Tetration

$$2 / 1\frac{5}{7}$$

First: Turn the mixed numbers into an improper fraction, use this formula (can you see why it's true?):

$$a\frac{b}{c}=\frac{ac + b}{c}$$

We get:

$$1\frac{5}{7}= \frac{1*7+5}{7}=\frac{12}{7}$$

To divide a number by a fraction is the same as to muliply the number by the multiplicative inverse of the fraction:

$$a/\frac{b}{c}= a*\frac{c}{b}$$

We get:

$$2 / \frac{12}{7}=2*\frac{7}{12}=\frac{14}{12}=\frac{7}{6}$$

G = g₆₄     Where g₁ = 3↑↑↑↑3  and g_n = 3↑^g_n-1 3

Here I've used knuth's up-arrow notation, whice is used to indicate different levels of hyperoperations. 

Graham's number is so gigantic that even it's number of digits is more than a googleplex. Much, MUCH more indeed. 

Remember the formula:

C = pi*d 

Where C is the circumference, pi is the constant pi≈ 3.14 and d is the diameter of the circle.

Also remember that the diameter is twice the radius (witch makes sense when you think about it)

d = 2r 

Order of operations:

1. Solve what's inside the paranthesis

2. Multiply (*) / divide (:)

3. Add (+) / subtract (-)

3x + 2(x + 7) - 5 = 4(x + 3) - 3(x + 1)

3x + 2x +14 - 5 = 4x + 12 - 3x - 3   

5x + 9 = x + 9      You'd typically like to have the x'es on the lift side

                            Move the x to the left, and the nine on the left side over to the right side

4x = 0

x = 0 

It's just 240/12

Indeed 1/x of y is y/x for all y and all x ≠ 0

f(x) = -7x + 11, determine f(10)

f(10) = -7*10 + 11 = -70 +11 = -59

" f(x) = -2 "  just means that the function equals -2 no matter what x is. 

I'm not sure I understand your question ?

Yeah, or ten-ty-one or something like that :)

I guess our close ancestors wanted the small natural numbers (positive integers) to have their own unique names. 

I've heard a story onece about a child who learned to count, he said:

" ... sixteen, seventeen, eighteen, nineteen, tenteen, eleventeen, twelveteen, thirteen... WHAT ?"

Call the amount of money before the depisit x. Then 500$ is added. Now you have $4,732. Can you take over from here?

Is it reasonable? $4,732 ≈ 5 000$, right? And you add just 500$. That tells you that the original amount of money must have been quiet ...

I agree with Melody. Just rename "a number" "x", set up what it equals, and add (plus) or subtract (minus) the same value on both sides of the equality sign (=). 

Have a go! We'll help you if you get stuck. Or read my answer on "A number minus 3 is -8".