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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 #1811 : Mathematical Relationships And Basic Graphs

$\frac{2}{3}+\frac{3}{8}=$

Possible Answers:

$\frac{5}{11}$

$\frac{25}{24}$

$\frac{5}{8}$

$\frac{6}{11}$

$1\frac{1}{24}$

Correct answer:

$1\frac{1}{24}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 3 and 8 is 24. Multiply the first fraction by 8 divided by 8 and the second by 3 divided by 3 . Then add or subtract the resulting fractions.

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Example Question #1812 : Mathematical Relationships And Basic Graphs

$\frac{9}{11}+\frac{1}{3}=$

Possible Answers:

$3\frac{1}{3}$

$2\frac{10}{14}$

$\frac{10}{14}$

$\frac{15}{33}$

$1\frac{5}{33}$

Correct answer:

$1\frac{5}{33}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 11 and 3 is 33. Multiply the first fraction by 3 divided by 3 and the second by 11 divided by 11 . Then add or subtract the resulting fractions.

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Example Question #1813 : Mathematical Relationships And Basic Graphs

$\frac{1}{9}+\frac{3}{6}=$

Possible Answers:

$\frac{4}{15}$

$\frac{11}{18}$

$\frac{3}{15}$

$\frac{4}{6}$

Correct answer:

$\frac{11}{18}$

Explanation:

Convert each fraction to incorporate a common denominator. The least common denominator of 9 and 6 is 18. Multiply the first fraction by 2 divided by 2 and the second by 3 divided by 3 . Then add or subtract the resulting fractions.È

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Example Question #1814 : Mathematical Relationships And Basic Graphs

Add the fractions: $\frac{3}{8}+\frac{7}{12}+\frac{1}{24}$

Possible Answers:

$\frac{17}{12}$

$\frac{27}{4}$

$\frac{23}{12}$

Correct answer:

Explanation:

In order to add the numerators of the fractions, we will need a least common denominator. The LCD can be visually identified as 24, since this is the least number that is divisible by all the denominators.

Convert the fractions.

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

Simplify the numerator.

$\frac{9}{24}+\frac{14}{24}+\frac{1}{24} = \frac{24}{24}=1$

The answer is:

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Example Question #107 : Adding And Subtracting Fractions

Jimmy eats a pie. At the start, the pie starts as one whole. He ate three fifths of the whole pie for lunch, and one tenth of the whole pie for dinner. How much of the pie remains?

Possible Answers:

$\frac{3}{20}$

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{1}{2}$

$\frac{3}{10}$

Correct answer:

$\frac{3}{10}$

Explanation:

Set up an expression to solve how much pizza Jimmy will have left.

$1-\frac{3}{5}-\frac{1}{10}$

Convert each term to the least common denominator, 10.

$\frac{10}{10}-\frac{6}{10}-\frac{1}{10} = \frac{3}{10}$

The answer is: $\frac{3}{10}$

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Example Question #108 : Adding And Subtracting Fractions

Add the fractions: $\frac{3}{4}+\frac{5}{14}$

Possible Answers:

$\frac{31}{14}$

$\frac{31}{8}$

$\frac{7}{4}$

$\frac{17}{14}$

$\frac{31}{28}$

Correct answer:

$\frac{31}{28}$

Explanation:

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

4-[4,8,12,16,20,24,28]

14-[14,28]

The fractions can be converted with a denominator of 28.

$\frac{3}{4}+\frac{5}{14} = \frac{21}{28}+\frac{10}{28} = \frac{31}{28}$

The answer is: $\frac{31}{28}$

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Example Question #107 : Adding And Subtracting Fractions

Add the fractions: $\frac{11}{7}+\frac{13}{8}+\frac{1}{28}$

Possible Answers:

$\frac{47}{28}$

$\frac{181}{56}$

$\frac{87}{28}$

$\frac{33}{23}$

$\frac{15}{7}$

Correct answer:

$\frac{181}{56}$

Explanation:

In order to determine the least common denominator of the three fractions, we can write out the multiples of each term.

7-[7,14,21,28...56]

8-[8,16,24,32,40,48,56]

28-[28,56]

Convert each fraction to a denominator of 56.

$\frac{11}{7}+\frac{13}{8}+\frac{1}{28} = \frac{11\times 8}{56}+ \frac{13\times 7}{56}+ \frac{2}{56}$

Simplify the numerator.

$\frac{88}{56}+ \frac{91}{56}+ \frac{2}{56}= \frac{181}{56}$

The answer is: $\frac{181}{56}$

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Example Question #111 : Adding And Subtracting Fractions

Subtract the fractions: $-\frac{9}{4}-\frac{11}{2}$

Possible Answers:

$-\frac{31}{4}$

$-\frac{5}{2}$

$-\frac{11}{4}$

$-\frac{13}{4}$

Correct answer:

$-\frac{31}{4}$

Explanation:

In order to subtract the fractions, we will need to change the second fraction to a fraction of a common denominator.

Multiply the top and bottom of the second fraction to get the fraction with common denominators as the first fraction.

$-\frac{9}{4}-\frac{11}{2}=-\frac{9}{4}-\frac{11(2)}{2(2)}= -\frac{9}{4}-\frac{22}{4}$

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

The answer is: $-\frac{31}{4}$

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Example Question #112 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{9}{2}-\frac{9}{7}-\frac{9}{28}$

Possible Answers:

$\frac{99}{28}$

$\frac{9}{7}$

$\frac{81}{28}$

$\frac{51}{14}$

Correct answer:

$\frac{81}{28}$

Explanation:

In order to simplify the numerator, we will need to determine the least common denominator.

Visually, we can see that 28 is the least common denominator because this is the minimal number divided by all three of the denominators.

Convert the fractions with a denominator of 28.

$\frac{9}{2}-\frac{9}{7}-\frac{9}{28}=\frac{9(14)}{2(14)}-\frac{9(4)}{7(4)}-\frac{9}{28}$

Simplify the expression.

$\frac{126}{28}-\frac{36}{28}-\frac{9}{28} = \frac{81}{28}$

The answer is: $\frac{81}{28}$

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Example Question #113 : Adding And Subtracting Fractions

Add the fractions: $\frac{7}{5}+\frac{1}{8}+\frac{9}{20}$

Possible Answers:

$\frac{79}{40}$

$\frac{23}{8}$

$\frac{41}{20}$

$\frac{79}{20}$

$\frac{97}{40}$

Correct answer:

$\frac{79}{40}$

Explanation:

In order to add the fractions, we will need to determine the least common denominator. Write out the factors for each denominator. Do not multiply all three denominators together.

5-[5,10,15,20,25,30,35,40]

8-[8,16,24,32,40]

20-[20,40]

The least common denominator is 40. Convert each fraction.

$\frac{7}{5}+\frac{1}{8}+\frac{9}{20}=\frac{7(8)}{5(8)}+\frac{1(5)}{8(5)}+\frac{9(2)}{20(2)}$

Simplify the fractions. The numerators can be added when the denominators are common.

$\frac{56}{40}+\frac{5}{40}+\frac{18}{40} =\frac{79}{40}$

The answer is: $\frac{79}{40}$

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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 #1811 : Mathematical Relationships And Basic Graphs

Example Question #1812 : Mathematical Relationships And Basic Graphs

Example Question #1813 : Mathematical Relationships And Basic Graphs

Example Question #1814 : Mathematical Relationships And Basic Graphs

Example Question #107 : Adding And Subtracting Fractions

Example Question #108 : Adding And Subtracting Fractions

Example Question #107 : Adding And Subtracting Fractions

Example Question #111 : Adding And Subtracting Fractions

Example Question #112 : Adding And Subtracting Fractions

Example Question #113 : Adding And Subtracting Fractions

All Algebra II Resources

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