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Algebra II : Adding and Subtracting Fractions

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Example Questions

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: $\frac{9}{49}$

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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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Example Question #123 : Fractions

Subtract the fractions: $\frac{12}{21}-\frac{48}{28}$

Possible Answers:

$-\frac{16}{7}$

$-\frac{8}{7}$

$-\frac{4}{7}$

$-\frac{23}{14}$

$\frac{23}{14}$

Correct answer:

$-\frac{8}{7}$

Explanation:

To simplify the fractions, first reduce the fractions. This will minimize the effort having to multiply double digits in the numerator and denominator.

$\frac{12}{21}-\frac{48}{28} = \frac{3\times 4}{3\times 7}-\frac{4\times 12}{4\times 7}$

The fractions become:

$\frac{4}{7}-\frac{12}{7} = -\frac{8}{7}$

The answer is: $-\frac{8}{7}$

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Example Question #1801 : Mathematical Relationships And Basic Graphs

$\frac{4}{5}+\frac{5}{6}=$

Possible Answers:

$\frac{9}{11}$

$1\frac{19}{30}$

$\frac{9}{30}$

$\frac{20}{30}$

Correct answer:

$1\frac{19}{30}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 5 and 6 is 30. Multiply the first fraction by 6 divided by and the second by 5 divided by 5. Then add or subtract the resulting fractions.

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Example Question #1802 : Mathematical Relationships And Basic Graphs

$\frac{1}{14}+\frac{1}{21}$

Possible Answers:

$\frac{2}{21}$

$\frac{1}{35}$

$\frac{1}{42}$

$\frac{2}{21}$

$\frac{2}{35}$

Correct answer:

$\frac{1}{42}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 14 and 21 is 42. Multiply the first fraction by 3divided by 3 and the second by 2 divided by 2 . Then add or subtract the resulting fractions.

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Example Question #1803 : Mathematical Relationships And Basic Graphs

$\frac{3}{25}+\frac{1}{5}=$

Possible Answers:

$\frac{4}{30}$

$\frac{8}{25}$

$\frac{4}{5}$

$\frac{8}{30}$

$\frac{3}{30}$

Correct answer:

$\frac{8}{25}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 25 and 5 is 25. Multiply the second fraction by 5 divided by 5 . Then add or subtract the resulting fractions.

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Example Question #1804 : Mathematical Relationships And Basic Graphs

$\frac{7}{16}+\frac{3}{24}=$

Possible Answers:

$\frac{10}{40}$

$\frac{27}{40}$

$\frac{21}{40}$

$\frac{10}{24}$

$\frac{27}{48}$

Correct answer:

$\frac{27}{48}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 16 and 24 is 48. Multiply the first fraction by 3divided by 3 and the second by 2 divided by 2 . Then add or subtract the resulting fractions.

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Example Question #1805 : Mathematical Relationships And Basic Graphs

$\frac{4}{11}+\frac{7}{13}=$

Possible Answers:

$5\frac{9}{24}$

$\frac{11}{24}$

$\frac{11}{13}$

$\frac{129}{143}$

$1\frac{4}{24}$

Correct answer:

$\frac{129}{143}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 11 and 13 is 143. Multiply the first fraction by 13 divided by 13 and the second by 11 divided by 11 . Then add or subtract the resulting fractions.

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Example Question #1806 : Mathematical Relationships And Basic Graphs

$\frac{3}{7}-\frac{5}{13}=$

Possible Answers:

$\frac{8}{13}$

$3\frac{14}{20}$

$\frac{8}{20}$

$\frac{4}{91}$

$\frac{15}{20}$

Correct answer:

$\frac{4}{91}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 7 and 13 is 91. Multiply the first fraction by 13 divided by 13 and the second by 7 divided by 7 . Then add or subtract the resulting fractions.

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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 #111 : Fractions

Example Question #121 : Fractions

Example Question #122 : Fractions

Example Question #123 : Fractions

Example Question #1801 : Mathematical Relationships And Basic Graphs

Example Question #1802 : Mathematical Relationships And Basic Graphs

Example Question #1803 : Mathematical Relationships And Basic Graphs

Example Question #1804 : Mathematical Relationships And Basic Graphs

Example Question #1805 : Mathematical Relationships And Basic Graphs

Example Question #1806 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

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