Rational Numbers Vs Integers. When to apply what.
Algebra

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1(1/3) or a = 1/3; 1a you would assume 1*a or 1/1*1/3; However my question is if you're using rational numbers wouldn't 1+a be hypothetically correct to assume 1+a could be 1a? Because if you replace a it's 11/3 as it is a rational number. 1 and 1/3 is a hypothetical possibility. If so then how should I know when to apply what? For example 11/3 Wouldn't that be 1*1/3 but in rational numbers it would be 1+1/3?
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General math notation is as follows:
ab = a multiplied by b = a*b
a+b = a plus b
The notation  is specifically reserved for "absolute value". You will never see this character used except to denote the absolute value function. Hence:
1a means 1 multiplied by the absolute value of a. It does not mean 1 + a.
1 is a rational number AND an integer. 1/3 is a rational number, but it is not an integer.
1+a DOES NOT equal 1a, as follows:
1+(1/3) = 1* 1/3
3/3 + 1/3 = 1/3
4/3 DOES NOT equal 1/3.
So you cannot say 1+a = 1a. In fact, that is incorrect in every circumstance.
Sorry for incorrect notation. I wanted to ask: can 1 1/3rd be written as 1 a; a = 1/3 or is this messy and frowned upon. I would believe so. I would assume you should write it as a = 1+1/3'rd but I am just trying to tell me self otherwise for no reason. It's not really a big problem I can still do just about everything I need to do it's just I came across this when I was testing myself. I felt like trying to figure it out but I am bad at asking questions apparently.
It's perfectly valid to write 1 1/3, as read "one and one third". There's nothing wrong with that :)
4/3 is the easiest way to write the equivalent expression as one character. Both are completely correct. The only time it actually matters is within algebra expressions: If you do not correctly separate (1 & 1/3) from other terms, it can end up being confusing.
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