I see you're still dumping your homework on us.
We don't do homework -- but we'll be glad to check your answers or explain problems you don't understand.
1. I think it is -7x-7x-7x-7x-7
8. 0.57 as a fraction is 57/100, that is a rational number. 57/100 as a kdecimal is 0.57 which is still a rational number.
Thank You Sooooo Much For Checking My Answers! :)
I'm not going to just answer these for you. So here goes: the symbol "^" is called a caret. It is the mathematical sign for an exponent. It is simply a shorthand way of writing a set of repeating multiplications, just like multiplication is shorthand for addition. For example, would you rather write 4+4+4+4+4+4+4+4 or simply 4x8? That's all multiplication is, a shortcut way of writing out repeating additions. This is the same case for exponents, but with exponents we are repeating multiplication. So you can write either 4x4x4x4x4x4x4x4 or you can write 4^8. Either way, you get the same answer: 65,536. That should help you solve the first few problems, although if you reduce #2 to a number, you will realize it is not included in the answers.
FRACTIONS: think of fractions as a thing, like a sock, or a shirt. 1 shirt plus 2 shirts equals 3 shirts. Or 1 sixth plus 2 sixths equals 3 sixths. When you divide a fraction by another fraction, this is the same thing as multiplying by the inverse of the denominator fraction. So (a/b) / (c/d) is the same as (a/b) * (d/c).
RATIONALS: a rational number is any number that can be expressed in a fraction a/b where a and b are integers or whole numbers (1 or 2 or 3, etc. - not 2.67 etc) and b is not zero.
IRRATIONALS: any real number that cannot be expressed as a/b where a and b are integers and b is not zero. The most famous is irrational numbers is pi, or 3.14159....
For #7, get a common denominator (the numbers on the bottom of the fractions, the quotient, are both the same number - in this case they should both be six, so you only ned to change one of them, the 2/3, so that it has a six on the bottom. To change a fraction, you have to do to the top what you do to the bottom. So if you had 4/5 and you needed the 5 in the denominator to be a 10, then you would multiply it by 2. But you would also need to multiply the top by 2, so you would have (4/5)*(2/2) = (8/10). And if I was adding 8/10 to 12/10 then I would have this:
(8/10) + (12/10) = (8+12)/10 = 20/10 = 2/1 = 2
Remember that fractions are like things, like socks or shirts- if you have 8 socks and add 12 socks, then you get 20 socks. So if you have 8 tenths and add 12 tenths then you get 20 tenths -- in other words the denominator does not change - it doesn't become twenty twentieths.
Wrong: 2, 3, 7
The others are right.