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Algebra II : Mathematical Relationships and Basic Graphs

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Example Questions

Example Question #141 : Fractions

Subtract the following fractions: $\frac{5}{9}-\frac{4}{27}$

Possible Answers:

$\frac{11}{9}$

$\frac{1}{9}$

$\frac{5}{9}$

$\frac{11}{27}$

$-\frac{11}{27}$

Correct answer:

$\frac{11}{27}$

Explanation:

To subtract the numerators, we will need a least common denominator. Visually, we can notice that the LCD is 27 because this number is the least possible value that is divisible by both denominators.

Convert the fractions.

$\frac{5}{9}-\frac{4}{27}=\frac{5(3)}{9(3)}-\frac{4}{27} = \frac{15}{27}-\frac{4}{27}$

Subtract the numerators. The denominators will remain the same.

The answer is: $\frac{11}{27}$

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Example Question #1822 : Mathematical Relationships And Basic Graphs

Add the fractions: $\frac{7}{8}+\frac{5}{3}+\frac{1}{2}$

Possible Answers:

$\frac{37}{48}$

$\frac{21}{8}$

$\frac{73}{24}$

$\frac{145}{48}$

$\frac{73}{48}$

Correct answer:

$\frac{73}{24}$

Explanation:

Convert all fractions to a least common denominator.

The least common denominator is 24.

$\frac{7(3)}{8(3)}+\frac{5(8)}{3(8)}+\frac{1(12)}{2(12)}=\frac{21}{24}+\frac{40}{24}+\frac{12}{24}$

Now that the denominators are the same, add the numerators.

The answer is: $\frac{73}{24}$

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Example Question #1823 : Mathematical Relationships And Basic Graphs

Add the fractions: $\frac{1}{9}+(-\frac{7}{3})$

Possible Answers:

$\frac{11}{3}$

$-\frac{5}{3}$

$-\frac{20}{9}$

$\frac{22}{3}$

$\frac{22}{9}$

Correct answer:

$-\frac{20}{9}$

Explanation:

A positive and a negative sign will result in a negative sign.

$\frac{1}{9}+(-\frac{7}{3})=\frac{1}{9}-\frac{7}{3}$

Find the least common denominator and convert the second fraction so that both fractions have the same denominator.

$\frac{1}{9}-\frac{7}{3}=\frac{1}{9}-\frac{7(3)}{3(3)} = \frac{1}{9}-\frac{21}{9}$

The answer is: $-\frac{20}{9}$

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Example Question #142 : Fractions

Add the fractions: $\frac{6}{11}+\frac{1}{22}+\frac{2}{33}$

Possible Answers:

$\frac{2}{3}$

$\frac{13}{18}$

$\frac{7}{12}$

$\frac{43}{66}$

$\frac{10}{33}$

Correct answer:

$\frac{43}{66}$

Explanation:

In order to solve the fractions, we will need to determine the least common denominator.

Write out the multiples of each denominator.

11-[11,22,33,44,55,66]

22-[22,44,66]

33-[33,66]

We can see that each term has an LCD of 66.

Convert the fractions.

$\frac{6}{11}+\frac{1}{22}+\frac{2}{33}=\frac{6(6)}{11(6)}+\frac{1(3)}{22(3)}+\frac{2(2)}{33(2)}$

Simplify the numerators.

$\frac{36}{66}+\frac{3}{66}+\frac{4}{66} = \frac{43}{66}$

The answer is: $\frac{43}{66}$

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Example Question #142 : Fractions

Add the fractions: $\frac{1}{4}+\frac{5}{3}+\frac{7}{5}$

Possible Answers:

$\frac{199}{60}$

$\frac{20}{3}$

$\frac{46}{3}$

$\frac{10}{3}$

$\frac{13}{60}$

Correct answer:

$\frac{199}{60}$

Explanation:

Determine the least common denominator.

Multiply all denominators together.

$4\cdot3\cdot5 = 60$

Change all the fractions with this denominator.

$\frac{1}{4}+\frac{5}{3}+\frac{7}{5} = \frac{1(3)(5)}{4(3)(5)}+\frac{5(4)(5)}{3(4)(5)}+\frac{7(3)(4)}{5(3)(4)}$

Simplify the numerator.

$\frac{15}{60}+\frac{100}{60}+\frac{84}{60} = \frac{199}{60}$

The answer is: $\frac{199}{60}$

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Example Question #1826 : Mathematical Relationships And Basic Graphs

Add the fractions: $\frac{3}{5}+\frac{1}{8}+\frac{39}{40}$

Possible Answers:

$\frac{27}{10}$

$\frac{17}{20}$

$\frac{41}{80}$

$\frac{17}{10}$

$\frac{21}{20}$

Correct answer:

$\frac{17}{10}$

Explanation:

To add the numerators, we will need to change the fractions with a least common denominator. Visually, we can see that the LCD is 40 because this is the smallest number that is divisible by all three denominators.

Multiply the numerator by what was multiplied on the denominator to get the LCD for each fraction.

$\frac{3}{5}+\frac{1}{8}+\frac{39}{40}=\frac{24}{40}+\frac{5}{40}+\frac{39}{40}$

Simplify the numerators by addition. The denominators will remain the same.

$\frac{24}{40}+\frac{5}{40}+\frac{39}{40} = \frac{68}{40}$

Reduce the fraction.

$\frac{68}{40} = \frac{17\times 4}{10 \times 4} = \frac{17}{10}$

The answer is: $\frac{17}{10}$

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Example Question #4481 : Algebra Ii

Evaluate: $\frac{2}{7}-\frac{2}{21}-\frac{2}{3}$

Possible Answers:

$-\frac{3}{4}$

$-\frac{10}{21}$

$-\frac{8}{21}$

$-\frac{1}{3}$

Correct answer:

$-\frac{10}{21}$

Explanation:

Convert all fractions to a common denominator. The common denominator is 21.

$\frac{2}{7}-\frac{2}{21}-\frac{2}{3} = \frac{6}{21}-\frac{2}{21}-\frac{14}{21}$

Now that the denominators are alike, we can subtract the numerators.

The answer is: $-\frac{10}{21}$

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Example Question #4482 : Algebra Ii

Subtract the fractions: $\frac{5}{9}-\frac{1}{3}-\frac{5}{12}$

Possible Answers:

$-\frac{1}{4}$

$\frac{7}{36}$

$-\frac{7}{36}$

$-\frac{23}{36}$

$\frac{1}{4}$

Correct answer:

$-\frac{7}{36}$

Explanation:

Determine the least common denominator by writing out the multiples for each term.

9-[9,18,27,36]

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

12-[12,24,36]

The least common denominator is 36.

Convert all fractions.

$\frac{5}{9}-\frac{1}{3}-\frac{5}{12} = \frac{5(4)}{9(4)}-\frac{1(12)}{3(12)}-\frac{5(3)}{12(3)}$

Simplify the right side.

$\frac{20}{36}-\frac{12}{36}-\frac{15}{36}$

Subtract the numerators. The denominator remains the same.

The answer is: $-\frac{7}{36}$

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Example Question #122 : Adding And Subtracting Fractions

Add the fractions: $\frac{1}{4}+\frac{3}{8}+\frac{1}{12}$

Possible Answers:

$\frac{17}{48}$

$\frac{17}{12}$

$\frac{2}{3}$

$\frac{17}{24}$

$\frac{19}{48}$

Correct answer:

$\frac{17}{24}$

Explanation:

In order to add the fractions, we will need to determine the least common denominator. Write out the multiples of the denominators.

4-[4,8,12,16,20,24]

8-[8,16,24]

12-[12,24]

The LCD is 24. Convert the fractions.

$\frac{1(6)}{4(6)}+\frac{3(3)}{8(3)}+\frac{1(2)}{12(2)}=\frac{ 6}{24}+\frac{9}{24}+\frac{2}{24}$

Combine the numerators, but do not change the denominators.

The answer is: $\frac{17}{24}$

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Example Question #121 : Adding And Subtracting Fractions

Solve: $\frac{3}{5}-\frac{2}{7} -\frac{1}{2}$

Possible Answers:

$\frac{13}{35}$

$-\frac{13}{35}$

$\frac{2}{13}$

$\frac{4}{35}$

$-\frac{13}{70}$

Correct answer:

$-\frac{13}{70}$

Explanation:

Identify the least common denominator.

(5)(7)(2) =70

Convert the fractions.

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

Simplify the terms.

$\frac{42}{70}-\frac{20}{70}-\frac{35}{70} = -\frac{13}{70}$

The answer is: $-\frac{13}{70}$

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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 #141 : Fractions

Example Question #1822 : Mathematical Relationships And Basic Graphs

Example Question #1823 : Mathematical Relationships And Basic Graphs

Example Question #142 : Fractions

Example Question #142 : Fractions

Example Question #1826 : Mathematical Relationships And Basic Graphs

Example Question #4481 : Algebra Ii

Example Question #4482 : Algebra Ii

Example Question #122 : Adding And Subtracting Fractions

Example Question #121 : Adding And Subtracting Fractions

All Algebra II Resources

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