Multiplying and Dividing Factorials - Math

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Question

Stewie has $\frac{5!}{3!}$ marbles in a bag. How many marbles does Stewie have?

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Answer

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

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Question

Solve the following expression.

$\frac{10!}{8!}$

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Answer

$\frac{10!}{8!}=\frac{10987654321}{87654321}$

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

$\frac{1098!}{8!}=10*9=90$

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Question

Which of the following is equivalent to $6!\times4!$ ?

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Answer

This is a factorial question. The formula for factorials is $n! = n\times(n-1)\times(n-2)\times...\times1$ .

$6!=6\times5\times4! = 30\times 4!$

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Question

Which of the following is NOT the same as $\frac{6!\times5!}{4!}$ ?

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Answer

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

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Question

Solve:

$\frac{10!}{7!}$

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Answer

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for $10\cdot9\cdot8$ in the numerator. Multiply those together to get 720.

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Question

Simplify $\frac{ 8!}{6!}$ .

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Answer

Thus, $\frac{8!}{6!} = 8*7$ since the remaining terms cancel out. 56 is the simplified result.

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Question

Simplify and solve $\frac{100!}{97!}$ .

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Answer

Remember a number followed by a ! is a factorial. A factorial is the product of the given number and all of the numbers smaller than it down to zero. For example, .

Rather than do all of the math involved for , notice that $\frac{100!}{97!}$ is the same as $\frac{1009998*97!}{97!}$

From here, the 's cancel out, leaving us with .

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Question

Which of the following is equivalent to $6!\times4!$ ?

Tap to reveal answer

Answer

This is a factorial question. The formula for factorials is $n! = n\times(n-1)\times(n-2)\times...\times1$ .

$6!=6\times5\times4! = 30\times 4!$

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Question

Stewie has $\frac{5!}{3!}$ marbles in a bag. How many marbles does Stewie have?

Tap to reveal answer

Answer

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

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Question

Solve the following expression.

$\frac{10!}{8!}$

Tap to reveal answer

Answer

$\frac{10!}{8!}=\frac{10987654321}{87654321}$

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

$\frac{1098!}{8!}=10*9=90$

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Question

Which of the following is NOT the same as $\frac{6!\times5!}{4!}$ ?

Tap to reveal answer

Answer

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

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Question

Solve:

$\frac{10!}{7!}$

Tap to reveal answer

Answer

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for $10\cdot9\cdot8$ in the numerator. Multiply those together to get 720.

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Question

Simplify $\frac{ 8!}{6!}$ .

Tap to reveal answer

Answer

Thus, $\frac{8!}{6!} = 8*7$ since the remaining terms cancel out. 56 is the simplified result.

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Question

Simplify and solve $\frac{100!}{97!}$ .

Tap to reveal answer

Answer

Remember a number followed by a ! is a factorial. A factorial is the product of the given number and all of the numbers smaller than it down to zero. For example, .

Rather than do all of the math involved for , notice that $\frac{100!}{97!}$ is the same as $\frac{1009998*97!}{97!}$

From here, the 's cancel out, leaving us with .

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Question

Which of the following is equivalent to $6!\times4!$ ?

Tap to reveal answer

Answer

This is a factorial question. The formula for factorials is $n! = n\times(n-1)\times(n-2)\times...\times1$ .

$6!=6\times5\times4! = 30\times 4!$

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Question

Stewie has $\frac{5!}{3!}$ marbles in a bag. How many marbles does Stewie have?

Tap to reveal answer

Answer

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

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Question

Solve the following expression.

$\frac{10!}{8!}$

Tap to reveal answer

Answer

$\frac{10!}{8!}=\frac{10987654321}{87654321}$

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

$\frac{1098!}{8!}=10*9=90$

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Question

Which of the following is NOT the same as $\frac{6!\times5!}{4!}$ ?

Tap to reveal answer

Answer

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

← Didn't Know|Knew It →

Question

Solve:

$\frac{10!}{7!}$

Tap to reveal answer

Answer

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for $10\cdot9\cdot8$ in the numerator. Multiply those together to get 720.

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Question

Simplify $\frac{ 8!}{6!}$ .

Tap to reveal answer

Answer

Thus, $\frac{8!}{6!} = 8*7$ since the remaining terms cancel out. 56 is the simplified result.

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Knew It

Multiplying and Dividing Factorials - Math

Stewie has marbles in a bag. How many marbles does Stewie have?

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so Alternative Solution

Solve the following expression.

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

Which of the following is equivalent to ?

This is a factorial question. The formula for factorials is .

Which of the following is NOT the same as ?

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

Solve:

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for in the numerator. Multiply those together to get 720.

Simplify .

Thus, since the remaining terms cancel out. 56 is the simplified result.

Simplify and solve .

Remember a number followed by a ! is a factorial. A factorial is the product of the given number and all of the numbers smaller than it down to zero. For example, . Rather than do all of the math involved for , notice that is the same as From here, the 's cancel out, leaving us with .

Which of the following is equivalent to ?

This is a factorial question. The formula for factorials is .

Stewie has marbles in a bag. How many marbles does Stewie have?

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so Alternative Solution

Solve the following expression.

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

Which of the following is NOT the same as ?

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

Solve:

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for in the numerator. Multiply those together to get 720.

Simplify .

Thus, since the remaining terms cancel out. 56 is the simplified result.

Simplify and solve .

Remember a number followed by a ! is a factorial. A factorial is the product of the given number and all of the numbers smaller than it down to zero. For example, . Rather than do all of the math involved for , notice that is the same as From here, the 's cancel out, leaving us with .

Which of the following is equivalent to ?

This is a factorial question. The formula for factorials is .

Stewie has marbles in a bag. How many marbles does Stewie have?

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so Alternative Solution

Solve the following expression.

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

Which of the following is NOT the same as ?

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

Solve:

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for in the numerator. Multiply those together to get 720.

Simplify .

Thus, since the remaining terms cancel out. 56 is the simplified result.

Stewie has $\frac{5!}{3!}$ marbles in a bag. How many marbles does Stewie have?

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

Solve the following expression.

$\frac{10!}{8!}$

$\frac{10!}{8!}=\frac{10987654321}{87654321}$

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

$\frac{1098!}{8!}=10*9=90$

Which of the following is equivalent to $6!\times4!$ ?

This is a factorial question. The formula for factorials is $n! = n\times(n-1)\times(n-2)\times...\times1$ .

$6!=6\times5\times4! = 30\times 4!$

Which of the following is NOT the same as $\frac{6!\times5!}{4!}$ ?

Solve:

$\frac{10!}{7!}$

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for $10\cdot9\cdot8$ in the numerator. Multiply those together to get 720.

Simplify $\frac{ 8!}{6!}$ .

Thus, $\frac{8!}{6!} = 8*7$ since the remaining terms cancel out. 56 is the simplified result.

Simplify and solve $\frac{100!}{97!}$ .

Which of the following is equivalent to $6!\times4!$ ?

This is a factorial question. The formula for factorials is $n! = n\times(n-1)\times(n-2)\times...\times1$ .

$6!=6\times5\times4! = 30\times 4!$

Stewie has $\frac{5!}{3!}$ marbles in a bag. How many marbles does Stewie have?

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

Solve the following expression.

$\frac{10!}{8!}$

$\frac{10!}{8!}=\frac{10987654321}{87654321}$

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

$\frac{1098!}{8!}=10*9=90$

Which of the following is NOT the same as $\frac{6!\times5!}{4!}$ ?

Solve:

$\frac{10!}{7!}$

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for $10\cdot9\cdot8$ in the numerator. Multiply those together to get 720.

Simplify $\frac{ 8!}{6!}$ .

Thus, $\frac{8!}{6!} = 8*7$ since the remaining terms cancel out. 56 is the simplified result.

Simplify and solve $\frac{100!}{97!}$ .

Which of the following is equivalent to $6!\times4!$ ?

This is a factorial question. The formula for factorials is $n! = n\times(n-1)\times(n-2)\times...\times1$ .

$6!=6\times5\times4! = 30\times 4!$

Stewie has $\frac{5!}{3!}$ marbles in a bag. How many marbles does Stewie have?

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

Solve the following expression.

$\frac{10!}{8!}$

$\frac{10!}{8!}=\frac{10987654321}{87654321}$

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

$\frac{1098!}{8!}=10*9=90$

Which of the following is NOT the same as $\frac{6!\times5!}{4!}$ ?

Solve:

$\frac{10!}{7!}$

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for $10\cdot9\cdot8$ in the numerator. Multiply those together to get 720.

Simplify $\frac{ 8!}{6!}$ .

Thus, $\frac{8!}{6!} = 8*7$ since the remaining terms cancel out. 56 is the simplified result.