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Algebra II : Adding and Subtracting Fractions

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Example Question #51 : Adding And Subtracting Fractions

$\frac{4}{7}+\frac{2}{3}$

Possible Answers:

$1\frac{5}{26}$

$1\frac{5}{21}$

$\frac{5}{21}$

$1\frac{6}{21}$

Correct answer:

$1\frac{5}{21}$

Explanation:

To add fractions, first find the common denominator. In this case, it's 21.

Then, multiply the numerators to get:

$\frac{12}{21}+\frac{14}{21}$ .

Then, add the numerators to get $\frac{26}{21}$ , which is $1\frac{5}{21}$ .

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Example Question #81 : Fractions

Add/Subtract $\frac {2}{3}-\frac {4}{7}+\frac {3}{2}$

Possible Answers:

$\frac{42}{67}$

$\frac{67}{42}$

$\frac{-67}{42}$

Correct answer:

$\frac{67}{42}$

Explanation:

Step 1: Find the Lowest Common Denominator (LCD) of all fractions. We can get the lowest denominator by writing out multiples of each denominator until we get a match on all three:

$3: 3,6,9,12,15,18,21,24,27,30,33,36,39,{\color{Blue} 42}$
$7: 7,14,21,28,35,{\color{Blue} 42}$
$2: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,{\color{Blue} 42}$

We see that the LCD is .

Step 2: Change all fractions into denominator .

$\frac {2}{3}=\frac {x}{42}$

Cross-Multiply:

$\frac {{\color{Red} 2}}{{\color{Blue} 3}}=\frac {\color{Blue} x}{{\color{Red} 42}}=3x=84->x=28$

The first fraction is $\frac {28}{42}$

Second Fraction: $\frac {-4}{7}=\frac {-24}{42}$

Third Fraction: $\frac {3}{2}=\frac {63}{42}$

Step 3: Re-Write the equations:

$\frac {28}{42}-\frac {24}{42}+\frac {63}{42}=\frac {28-24+63}{42}=\frac {67}{42}$

The final answer is $\frac {67}{42}$

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Example Question #81 : Fractions

Simplify: $x=\frac{5}{7} +\frac{1}{4}$ .

Possible Answers:

$\frac{15}{28}$

$\frac{27}{11}$

$\frac{27}{28}$

$\frac{1}{6}$

$\frac{6}{7}$

Correct answer:

$\frac{27}{28}$

Explanation:

To simplify, we multiply each fraction by the denominator of the other:

$x=\frac{20}{28} +\frac{7}{28}$

Then we add the numerators:

$x=\frac{27}{28}$

We can't simplify our answer, so we're done.

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Example Question #83 : Fractions

Simplify: $x= \frac{5}{7} + 2\frac{1}{3}$

Possible Answers:

$3\frac{27}{29}$

$2\frac{22}{21}$

$\frac{64}{21}$

$\frac{17}{19}$

Correct answer:

$\frac{64}{21}$

Explanation:

First, let's start by putting everything into proper fractions:

$x=\frac{5}{7}+\frac{7}{3}$

Next, we find a common denominator by multiplying each fraction by the denominator of the other fraction:

$x=\frac{15}{21}+\frac{49}{21}$

Finally, we add numerators together:

$x=\frac{64}{21}$

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Example Question #84 : Fractions

Add the fractions: $\frac{7}{10} + \frac{1}{5}+\frac{2}{3}$

Possible Answers:

$\frac{1}{15}$

$\frac{5}{6}$

$\frac{5}{9}$

$\frac{29}{30}$

$\frac{47}{30}$

Correct answer:

$\frac{47}{30}$

Explanation:

In order to add the fractions, the denominators must be common.

Find the least common denominator. The least common denominator is since this is the smallest number possible that is divisible by all three denominators.

Convert the fractions. Multiply the top with what was multiplied to the denominators to achieve the least common denominator.

$\frac{7}{10} + \frac{1}{5}+\frac{2}{3} = \frac{21}{30}+\frac{6}{30}+\frac{20}{30} = \frac{47}{30}$

The answer is: $\frac{47}{30}$

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Example Question #81 : Fractions

Solve the fractions: $\frac{3}{8}+\frac{1}{4}-\frac{3}{10}$

Possible Answers:

$\frac{13}{40}$

$\frac{13}{80}$

$\frac{1}{22}$

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

$\frac{17}{120}$

Correct answer:

$\frac{13}{40}$

Explanation:

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

The least common denominator is since this is the least number that all three denominators are divisible by.

Convert all the fractions.

$\frac{3(5)}{8(5)}+\frac{1(10)}{4(10)}-\frac{3(4)}{10(4)}=\frac{15}{40}+\frac{10}{40}-\frac{12}{40}$

The answer is: $\frac{13}{40}$

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Example Question #86 : Fractions

Add the fractions: $\frac{6}{7}+\frac{1}{11}$

Possible Answers:

$\frac{73}{77}$

$\frac{1}{11}$

$\frac{7}{18}$

$\frac{7}{17}$

$\frac{3}{7}$

Correct answer:

$\frac{73}{77}$

Explanation:

Find the least common denominator by multiplying the denominators together and convert the fractions.

$\frac{6}{7}+\frac{1}{11} = \frac{6(11)}{7(11)}+ \frac{1(7)}{7(11)} =\frac{6(11)+1(7)}{77}$

Now that the denominators are common, we can simplify the numerator.

$\frac{6(11)+1(7)}{77} =\frac{66+7}{77}= \frac{73}{77}$

The answer is: $\frac{73}{77}$

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Example Question #87 : Fractions

Subtract the fractions: $\frac{1}{16}-\frac{2}{3}$

Possible Answers:

$\frac{35}{48}$

$-\frac{29}{48}$

$-\frac{9}{16}$

$-\frac{35}{48}$

$\frac{9}{16}$

Correct answer:

$-\frac{29}{48}$

Explanation:

Notice that the first term is smaller than the second term.

Convert the fractions to a common denominator by multiplying both denominators together. The least common denominator is not 16!

$16\times 3=48$

Convert both fractions with this LCD.

$\frac{1(3)}{16(3)}-\frac{2(16)}{3(16)} = \frac{3}{48}-\frac{32}{48}$

Subtract the numerators.

The answer is: $-\frac{29}{48}$

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Example Question #88 : Fractions

Add the following fractions: $\frac{2}{3}+\frac{7}{9}+\frac{1}{2}$

Possible Answers:

$\frac{3}{2}$

$\frac{4}{3}$

$\frac{31}{18}$

$\frac{35}{18}$

$\frac{5}{6}$

Correct answer:

$\frac{35}{18}$

Explanation:

In order to add and combine the numerators, we will need a similar denominator.

The least common denominator is , since this is the smallest number that is divisible by all the denominators in the expression.

Concert all fractions with this denominator.

$\frac{2}{3}+\frac{7}{9}+\frac{1}{2}=\frac{2(6)}{3(6)}+\frac{7(2)}{9(2)}+\frac{1(9)}{2(9)}$

Simplify the terms.

$\frac{12}{18}+\frac{14}{18}+\frac{9}{18}=\frac{35}{18}$

The answer is: $\frac{35}{18}$

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Example Question #89 : Fractions

Subtract the following fractions: $6\frac{2}{9}- 14\frac{1}{3}$

Possible Answers:

$\frac{19}{9}$

$-\frac{73}{9}$

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

$\frac{13}{6}$

$-\frac{70}{9}$

Correct answer:

$-\frac{73}{9}$

Explanation:

Convert both fractions to improper fractions.

The numerator can be obtained by multiplying the denominator with the whole number, and then add the numerator. Denominators remain the same.

$6\frac{2}{9}- 14\frac{1}{3}=\frac{(9\times 6)+2}{9}-\frac{(3\times 14)+1}{3}$

Simplify both fractions.

$\frac{56}{9}-\frac{43}{3}$

Convert the second fraction so that it has the same denominator as the first fraction.

$\frac{56}{9}-\frac{43(3)}{3(3)}=\frac{56}{9}-\frac{129}{9} =-\frac{73}{9}$

The answer is: $-\frac{73}{9}$

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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 #51 : Adding And Subtracting Fractions

Example Question #81 : Fractions

Example Question #81 : Fractions

Example Question #83 : Fractions

Example Question #84 : Fractions

Example Question #81 : Fractions

Example Question #86 : Fractions

Example Question #87 : Fractions

Example Question #88 : Fractions

Example Question #89 : Fractions

All Algebra II Resources

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