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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #91 : Fractions

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

Possible Answers:

$-\frac{30}{7}$

$-\frac{11}{60}$

$-\frac{41}{60}$

$-\frac{15}{4}$

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:

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

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

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

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

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

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 #62 : Adding And Subtracting Fractions

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

Possible Answers:

$\frac{5}{49}$

$\frac{10}{49}$

$\frac{20}{49}$

$\frac{11}{42}$

$\frac{5}{21}$

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 #63 : Adding And Subtracting Fractions

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

Possible Answers:

$2\frac{5}{12}$

$3\frac{3}{4}$

$4\frac{3}{4}$

$3\frac{7}{12}$

$1\frac{1}{10}$

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 #64 : Adding And Subtracting Fractions

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

Possible Answers:

$\frac{55}{9}$

$\frac{55}{12}$

$\frac{23}{9}$

$\frac{23}{12}$

$\frac{55}{6}$

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 #65 : Adding And Subtracting Fractions

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

Possible Answers:

$\frac{17}{12}$

$-\frac{2}{9}$

$-\frac{1}{3}$

$\frac{1}{3}$

$-\frac{17}{12}$

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 #66 : Adding And Subtracting Fractions

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

Possible Answers:

$-\frac{43}{120}$

$-\frac{43}{60}$

$\frac{43}{60}$

$-\frac{13}{120}$

$\frac{7}{10}$

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 #67 : Adding And Subtracting Fractions

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

Possible Answers:

$\frac{5}{18}$

$\frac{17}{18}$

$\frac{13}{18}$

$\frac{19}{18}$

$\frac{19}{13}$

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 #68 : Adding And Subtracting Fractions

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

Possible Answers:

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

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

$\frac{1}{4}$

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

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

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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Example Question #71 : Adding And Subtracting Fractions

Solve: $\frac{4}{3}-\frac{25}{24}$

Possible Answers:

$-\frac{4}{7}$

$-\frac{6}{7}$

$-\frac{21}{8}$

$\frac{7}{12}$

$\frac{7}{24}$

Correct answer:

$\frac{7}{24}$

Explanation:

In order to add or subtract the numerator, we will need common denominators.

The least common denominator is 24.

Convert the first fraction to the common denominator by multiplying both the top and bottom by 8.

$\frac{4}{3}-\frac{25}{24}=\frac{4(8)}{3(8)}-\frac{25}{24} = \frac{32}{24}-\frac{25}{24}$

Subtract the numerator only. The denominator will remain the same.

The answer is: $\frac{7}{24}$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #91 : Fractions

Example Question #62 : 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 #67 : Adding And Subtracting Fractions

Example Question #68 : Adding And Subtracting Fractions

Example Question #71 : Adding And Subtracting Fractions

All Algebra II Resources

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