Tutor profile: Raika S.
What's the difference between 2/0 and 0/0?
2/0 is undefined, which means say 2/0 does have an answer "x". Thinking about division as the revers of multiplication, that means 0 times "x" has to equal 2, but 0 times anything is always 0! So this is impossible, therefore there is no answer! 0/0 is indeterminate, which the difference is say 0/0 equals some number "x", that means 0 times "x" has to be 0, but then what is 0? 0 times anything is 0, which means "x" can be anything! Meaning it can't be determined! So we say it's indeterminate!
Why is 2^0 equal to 1?
So to start with, say we have a fraction 2^2/2^2, this of course is just 4/4 which is 1, but what if I wrote it with a negative exponent! Such as 2^2 times 2^-2, okay if we have the same base what is the rule for simplifying? It's adding so if we add our power (2+ -2) we get 0! which means 1= 2^2/2^2 = 2^2 * 2^-2 = 2^0 Therefore 2^0 must be 1!
The sum of three consecutive numbers is 72, what is the smallest of the three numbers?
First thinking about what consecutive means, these are numbers such as 1, 2, 3. But we don't know what the first one is so we need a variable to represent this unknown, "x"! Okay so I know x + the other two numbers should be 72 and thinking about consecutive these are numbers that are one plus each other. So we can set up an equation like this: x + (x+1) + (x+2) = 72 All three numbers are accounted for so if we simplify: 3x + 3 = 72 3x = 69 x= 23 So the first one must be 23! The rest are 1 plus that so 23, 24, and 25 but the smallest is 23 so that is our answer!
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