Adding and Subtracting Fractions - Algebra II

Card 0 of 568

Question

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

Answer

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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Question

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

Answer

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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Question

$\frac{4}{9}-\frac{2}{7}=$

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 9 and 7 is 63. Multiply the first fraction by 7 divided by 7 and the second by 9 divided by 9 . Then add or subtract the resulting fractions.

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Question

$\frac{6}{8}+\frac{5}{7}=$

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 8 and 7 is 56. Multiply the first fraction by 7 divided by 7 and the second by 8 divided by 8 . Then add or subtract the resulting fractions.

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Question

$\frac{1}{6}+\frac{4}{5}=$

Answer

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

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

Add the fractions:

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

Answer

When adding fractions, the first thing we need to do is get a common denominator.

$\frac{3}{5}\cdot \frac{2}{2}=\frac{6}{10}$

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

$\frac{6}{10}+\frac{1}{10}=\frac{7}{10}$

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Question

Add the following fractions: $\frac{2}{a}+\frac{2}{a^3b}$

Answer

To be able to add the fractions, we will need to determine the least common denominator.

The least common denominator is since this is the minimal term that is both divisible by and itself.

Convert only the first fraction with the denominator of .

$\frac{2}{a}+\frac{2}{a^3b}= \frac{2(a^2b)}{a(a^2b)}+\frac{2}{a^3b} = \frac{2a^2b+2}{a^3b}$

The answer is: $\frac{2a^2b+2}{a^3b}$

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Question

Subtract the fractions: $\frac{1}{30}- \frac{3}{4}$

Answer

To subtract the fractions, we will need to find the least common denominator.

Write out the factors for both denominators.

Multiply four by 15 to get the least common denominator.

The least common denominator is .

Convert both fractions.

$\frac{1}{30}- \frac{3}{4}= \frac{2}{60}-\frac{45}{60} = -\frac{43}{60}$

The answer is: $-\frac{43}{60}$

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Question

Simplify $\frac{2}{3}+\frac{1}{4}+\frac{5}{6}$

Answer

Find the least common denominator (LCD) and convert each fraction to the LCD and then add. Simplify as necessary.

$\frac{2}{3}+\frac{1}{4}+\frac{5}{6}=\frac{8}{12}+\frac{3}{12}+\frac{10}{12}=\frac{21}{12}$

The result is an improper fraction because the numerator is larger than the denominator and can be simplified and converted to a mix numeral.

$\frac{21}{12}=\frac{7}{4}=1\frac{3}{4}$

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Question

Simplify the expression.

$\frac{x-3y}{6x^{3}y}-\frac{x+3y}{6x^{3}y}$

Answer

Since the denominator is the same in both expressions, we can perform the subtraction in the numerator. The result will have the same denominator of 6x3y.

$\frac{x-3y-(x+3y)}{6x^{3}y}$

$\frac{-6y}{6x^{3}y}$

Simplify the expression:

$\frac{-1}{x^{3}}$

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Question

Find the solution: $\frac{1}{3} \cdot \frac{2}{1} \cdot \frac{3}{5} \cdot \frac{5}{8} \cdot \frac{8}{9} \cdot \frac{9}{1} \cdot \frac{2}{3}$

Answer

Multiply all the nominators and the denominators separately.

Then, simplify the solution untill you get an answer that is an option on the exam.

$\frac{1}{3} \cdot \frac{2}{1} \cdot \frac{3}{5} \cdot \frac{5}{8} \cdot \frac{8}{9} \cdot \frac{9}{1} \cdot \frac{2}{3}=\frac{4320}{3240}=\frac{4}{3}$

An alternate, quicker solution would be to cancel out any matching denominators and nominators.

Once that is done, the equation simpifies to $2 \cdot \frac{2}{3}=\frac{4}{3}$

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Question

Suppose a recipe calls for $\frac{2}{3}$ cup of flour, $\frac{7}{12}$ cup of cinnamon, and $\frac{3}{4}$ cup of sugar.

How many cups of ingredients total does the recipe call for?

Answer

To solve, we must first find a common denominator between 3, 4, and 12. All 3 numbers are factors of 12 and therefore 12 can be the common denominator. Then the numerators must be multiplied by the same factor as the demominator was.

This gives us our new fractions:

$\frac{2}{3}\bigg(\frac{4}{4}\bigg) + \frac{3}{4}\bigg(\frac{3}{3}\bigg)+ \frac{7}{12}$

Next, we add the numerators, but our denominators stay the same:

$\frac{8+9+7}{12}=\frac{24}{12}$ .

Lastly, we simplify to get as our answer.

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Question

Simplify the following fraction:

$\frac{12}{39}$

Answer

Determine the factors of both the numerator and the denominator:

$12 = 2 \times 2 \times 3$

$39 = 3 \times 13$

We notice that 3 is a factor of both 12 and 39 so we can simplify by dividing both 12 and 39 by 3.

$\frac{12}{3}=4$

$\frac{39}{3}=13$

The result is therefore,

$\frac{4}{13}$

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Question

Find the simplified result:

$\frac{5}{6} + \frac{7}{8}$

Answer

Start by making both fractions into the same denominator. One option is $6 \times 8 = 48$

Then adjust the numerators by multiplying each fraction's numerator by the other fraction's denominator:

$\frac{5}{6}\cdot \frac{8}{8}+ \frac{7}{8}\cdot \frac{6}{6}$

$=\frac{40}{48}+\frac{42}{48}$

Then add the adjusted numerators:

$=\frac{82}{48}$

Then we simplify by dividing both numerator and denominator by 2:

$=\frac{2 \cdot 41}{2 \cdot 24}=\frac{41}{24}$

which gives us the final result.

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Question

Find the result. (It does not need to be simplified).

$\frac{9}{10}-\frac{4}{5}$

Answer

We start by adjusting both equations to the same denominator.

Notice that the denominator of the second term is a factor of the denominator of the first term. Therefore we only need to adjust the second term by multiplying both numerator and denominator by 2:

$\frac{9}{10}-\frac{4 \cdot 2}{5 \cdot 2}= \frac{9}{10}-\frac{8}{10}$

Now we need to subtract the numerators:

$=\frac{1}{10}$

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Question

What is the sum of $\frac{2}{5}$ and ${}1\frac{3}{5}$ ?

Answer

Convert the mixed number to an improper fraction.

Then add the numerators together and keep the common denominator.

Finally, simplify.

$\frac{2}{5}+1\frac{3}{5}=\frac{2}{5}+\frac{8}{5}=\frac{10}{5}=2$

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Question

Add:

$\frac{1}{x}+ \frac{4}{x-1}$

Answer

To add rational expressions, you must find the common denominator. In this case, it's .

Next, you must change the numerators to offset the new denominator.

$\frac{1}{x}$ becomes $\frac{x-1}{x(x-1)}$ and $\frac{4}{x-1}$ becomes $\frac{4(x)}{(x-1)x}$ .

Now you can combine the numerators: .

Put that over the denomiator and see if you can simplify/factor further. In this case, you can't.

Therefore, your final answer is:

$\frac{5x-1}{x^2-1}$ .

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