Rational numbers are numbers that can be expressed as a fraction (ratio). Irrational numbers can not be expressed like that (like sqrt(2)).
To prove your statement, assume the opposite until you have a contradiction.
If the result of adding them would be rational, then your irrational number can be expressed as the difference of two rational numbers, which itself is also a rational number. That cannot be, because it should be an irrational number. This contradiction forces that rational + irrational = irrational.
You can reason the same way for multiplication. Suppose rational * irrational = rational, you find that your irrational can be expressed as the fration of two rationals, which is a contradiction.
Answer:
3
Step-by-step explanation:
3 + (-8) - (-8)
= 3 - 8 + 8
= 3
If you have a fraction, you can multiply any constant, if you do it on both the top and bottom and get the same answer. For example, multiply 2 on both sides of 1/3 to get 2/6, or 3 times 1/3 to get 3/9. So 2/6 or 3/9 would work.
Answer:
Multiply both sides by 
Step-by-step explanation:
Given
Required
Get an equivalent of 
To do this, we simply multiply through by
Answer:
1:5.8
Step-by-step explanation:
I think: Substitute what X would be for one then solve; do the same for if X was 5 then set up a ratio and simplify
