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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 #82 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{5}{9}-\frac{7}{36}$

Possible Answers:

$\frac{9}{20}$

$-\frac{23}{36}$

$\frac{23}{36}$

$\frac{13}{36}$

$-\frac{1}{3}$

Correct answer:

$\frac{13}{36}$

Explanation:

In order to subtract these fractions, we will need to determine the least common denominator, or LCD.

By visualization, the LCD is 36 because this is the smallest number that is divisible by both denominators.

Convert both fractions.

$\frac{5}{9}-\frac{7}{36} = \frac{5(4)}{9(4)}-\frac{7}{36} = \frac{20}{36}-\frac{7}{36}$

Subtract the numerators. The denominators will remain the same.

The answer is: $\frac{13}{36}$

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Example Question #83 : Adding And Subtracting Fractions

Add the fractions: $\frac{5}{2}+\frac{4}{3}+\frac{3}{4}$

Possible Answers:

$\frac{37}{12}$

$\frac{4}{3}$

$\textup{The answer is not given.}$

$\frac{55}{12}$

$\frac{1}{2}$

Correct answer:

$\frac{55}{12}$

Explanation:

To convert the denominators, we will need to determine the least common denominator. Write out some factors for each denominator.

2-[2,4,6,8,10,12]

3-[3,6,9,12]

4-[4,8,12]

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

$\frac{5}{2}+\frac{4}{3}+\frac{3}{4}=\frac{5(6)}{2(6)}+\frac{4(4)}{3(4)}+\frac{3(3)}{4(3)}$

$=\frac{30}{12}+\frac{16}{12}+\frac{9}{12}$

Now that the denominators are common, add the numerators.

The answer is: $\frac{55}{12}$

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Example Question #84 : Adding And Subtracting Fractions

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

Possible Answers:

$\frac{51}{28}$

$\frac{27}{28}$

$\frac{37}{28}$

$\frac{47}{28}$

$\frac{37}{29}$

Correct answer:

$\frac{37}{28}$

Explanation:

First, identify the common denominator. In this case, it's 28. Now, offset the fractions to get the common denominator:

$\frac{4}{7}=\frac{16}{28}$

$\frac{3}{4}=\frac{21}{28}$

Combine the numerators:

16+21=37

Put that over the denominator:

$\frac{37}{28}$

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Example Question #85 : Adding And Subtracting Fractions

Add the fractions: $\frac{4}{9}+\frac{11}{27}+\frac{1}{18}$

Possible Answers:

$\frac{49}{54}$

$\frac{16}{27}$

$\frac{26}{27}$

$\frac{8}{3}$

$\frac{7}{18}$

Correct answer:

$\frac{49}{54}$

Explanation:

Determine the least common denominator by writing some of the factors of each denominator.

9-[9,18,27,36,45,54]

27-[27,54]

18-[18,36,54]

Convert the fractions to a denominator of 54.

$\frac{4}{9}+\frac{11}{27}+\frac{1}{18}=\frac{4(6)}{9(6)}+\frac{11(2)}{27(2)}+\frac{1(3)}{18(3)}$

Rewrite the fractions.

$\frac{24}{54}+\frac{22}{54}+\frac{3}{54} = \frac{49}{54}$

The answer is: $\frac{49}{54}$

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Example Question #86 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{8}{5}-\frac{9}{11}$

Possible Answers:

$\frac{43}{55}$

$\frac{59}{11}$

$-\frac{1}{5}$

$-\frac{13}{55}$

$\frac{23}{55}$

Correct answer:

$\frac{43}{55}$

Explanation:

Both fractions have unlike denominators. To determine the least common denominator, multiply both denominators together and convert the fractions.

$\frac{8}{5}-\frac{9}{11}=\frac{8(11)}{5(11)}-\frac{9(5)}{11(5)}$

Simplify the fractions.

$\frac{88}{55}- \frac{45}{55} = \frac{43}{55}$

The answer is: $\frac{43}{55}$

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Example Question #87 : Adding And Subtracting Fractions

Add the fractions: $\frac{1}{44}-\frac{1}{8}$

Possible Answers:

$-\frac{9}{88}$

$-\frac{3}{44}$

$\frac{13}{88}$

$-\frac{13}{88}$

$\frac{9}{88}$

Correct answer:

$-\frac{9}{88}$

Explanation:

Convert both fractions to a common denominator.

Multiply the top and bottom of the first fraction by two, and the top and bottom of the second fraction by eleven, which will provide the least common denominator.

$\frac{1}{44}-\frac{1}{8} = \frac{1(2)}{44(2)}-\frac{1(11)}{8(11)}$

Reduce the fractions.

$\frac{2}{88}-\frac{11}{88} = -\frac{9}{88}$

The answer is: $-\frac{9}{88}$

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Example Question #88 : Adding And Subtracting Fractions

Add the fractions: $\frac{5}{2}+\frac{9}{4}+\frac{13}{6}$

Possible Answers:

$\frac{83}{12}$

$\frac{41}{6}$

$\frac{37}{6}$

$\frac{23}{3}$

$\frac{73}{12}$

Correct answer:

$\frac{83}{12}$

Explanation:

Convert the fractions to a least common denominator in order to add the numerators. Write out the factors for each denominator to determine the LCD.

2-[2,4,6,8,10,12]

4-[4,8,12]

6-[6,12]

The LCD is 12.

$\frac{5}{2}+\frac{9}{4}+\frac{13}{6} =\frac{5(6)}{2(6)}+\frac{9(3)}{4(3)}+\frac{13(2)}{6(2)}$

Simplify the fractions.

$\frac{30}{12}+\frac{27}{12}+\frac{26}{12} = \frac{83}{12}$

The answer is: $\frac{83}{12}$

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Example Question #111 : Fractions

Determine the value of: $\frac{9}{7}-\frac{8}{49}$

Possible Answers:

$\frac{7}{11}$

$\frac{11}{49}$

$\frac{1}{49}$

$\frac{11}{7}$

$\frac{55}{49}$

Correct answer:

$\frac{55}{49}$

Explanation:

To subtract the numerators, change the first fraction to a common denominator.

The least common denominator, or LCD, is 49 since this number is the minimal value divisible by both denominators.

Convert the fraction.

$\frac{9}{7}-\frac{9}{49}=\frac{9(7)}{7(7)}-\frac{8}{49}=\frac{63}{49}-\frac{8}{49}$

The answer is: $\frac{55}{49}$

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Example Question #121 : Fractions

Determine the value of: $\frac{2}{7}-\frac{5}{49}$

Possible Answers:

$\frac{3}{16}$

$\frac{3}{49}$

$\frac{9}{49}$

$\frac{1}{7}$

$\frac{9}{16}$

Correct answer:

$\frac{9}{49}$

Explanation:

In order to subtract the numerators, it is necessary to change the first fraction to a common denominator.

The least common denominator is 49 since this value is the smallest number divisible by both denominators.

Convert the fraction.

$\frac{2}{7}-\frac{5}{49}=\frac{2(7)}{7(7)}-\frac{5}{49}=\frac{14}{49}-\frac{5}{49}$

The answer is: $\frac{9}{49}$

Report an Error

Example Question #122 : Fractions

Add the fractions: $\frac{3}{7}+\frac{1}{70}+\frac{7}{20}$

Possible Answers:

$\frac{33}{40}$

$\frac{119}{140}$

$\frac{39}{70}$

$\frac{5}{7}$

$\frac{111}{140}$

Correct answer:

$\frac{111}{140}$

Explanation:

To solve this expression, determine the least common denominator. There is no need to multiply all the denominators together.

Write the factors for each denominator.

70-[70,140]

20-[20,40,60,80,100,120,140]

7-[7,14,21,28,...,70,...,140]

We can see that the LCD is 140.

Convert all fractions.

$\frac{3}{7}+\frac{1}{70}+\frac{7}{20}=\frac{3(20)}{7(20)}+\frac{1(2)}{70(2)}+\frac{7(7)}{20(7)}$

Simplify the fractions.

$\frac{60}{140}+\frac{2}{140}+\frac{49}{140} = \frac{111}{140}$

The answer is: $\frac{111}{140}$

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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 #82 : Adding And Subtracting Fractions

Example Question #83 : Adding And Subtracting Fractions

Example Question #84 : Adding And Subtracting Fractions

Example Question #85 : Adding And Subtracting Fractions

Example Question #86 : Adding And Subtracting Fractions

Example Question #87 : Adding And Subtracting Fractions

Example Question #88 : Adding And Subtracting Fractions

Example Question #111 : Fractions

Example Question #121 : Fractions

Example Question #122 : Fractions

All Algebra II Resources

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