Tetration

Multiply numerator (top) by numerator and denominator (bottom) by denominator.

$$-\frac{2}{5}*\frac{6}{7}=$$

$$-\frac{12}{35}$$

It's an intresting question, though. 

Simplifying rational numbers w/ several digits in both the numerator and denominator, by hand, is certainly not somthing every adult know how to do. And one can learn A LOT from such problems: the times table, divisibility rules, prime numbers, coprimes, and so forth. But, indeed, many calculators solve this instantly.

Questions involving simplifying rational numbers occur pretty often, so parhaps it should be included in "Great Answers to Learn From" or sth. I haven't looked into the matter yet...

I'll probably refer to Wolfram Alpha for any related questions in future posts.

Well, both the denominator (bottom) and numerator (top) is even numbers (divisible by 2), so you can divide them by 2. You'll get:

39/137

Since the digit sum of the numerator is divisible by 3, the whole number must be divisible by 3. What about the denominator? Nah, it's digit sum is 11, so the whole number isn't divisible by three. 

But, we have nontheless gotten further in our solving. Since 39 is divisible by 3, we can much easier factorize it:

39/ 3 = 13       =>     3*13 = 39

Now all we have to do is to check if 137 is divisible by 11. (We have already checked for 3). 

No. 137 isn't divisible by 11. 

Since 39 and 137 doesn't have any factors in common, the simplest version of the original fraction is:

39/137

The formula for the area of a circle is:

A = pi * r²

And to get the volume of a cylinder, simply multiply by the heigth:

V = pi * r²h

Thus:

V ≈ 3.14 * 10 cm * 10 cm * 6.5 cm = <your answer> cm³

*** Thx ***

Order of operations:

1. Solve the paranthesis

2. Multiply(*) / divide (:)

3. Add (+) / subtract (-)

3x - 2(x - 3) = 5x + 4(x + 5)       Solve the paranthesis. I'll use this formula: a - b = -(b - a), It'll make easier

                                                  to avoid careless mistakes based on multiple minuses.

3x + 2(3 - x) = 5x + 4x + 20       Combine like terms, solve the last parantesis

3x + 6 - 2x = 9x + 20                 Combine like terms once again. Move the six over to the right,

                                                 Remember: You wanna end up w/ the variables on the left, and numbers on

                                                 the right

x = 9x + 14                               Move the 9x over

-8x = 14                                   Divide by -8

x = - 7/4

I have the Wolfram Alpha page in front of me, and it says that y = 8.

Order of operations:

1. Solve the paranthesis

2. Multiply(*) / divide (:)

3. Add (+) / subtract (-)

EITHER:

-16 = 6(y - 8) - 2y                    use the formula a - b = -(b - a) to get rid of minuses:

16 = 6(8 - y) + 2y        

16 = 48 - 6y + 2y = 48 - 4y             Get all numbers over to the right side        

0 = 32 - 4y                                       Move your variable to the left side

4y = 32

y = 8

OR: 

-16 = 6(y - 8) - 2y          Solve the paranthesis:

-16 = 6y - 48 -2y            Combine like terms:

-16 = 4y - 48                   Add 48 to both sides:

32 = 4y 

4y = 32                          Divide both sides by 4:

y = 8

This number is written in scientific notation. A number written in scientific notation has this form:

a * 10^b 

So your number is actually 2.23 * 10^-11