What algorithms will produce the correct result of the sum of a+b where in a and b represent any rational number

As rational number includes natural number, whole number ,integers  also.

⇒Natural number(1,2,3,4....) is a rational number also.

So, when A= Natural number , B=Any other natural number

Just add two natural number using simple law of addition.

⇒As Whole numbers(0,1,2,3,...) are Rational number also.

So If A=any whole number, B=Any other whole number

Add the whole number in any order using law of addition.

⇒Coming to integers (....-123,....-5,...-1,....12,....59,.....) By taking any two integers ,

1. Both of them are positive add using simple law of addition.

2. One of them is positive and other is negative , if larger one has positive sign before it just subtract smaller one from larger one and put positive sign before the result.and if larger one has negative sign before it ,subtract smaller one from larger one and put negative sign before the result.

⇒If both of them are negative , just add the two integers and apply negative sign before the result.

4. Rational number as fractions ,

A=m/n and B=p/q

A+B=m/n + p/q

find LCM of n and q.

If n and q are co-prime multiply n and q to get the LCM.For example if n=5, q=7, then LCM=5×7=35

If n and q are not co-prime find the factors of n and q .take out the common factors and then multiply the common factors with those factors which are not common.

For example, n=15, q=20

15=5×3

20=2×2×5

common factor=5

non common factor=2,2,3

LCM=5×2×2×3=60

Suppose LCM(n,q)= K

⇒p/q+m/n

=

So ,

which is the way to find LCM of rational number when theyare fractions.

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation: