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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #4611 : Algebra Ii

Divide the fractions: $\frac{3}{12}\div \frac{1}{\frac{3}{5}}$

Possible Answers:

$\frac{3}{20}$

$\frac{12}{5}$

$\frac{20}{3}$

$\frac{3}{10}$

$\frac{1}{10}$

Correct answer:

$\frac{3}{20}$

Explanation:

Reduce the first fraction.

$\frac{1}{4}\div \frac{1}{\frac{3}{5}}$

Simplify the complex fraction by using first using a division sign to rewrite the terms. Convert the division sign to a multiplication sign and take the reciprocal of the second term.

$\frac{1}{\frac{3}{5}} = 1 \div \frac{3}{5} = 1 \times \frac{5}{3}=\frac{5}{3}$

Divide the fractions.

$\frac{1}{4}\div \frac{5}{3} = \frac{1}{4}\times \frac{3}{5}$

Simplify the fractions.

The answer is: $\frac{3}{20}$

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Example Question #271 : Fractions

Multiply the fractions: $\frac{1}{\frac{2}{3}}\cdot \frac{7}{\frac{5}{2}} \cdot \frac{\frac{2}{3}}{4}$

Possible Answers:

$\frac{10}{27}$

$\frac{1}{6}$

$\frac{56}{5}$

$\frac{7}{10}$

$\frac{14}{45}$

Correct answer:

$\frac{7}{10}$

Explanation:

We can multiply the numerators and denominators as is instead of dealing with each complex fraction.

$(1)(7)(\frac{2}{3}) = \frac{14}{3}$

$(\frac{2}{3})(\frac{5}{2})(4) = \frac{20}{3}$

Combine the terms as a complex fraction.

$\frac{1}{\frac{2}{3}}\cdot \frac{7}{\frac{5}{2}} \cdot \frac{\frac{2}{3}}{4} =\frac{\frac{14}{3}}{\frac{20}{3}}$

Rewrite this using a division sign, and then use the multiplication property of division to solve.

$\frac{\frac{14}{3}}{\frac{20}{3}} = \frac{14}{3} \div \frac{20}{3} = \frac{14}{3} \times \frac{3} {20} = \frac{14}{20}$

Reduce this fraction.

The answer is: $\frac{7}{10}$

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Example Question #272 : Fractions

Divide: $\frac{\frac{5}{9}}{\frac{2}{3}}+4$

Possible Answers:

$\frac{26}{5}$

$\frac{118}{27}$

$\frac{27}{118}$

$\frac{29}{6}$

$\frac{5}{26}$

Correct answer:

$\frac{29}{6}$

Explanation:

Simplify the complex fraction by first rewriting the expression using a division sign.

$\frac{\frac{5}{9}}{\frac{2}{3}}=\frac{5}{9}\div \frac{2}{3} = \frac{5}{9}\times \frac{3} {2}$

Multiply and reduce the fractions.

$\frac{15}{18} = \frac{5}{6}$

Add four to this fraction.

$\frac{5}{6}+4 = \frac{5}{6}+\frac{24}{6} = \frac{29}{6}$

The answer is: $\frac{29}{6}$

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Example Question #273 : Fractions

Divide the fractions: $\frac{\frac{7}{9}}{8}\div\frac{\frac{1}{3}}{4}$

Possible Answers:

$\frac{56}{3}$

$\frac{56}{9}$

$\frac{7}{72}$

$\frac{7}{6}$

$\frac{81}{7}$

Correct answer:

$\frac{7}{6}$

Explanation:

Simplify each complex fraction using the multiplication rule of dividing fractions.

$\frac{\frac{7}{9}}{8} = \frac{7}{9}\div 8 = \frac{7}{9}\times \frac{1}{8} = \frac{7}{72}$

$\frac{\frac{1}{3}}{4} = \frac{1}{3}\div 4 = \frac{1}{3}\times \frac{1}{4} = \frac{1}{12}$

Divide the fractions.

$\frac{7}{72} \div \frac{1}{12} = \frac{7}{72} \times \frac{12}{1}$

Reduce the fractions.

The answer is: $\frac{7}{6}$

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Example Question #274 : Fractions

Divide the fractions: $\frac{2}{3}\div \frac{\frac{1}{7}}{\frac{4}{5}}$

Possible Answers:

$\frac{7}{5}$

$\frac{56}{15}$

$\frac{15}{56}$

$\frac{35}{6}$

$\frac{5}{42}$

Correct answer:

$\frac{56}{15}$

Explanation:

Simplify the complex fraction first. Rewrite it using a division sign.

$\frac{\frac{1}{7}}{\frac{4}{5}} = \frac{1}{7} \div\frac{4}{5}$

We can change the division sign to a multiplication sign and take the reciprocal of the second fraction.

$\frac{1}{7} \times \frac{5}{4} = \frac{5}{28}$

Replace this fraction as the second fraction.

$\frac{2}{3}\div \frac{\frac{1}{7}}{\frac{4}{5}}=\frac{2}{3}\div \frac{5}{28}$

Apply the same rule for these fractions.

$\frac{2}{3}\div \frac{5}{28} = \frac{2}{3}\times \frac{28}{5}=\frac{56}{15}$

The answer is: $\frac{56}{15}$

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Example Question #275 : Fractions

Divide: $\frac{7}{\frac{4}{3}}\div \frac{\frac{2}{5}}{9}$

Possible Answers:

$\frac{945}{8}$

$\frac{56}{135}$

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

$\frac{35}{24}$

$\frac{7}{30}$

Correct answer:

$\frac{945}{8}$

Explanation:

Simplify each complex fraction by using the multiplicative rule of division.

Rewrite each term using a division sign and simplify by changing the division sign to a multiplication sign, and take the reciprocal of the second term.

$\frac{7}{\frac{4}{3}} = 7\div \frac{4}{3} = 7\times \frac{3} {4} = \frac{21}{4}$

$\frac{\frac{2}{5}}{9} = \frac{2}{5} \div 9 =\frac{2}{5} \times \frac{1}{9} = \frac{2}{45}$

Rewrite the fractions.

$\frac{7}{\frac{4}{3}}\div \frac{\frac{2}{5}}{9} = \frac{21}{4}\div \frac{2}{45}$

Repeat the process for these fractions.

$\frac{21}{4}\div \frac{2}{45} = \frac{21}{4}\times\frac{45}{2} = \frac{945}{8}$

The answer is: $\frac{945}{8}$

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Example Question #276 : Fractions

Divide the fractions: $\frac{5}{2}\div \frac{7}{11}$

Possible Answers:

$\frac{55}{14}$

$\frac{22}{35}$

$\frac{35}{22}$

$\frac{14}{55}$

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

Correct answer:

$\frac{55}{14}$

Explanation:

In order to divide the two fractions, we will need to change the division sign to multiplication, and take the reciprocal of the right side.

$\frac{5}{2}\div \frac{7}{11} = \frac{5}{2}\times \frac{11}{7} = \frac{55}{14}$

The answer is: $\frac{55}{14}$

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Example Question #107 : Multiplying And Dividing Fractions

Multiply

$\frac{3}{8}\times \frac{4}{9}$

Simplify answer to the simplest form.

Possible Answers:

72/12

7/72

12/17

12/72

1/6

Correct answer:

1/6

Explanation:

$\frac{3}{8}\times \frac{4}{9}$

1) In order to multiply fractions you first want multiply the two numerators together which will give you the multiplied numerator.

3*4=12 This gives you a multiplied numerator of .

2) Next you should do the same time to the denominator, which will give you the multiplied numerator. Unlike addition or subtraction of fractions you do not need to find a common denominator.

8*9=72

3) Putting the results together for numerators and denominators it becomes 12/72 , however you are not done with this problem, as the answer isn't fully simplified. In order to simplify it look for common factors in the numerator. The easiest way is to check if both the numerators are even numbers, in which case they are both divisible by .

In this case both the numerator and denominator are divisible by 2 so you it can be reduced to 6/36 .

4) Once you simplify the expression ask once more if the expression can be simplified more, as often times, including this case, it can be. Here you have a in the numerator and a in the denominator. Ask "what are both and divisible?" They are divisible by as well, but the simpler method would be divide them both by as they're both divisible by . Since this produces a in the numerator you are now done simplifying and your final answer is 1/6 .

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Example Question #1 : Imaginary Numbers

$\frac{-5+10i}{3+4i}=?$

Possible Answers:

1-2i

1+2i

$-\frac{5}{3}-\frac{5}{2}i$

$-\frac{5}{3}+\frac{5}{2}i$

-1+2i

Correct answer:

1+2i

Explanation:

$\frac{-5+10i}{3+4i}$

$=\frac{(-5+10i)(3-4i)}{(3+4i)(3-4i)}$

$=\frac{-15+20i+30i-40i^{2}}{9-16i^{2}}$

$=\frac{-15+50i+40}{9+16}$

$=\frac{25+50i}{25}$

=1+2i

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Example Question #1 : Imaginary Numbers

Multiply:

(7 + 3i) (1 - 2i)

Possible Answers:

7 - 17i

1 - 11i

13 - 11i

7 - 5i

13 - 17i

Correct answer:

13 - 11i

Explanation:

Use the FOIL technique:

(7 + 3i) (1 - 2i)

$= 7 \cdot 1 - 7 \cdot 2i + 3i \cdot 1 - 3i \cdot 2i$

$= 7 - 14i + 3i - 6i ^{2}$

= 7 - 14i + 3i - 6(-1)

= 7 - 14i + 3i +6

= 13 - 11i

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #4611 : Algebra Ii

Example Question #271 : Fractions

Example Question #272 : Fractions

Example Question #273 : Fractions

Example Question #274 : Fractions

Example Question #275 : Fractions

Example Question #276 : Fractions

Example Question #107 : Multiplying And Dividing Fractions

Example Question #1 : Imaginary Numbers

Example Question #1 : Imaginary Numbers

All Algebra II Resources

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