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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #71 : Adding And Subtracting Fractions

Sum the fractions: $\frac{7}{11}+\frac{1}{44}$

Possible Answers:

$\frac{8}{11}$

$\frac{29}{88}$

$\frac{8}{44}$

$\frac{29}{44}$

$\frac{5}{22}$

Correct answer:

$\frac{29}{44}$

Explanation:

In order to add the fractions, determine the least common denominator.

The LCD is 44 since this number is divisible by both 11 and 44.

Convert the fractions.

$\frac{7}{11}+\frac{1}{44} = \frac{7(4)}{11(4)}+\frac{1}{44}$

Add the numerator. The denominator remains the same.

The answer is: $\frac{29}{44}$

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Example Question #72 : Adding And Subtracting Fractions

Add the fractions: $\frac{2}{9}+ \frac{3}{7}$

Possible Answers:

$\frac{41}{63}$

$\frac{16}{63}$

$\frac{5}{63}$

$\frac{5}{16}$

$\frac{16}{41}$

Correct answer:

$\frac{41}{63}$

Explanation:

In order to add these fractions, it is necessary to find the least common denominator. We cannot add the numerators unless the denominators are the same,

Multiply the numerator and denominator together.

$9\times 7 =63$

Convert the fractions.

$\frac{2}{9}+ \frac{3}{7}=\frac{2(7)}{9(7)}+ \frac{3(9)}{7(9)}=\frac{14}{63}+\frac{27}{63}$

Add the numerators. The denominators will not change.

The answer is: $\frac{41}{63}$

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Example Question #72 : Adding And Subtracting Fractions

Solve: $\frac{2}{5}+\frac{1}{10}-\frac{9}{20}$

Possible Answers:

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{20}$

$\frac{1}{10}$

$\frac{1}{40}$

Correct answer:

$\frac{1}{20}$

Explanation:

To compute the sum of the fractions, we will need to determine the least common denominator.

The LCD is 20, since all this is the lowest number divisible by all the numbers of the denominators. Convert the fractions to this denominator.

$\frac{2}{5}+\frac{1}{10}-\frac{9}{20} = \frac{2(4)}{5(4)}+\frac{1(2)}{10(2)}-\frac{9}{20}$

Simplify the fractions.

$\frac{8}{20}+\frac{2}{20}-\frac{9}{20} = \frac{1}{20}$

The answer is: $\frac{1}{20}$

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Example Question #73 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{9}{23}-\frac{3}{46}$

Possible Answers:

$\frac{3}{46}$

$\frac{15}{23}$

$\frac{5}{12}$

$\frac{3}{23}$

$\frac{15}{46}$

Correct answer:

$\frac{15}{46}$

Explanation:

Convert the first fraction by multiplying the top and bottom by two.

$\frac{9(2)}{23(2)}-\frac{3}{46} = \frac{18}{46}-\frac{3}{46}$

Now that the denominators are common, the numerators can be subtracted.

The answer is: $\frac{15}{46}$

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Example Question #74 : Adding And Subtracting Fractions

Add the fractions: $\frac{3}{10}+\frac{3}{20}+\frac{3}{40}$

Possible Answers:

$\frac{21}{40}$

$\frac{5}{7}$

$\frac{21}{20}$

$\frac{41}{80}$

$\frac{9}{70}$

Correct answer:

$\frac{21}{40}$

Explanation:

The denominators are not common. To be able to add the numerators, we will need to determine the least common denominator.

By visualization, the LCD is 40 because this is the least number that is divisible by all three of the uncommon denominators.

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

$\frac{3}{10}+\frac{3}{20}+\frac{3}{40}=\frac{12}{40}+\frac{6}{40}+\frac{3}{40}=\frac{21}{40}$

The answer is: $\frac{21}{40}$

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Example Question #76 : Adding And Subtracting Fractions

Add: $\frac{\pi}{\pi+1}+\frac{\pi}{\pi-1}$

Possible Answers:

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

$\frac{4\pi^2}{\pi^2-1}$

$\frac{2\pi^2}{\pi^2-1}$

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

$\frac{\pi^2+2}{\pi^2-1}$

Correct answer:

$\frac{2\pi^2}{\pi^2-1}$

Explanation:

In order to add the fractions, we will need to determine the least common denominator. Multiply the two denominators together using the FOIL method.

$(\pi +1)(\pi -1) = \pi^2-\pi+\pi-1 = \pi^2-1$

Convert the fractions.

$\frac{\pi}{\pi+1}+\frac{\pi}{\pi-1}=\frac{\pi(\pi-1)}{(\pi+1)(\pi-1)}+\frac{\pi(\pi+1)}{(\pi-1)(\pi+1)}$

Simplify the terms of the numerator.

$\frac{\pi^2-\pi}{(\pi+1)(\pi-1)}+\frac{\pi^2+\pi}{(\pi-1)(\pi+1)}$

Combine the terms as one fraction.

$\frac{\pi^2-\pi+\pi^2+\pi}{(\pi+1)(\pi-1)} = \frac{2\pi^2}{\pi^2-1}$

The answer is: $\frac{2\pi^2}{\pi^2-1}$

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Example Question #75 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{1}{8}-\frac{7}{12}$

Possible Answers:

$\frac{17}{24}$

$\frac{11}{24}$

$-\frac{1}{36}$

$-\frac{17}{24}$

$-\frac{11}{24}$

Correct answer:

$-\frac{11}{24}$

Explanation:

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

Write out some factors for the two uncommon denominators.

8-[8,16,24]

12-[12,24]

We can convert both fractions with a common denominator of 24.

$\frac{1}{8}-\frac{7}{12} =\frac{1(3)}{8(3)}-\frac{7(2)}{12(2)} =\frac{3}{24}-\frac{14}{24}$

With similar denominators, we can subtract the numerators.

The answer is: $-\frac{11}{24}$

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Example Question #81 : Adding And Subtracting Fractions

Add the fractions: $\frac{5}{9}+\frac{7}{18}$

Possible Answers:

$\frac{17}{9}$

$\frac{2}{3}$

$\frac{17}{18}$

$\frac{5}{6}$

$\frac{8}{9}$

Correct answer:

$\frac{17}{18}$

Explanation:

In order to add the fractions, change the denominator of the first fraction so that both denominators are common.

$\frac{5(2)}{9(2)}+\frac{7}{18}$

Simplify the fractions.

$= \frac{10}{18}+\frac{7}{18} = \frac{17}{18}$

The answer is: $\frac{17}{18}$

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Example Question #81 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{2}{3}-\frac{5}{6}-\frac{7}{9}$

Possible Answers:

$-\frac{7}{18}$

$-\frac{2}{3}$

$-\frac{17}{9}$

$-\frac{17}{18}$

$-\frac{7}{8}$

Correct answer:

$-\frac{17}{18}$

Explanation:

Identify the least common denominator. Write out the factors for the denominators.

3-[3,6,9,12,15,18]

6-[6,12,18]

9-[9,18]

The least common denominator is 18. Convert all fractions to this denominator.

$\frac{2}{3}-\frac{5}{6}-\frac{7}{9}=\frac{12}{18}-\frac{15}{18}-\frac{14}{18}$

Since the denominators are common, we can subtract the numerators.

The answer is: $-\frac{17}{18}$

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Example Question #83 : Adding And Subtracting Fractions

Add: $\frac{1}{2}+\frac{3}{5}+\frac{5}{7}$

Possible Answers:

$\frac{64}{35}$

$\frac{9}{70}$

$\frac{127}{70}$

$\frac{9}{35}$

$\frac{137}{70}$

Correct answer:

$\frac{127}{70}$

Explanation:

In order to add the numerators of the fractions, we will need the least common denominator.

Multiply the denominators together.

$2\times 5\times 7 = 70$

Convert all fractions with this denominator.

$\frac{1}{2}+\frac{3}{5}+\frac{5}{7}=\frac{1(5)(7)}{2(5)(7)}+\frac{3(2)(7)}{5(2)(7)}+\frac{5(5)(2)}{7(5)(2)}$

Simplify the numerators.

$\frac{1}{2}+\frac{3}{5}+\frac{5}{7} =\frac{35}{70}+\frac{42}{70}+\frac{50}{70} = \frac{127}{70}$

The answer is: $\frac{127}{70}$

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #71 : Adding And Subtracting Fractions

Example Question #72 : Adding And Subtracting Fractions

Example Question #72 : Adding And Subtracting Fractions

Example Question #73 : Adding And Subtracting Fractions

Example Question #74 : Adding And Subtracting Fractions

Example Question #76 : Adding And Subtracting Fractions

Example Question #75 : Adding And Subtracting Fractions

Example Question #81 : Adding And Subtracting Fractions

Example Question #81 : Adding And Subtracting Fractions

Example Question #83 : Adding And Subtracting Fractions

All Algebra II Resources

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