Can You Multiply These Fractions?

Since the multiplication of a series of fractions is the product of all the numerators over the product of all the denominators, we can find the answer with $\frac { 9! }{ 10! } =\frac { 9! }{ 9!(10) } =\frac { 1 }{ 10 } =0.1$ .

The denominator of the previous fraction is cancelled by the numerator of the next fraction.This process gives $\frac{1}{10}=\boxed{0.1}$

simple, removing the numeraror/denominator remaining will be 1/10

Just use cancellation. For example:

1/2 x 2/3 = 1/3, because the 2s cancel out.

1/3 x 3/4 = 1/4, because the 3s cancel out.

1/4 x 4/5 = 1/5, because the 4s cancel out.

Just continue this to the end, and you are left with 1/10.

1/10 = 0.1, so the answer is 0.1

1/10... the 2s cancels each others, the 3s, the 4s...

$\frac{1}{2}$ x $\frac{2}{3}$ x $\frac{3}{4}$ x $\frac{4}{5}$ x $\frac{5}{6}$ x $\frac{6}{7}$ x $\frac{7}{8}$ x $\frac{8}{9}$ x $\frac{9}{10}$ multiply it all together = $\frac{1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9}{2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10}$ rearrange the terms and split back into new fractions = $\frac{2}{2}$ x $\frac{3}{3}$ x $\frac{4}{4}$ x $\frac{5}{5}$ x $\frac{6}{6}$ x $\frac{7}{7}$ x $\frac{8}{8}$ x $\frac{9}{9}$ x $\frac{1}{10}$ turn fractions that are 1 into 1 = 1 x 1 x 1 x 1 x 1 x 1 x 1 x1 x $\frac{1}{10}$ 1 goes away in multiplication = $\frac{1}{10}$

Cross out repeating numbers.

Cut out the denominator of the fraction by the next one - which means: - the answer is 0.1

All denominators are cancelled by the next of numerator. Only 1/10 will left so the answer is 0.1

Take logarithm both sides , assume right side as x , each successive log is canceled by previous member , in the end we are left with logx=log(1/10) , on comparing we get x=0.1

$\frac{n!}{(n+1)!}$ , if n eq 9 we got $\frac{9!}{10!}$ , eq $\frac{9!}{9!(10)}$ simplified by $\frac{1}{10}$ .

9!/10! =9!/9!*10 =1/10 =0.1

The dr. Of the previous fraction is cancelled by the nr of next fraction. Then it gives 1/10=0.1

the product of the numerators will be x, the product of the denominators will be 10x, therefpre the answer willbe x/10x=1/10

All of the numerators and denominators cancel except 1 and 10, ergo 1/10 or .1

9!/10! =1/10=0.1

This fraction is equivalent to 9!/10! since 10!=9!*10, the 9! is cancelled out with only a ten left, so we have 1/10, which is 0.1.

All the numbers cancel off except 1 & 10 Leaving 1/10 = 0.1

Remove 2, 3, 4, 5, 6, 7, 8, and 9. And you will find 1/10 and it means 0.1

9! / 10, then we can cancel 9! making it 1/10 =0.1

The way I did it (which was a bit too much) was: Let $n = 1$ , therefore, the product is written as: $\frac{n}{n+1} \times \frac{n+1}{n+2} \times \frac{n+2}{n+3} \times \frac{n+3}{n+4} \times \frac{n+4}{n+5} \times \frac{n+5}{n+6} \times \frac{n+6}{n+7} \times \frac{n+7}{n+8} \times \frac{n+8}{n+9}$ But most of the the denominators cancel each other, leaving: $n \times \frac{1}{n+9} = \frac{1}{10} = 0.1 \blacksquare$