\frac{41}{60}$

The answer is: $-\frac{41}{60}$

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Example Question #62 : Adding And Subtracting Fractions

Add the following fractions: $\frac{2}{a}+\frac{2}{a^3b}$

Possible Answers:

$\frac{2}{a+a^3b}$

$\frac{4}{a+a^3b}$

$\frac{2a^2b+2}{a^3b}$

$\frac{4a^2b+2}{a^3b}$

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

Correct answer:

$\frac{2a^2b+2}{a^3b}$

Explanation:

To be able to add the fractions, we will need to determine the least common denominator.

The least common denominator is a^3b since this is the minimal term that is both divisible by and itself.

Convert only the first fraction with the denominator of a^3b .

$\frac{2}{a}+\frac{2}{a^3b}= \frac{2(a^2b)}{a(a^2b)}+\frac{2}{a^3b} = \frac{2a^2b+2}{a^3b}$

The answer is: $\frac{2a^2b+2}{a^3b}$

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Example Question #63 : Adding And Subtracting Fractions

Add the following fractions: $\frac{1}{7}+\frac{4}{42}$

Possible Answers:

$\frac{11}{42}$

$\frac{20}{49}$

$\frac{5}{49}$

$\frac{10}{49}$

$\frac{5}{21}$

Correct answer:

$\frac{5}{21}$

Explanation:

In order to add the fractions, we will need a common denominator.

Notice that the largest denominator is divisible by seven. We can change just the first fraction to the least common denominator.

Rewrite the fraction.

$\frac{1}{7}+\frac{4}{42} = \frac{6}{42}+\frac{4}{42} = \frac{10}{42}$

Reduce this fraction by writing out the common factors of the numerator and denominator.

$\frac{10}{42} =\frac{2\times 5}{2\times 21} =\frac{5}{21}$

The answer is: $\frac{5}{21}$

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Example Question #64 : Adding And Subtracting Fractions

Determine the sum as a mixed fraction: $\frac{2}{3}+\frac{1}{4}+\frac{8}{3}$

Possible Answers:

$3\frac{7}{12}$

$2\frac{5}{12}$

$3\frac{3}{4}$

$4\frac{3}{4}$

$1\frac{1}{10}$

Correct answer:

$3\frac{7}{12}$

Explanation:

The denominators are not common. Convert the denominators to a least common denominator.

To obtain the LCD, we can multiply four times three.

$4\times 3=12$

This value is the least possible value divisible by four and three.

Convert the fractions. Multiply the numerators by what was multiplied on the denominator to get the LCD.

$\frac{2}{3}+\frac{1}{4}+\frac{8}{3}=\frac{2(4)}{12}+\frac{1(3)}{12}+\frac{8(4)}{12}$

Simplify the fractions and add the numerators. The denominator stays the same.

$\frac{8}{12}+\frac{3}{12}+\frac{32}{12} = \frac{43}{12}$

Forty three goes into twelve three times. The remainder is seven, which can be written as seven-twelves.

The answer is: $3\frac{7}{12}$

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Example Question #65 : Adding And Subtracting Fractions

Add the fractions: $\frac{7}{9}+\frac{16}{3}$

Possible Answers:

$\frac{55}{6}$

$\frac{55}{9}$

$\frac{55}{12}$

$\frac{23}{12}$

$\frac{23}{9}$

Correct answer:

$\frac{55}{9}$

Explanation:

In order to add these fractions, we will need a common denominator. Notice that the least common denominator is nine since it's the least number divisible by both denominators.

Convert the second fraction to the correct denominator.

$\frac{7}{9}+\frac{16}{3} = \frac{7}{9}+\frac{16(3)}{3(3)}$

Simplify the fractions.

$\frac{7}{9}+\frac{48}{9} = \frac{55}{9}$

The answer is: $\frac{55}{9}$

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Example Question #66 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{7}{3}-\frac{11}{12}$

Possible Answers:

$-\frac{1}{3}$

$\frac{17}{12}$

$-\frac{2}{9}$

$-\frac{17}{12}$

$\frac{1}{3}$

Correct answer:

$\frac{17}{12}$

Explanation:

The least common denominator is 12. Convert the first fraction to this denominator in order to subtract the numerators. The denominators will remain the same.

$\frac{7}{3}-\frac{11}{12}=\frac{7(4)}{3(4)}-\frac{11}{12}$

Simplify the fractions.

$\frac{28}{12}-\frac{11}{12} = \frac{17}{12}$

The answer is: $\frac{17}{12}$

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Example Question #61 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{1}{30}- \frac{3}{4}$

Possible Answers:

$-\frac{43}{60}$

$-\frac{43}{120}$

$-\frac{13}{120}$

$\frac{43}{60}$

$\frac{7}{10}$

Correct answer:

$-\frac{43}{60}$

Explanation:

To subtract the fractions, we will need to find the least common denominator.

Write out the factors for both denominators.

30-[30,60]

4-[4,8,12,16,20,24,...,48,52,56,60]

Multiply four by 15 to get the least common denominator.

The least common denominator is .

Convert both fractions.

$\frac{1}{30}- \frac{3}{4}= \frac{2}{60}-\frac{45}{60} = -\frac{43}{60}$

The answer is: $-\frac{43}{60}$

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Example Question #68 : Adding And Subtracting Fractions

Add the fractions: $\frac{2}{3}+\frac{1}{6}+\frac{2}{9}$

Possible Answers:

$\frac{13}{18}$

$\frac{19}{18}$

$\frac{5}{18}$

$\frac{17}{18}$

$\frac{19}{13}$

Correct answer:

$\frac{19}{18}$

Explanation:

Determine the least common denominator. Expand the factors for each denominator.

3-[3,6,9,12,15,18,21,24,27,30,33,36]

6-[6,12,18,24,30,36]

9-[9,18,27,36]

The least common denominator is .

$\frac{2}{3}+\frac{1}{6}+\frac{2}{9}=\frac{24}{36}+\frac{6}{36}+\frac{8}{36}$

Add the numerators.

$\frac{38}{36} = \frac{19\times 2}{18\times 2} = \frac{19}{18}$

The answer is: $\frac{19}{18}$

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Example Question #69 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{\sqrt2}{6}-\frac{\sqrt2}{24}$

Possible Answers:

$\frac{\sqrt{2}}{3}$

$\frac{\sqrt{2}}{6}$

$\frac{1}{4}$

$\frac{\sqrt{2}}{4}$

$\frac{\sqrt{2}}{8}$

Correct answer:

$\frac{\sqrt{2}}{8}$

Explanation:

In order to subtract these fractions, we will need to convert the first fraction with a common denominator of 24. Multiply the top and bottom by four.

$\frac{\sqrt2}{6}-\frac{\sqrt2}{24}=\frac{4\sqrt2}{6(4)}-\frac{\sqrt2}{24}$

Simplify the numerator by combining like-terms.

$\frac{3\sqrt2}{24}$

Simplify the fraction.

$\frac{3\sqrt2}{3 \times 8} = \frac{\sqrt{2}}{8}$

The answer is: $\frac{\sqrt{2}}{8}$

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Algebra II : Adding and Subtracting Fractions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #90 : Fractions

Example Question #61 : Adding And Subtracting Fractions

Example Question #62 : Adding And Subtracting Fractions

Example Question #63 : Adding And Subtracting Fractions

Example Question #64 : Adding And Subtracting Fractions

Example Question #65 : Adding And Subtracting Fractions

Example Question #66 : Adding And Subtracting Fractions

Example Question #61 : Adding And Subtracting Fractions

Example Question #68 : Adding And Subtracting Fractions

Example Question #69 : Adding And Subtracting Fractions

All Algebra II Resources

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