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Algebra II : Factorials

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Example Questions

Example Question #61 : Factorials

Divide the factorials: $\frac{3(2+3!)}{1-4!}$

Possible Answers:

$-\frac{360}{23}$

$-\frac{24}{23}$

$-\frac{87}{23}$

$\textup{Cannot be solved.}$

Correct answer:

$-\frac{24}{23}$

Explanation:

Simplify the factorials first.

$3! = 3\cdot2\cdot1 = 6$

$4! = 4\cdot3\cdot2\cdot1 = 24$

Replace the values back into the problem.

$\frac{3(2+3!)}{1-4!} = \frac{3(2+6)}{1-24} = \frac{24}{-23}$

The answer is: $-\frac{24}{23}$

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Example Question #201 : Mathematical Relationships And Basic Graphs

Simplify: $\frac{2(3!+4)}{(2+2)!}$

Possible Answers:

$\frac{181}{6}$

$\frac{5}{6}$

$\frac{10}{3}$

$\frac{91}{3}$

Correct answer:

$\frac{5}{6}$

Explanation:

Simplify the denominator.

$\frac{2(3!+4)}{(2+2)!}=\frac{2(3!+4)}{4!}$

Rewrite each factorial in the given fraction. Do not distribute the two through the quantity or this will change the value of the factorial.

$\frac{2(3!+4)}{4!} =\frac{2([3\times 2\times 1]+4)}{[4\times3\times 2\times 1] } = \frac{2(6+4)}{24}=\frac{2(10)}{24}=\frac{20}{24}$

Reduce this fraction.

The answer is: $\frac{5}{6}$

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Example Question #61 : Multiplying And Dividing Factorials

Divide the factorials: $\frac{2(3+2)!}{3!}$

Possible Answers:

120

604800

Correct answer:

Explanation:

To simplify this, we will need to evaluate the parentheses first. Do not distribute the integer two into the binomial, or the factorial value will change.

$\frac{2(3+2)!}{3!}=\frac{2(5)!}{3!}$

Expand the factorials.

$\frac{2(5)!}{3!} = \frac{2(5\cdot 4\cdot 3\cdot 2\cdot 1)}{3\cdot 2\cdot 1}$

Simplify the top and bottom terms.

$2(5\cdot 4) = 40$

The answer is:

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Example Question #62 : Multiplying And Dividing Factorials

Multiply: $(3!)(3+2)!(\frac{1}{4!})$

Possible Answers:

120

Correct answer:

Explanation:

Simplify the inner parentheses and expand the factorials.

$(3!)(3+2)!(\frac{1}{4!}) = (3\times 2\times 1)(5)!(\frac{1}{4 \times 3\times 2\times 1})$

Cancel out common terms.

$(5\times 4\times 3\times 2\times 1)(\frac{1}{4}) = 5\times 3\times 2\times 1$

The answer is:

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Example Question #65 : Factorials

Multiply: $\frac{2!}{3!}\cdot \frac{4!}{6!}$

Possible Answers:

$\frac{1}{60}$

$\frac{1}{30}$

$\frac{2}{15}$

$\frac{1}{90}$

$\frac{2}{15}$

Correct answer:

$\frac{1}{90}$

Explanation:

In order to solve this, we will need to expand all the factorials.

$\frac{2!}{3!}\cdot \frac{4!}{6!} = \frac{2\times1}{3\times2\times1}\cdot \frac{4\times3\times2\times1}{6\times5\times4\times3\times2\times1 }$

Cancel all the common terms and write the remaining numbers.

$\frac{1}{3 }\cdot \frac{1}{30} = \frac{1}{90}$

The answer is: $\frac{1}{90}$

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Example Question #61 : Factorials

Divide: $\frac{3(4!)}{2!+2!+3!}$

Possible Answers:

$\frac{18}{5}$

$\frac{36}{5}$

47900160

Correct answer:

$\frac{36}{5}$

Explanation:

In order to simplify the factorials, expand all the terms first.

$\frac{3(4!)}{2!+2!+3!} = \frac{3(4\times 3\times2\times 1)}{(2\times 1)+(2\times 1)+(3\times2\times 1)}$

Simplify the numerator and denominator.

$\frac{3(24)}{2+2+6} = \frac{72}{10}=\frac{36}{5}$

The answer is: $\frac{36}{5}$

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Example Question #62 : Factorials

Multiply: $0!\cdot (3+2!)\cdot 0!$

Possible Answers:

120

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

Correct answer:

Explanation:

Evaluate by expanding the factorial in the parentheses. The zero factorial is a special case which equals to one.

$0!\cdot (3+2!)\cdot 0! = 1\cdot (3+(2\times 1))\cdot 1 = 1\cdot (5) \cdot 1$

The answer is:

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Example Question #68 : Factorials

Divide: $\frac{3!}{5!}\div 3!$

Possible Answers:

$\frac{1}{120}$

$\frac{1}{60}$

$\frac{3}{10}$

$\frac{3}{40}$

$\frac{1}{40}$

Correct answer:

$\frac{1}{120}$

Explanation:

Evaluate by expanding the terms of the factorials.

$\frac{3!}{5!}\div 3! = \frac{3\times2\times1 }{5\times4\times3\times2\times1 }\div (3\times2\times1 )$

Cancel out the common terms in the first fraction.

$\frac{1 }{5\times4 }\div (3\times2\times1 )$

Change the division sign to a multiplication and take the reciprocal of the second quantity.

$\frac{1 }{5\times4 }\times \frac{1}{(3\times2\times1 )} =\frac{1}{120}$

The answer is: $\frac{1}{120}$

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Example Question #69 : Factorials

Solve: $\frac{(5+3)!}{2(2+2)!}$

Possible Answers:

440

1680

840

420

Correct answer:

840

Explanation:

Evaluate the terms in the parentheses first.

$\frac{(5+3)!}{2(2+2)!} =\frac{(8)!}{2(4)!}$

Expand the factorials.

$\frac{8\times7\times6\times5\times4\times3\times2\times1 }{2(4\times3\times2\times1 )}$

The fraction, after simplifying all the terms, becomes:

$\frac{8\times7\times6\times5}{2} = 4\times7\times6\times5 = 840$

The answer is: 840

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Example Question #212 : Mathematical Relationships And Basic Graphs

Solve the factorials: $\frac{3!}{5!} \cdot \frac{(1+5)!}{(3!+1)}$

Possible Answers:

$\frac{3}{2}$

$\frac{121}{480}$

$\frac{36}{7}$

600

$\frac{121}{140}$

Correct answer:

$\frac{36}{7}$

Explanation:

Simplify the terms in parentheses first.

$\frac{3!}{5!} \cdot \frac{(1+5)!}{(3!+1)} = \frac{3!}{5!} \cdot \frac{6!}{(3!+1)}$

Evaluate each factorial by writing out the terms.

$\frac{3\times 2\times 1}{5\times 4\times 3\times 2\times 1} \cdot \frac{6\times 5\times 4\times 3\times 2\times 1}{([3\times 2\times 1]+1)}$

Simplify the parentheses.

$\frac{3\times 2\times 1}{5\times 4\times 3\times 2\times 1} \cdot \frac{6\times 5\times 4\times 3\times 2\times 1}{7}$

Simplify all the common terms.

$\frac{6\times 3\times 2\times 1}{7} = \frac{36}{7}$

The answer is: $\frac{36}{7}$

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Algebra II : Factorials

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Factorials

Example Question #201 : Mathematical Relationships And Basic Graphs

Example Question #61 : Multiplying And Dividing Factorials

Example Question #62 : Multiplying And Dividing Factorials

Example Question #65 : Factorials

Example Question #61 : Factorials

Example Question #62 : Factorials

Example Question #68 : Factorials

Example Question #69 : Factorials

Example Question #212 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

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