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# Math Examples of Operations on Rational Numbers

• ## Divide -243/126 / -81/49?

Like addition and subtraction we don’t need to equalize the denominator we can multiply them as, numerator of 1st number *denominator of 2nd number/denominator of 1st number *numerator of  2nd In other words we can say  dividing the number is just  equivalent to multiplying the 1st number with the reciprocal of other.

We also need to see one thing the sign convention that’s also plays a very important role in the division  we need to know that in multiplication (+) *(+)= + , multiplication of (-) * (-) =+,multiplication of (-)* (+)= - and multiplication of (+) * (-) = - we can also remember these convention as if we have the same sign then the result will always be positive and if signs are negative then result will always be negative ,I think this is the simplest way to remember the sign convention.

So let’s see the problem, We need to factorize all the values 1st then we will apply division operation

243 can be factorized as 9*9*3,

126 can be factorized as 7*9*2,

81 can be factorize as 9*9,

49 can be factorize as 7*7,

Reciprocal of -81/49 is -49/81 so we need to multiply this reciprocal with -243/126,

Sign convention should be positive as we are having two same sign,

9*9*3*7*7/7*9*2*9*9,

9*9 gets cancel with 9*9 and 7 gets cancel with 7 so the required solution is,

3*7/9*2,

21/18.

We can also minimize this result for that we need to divide with the help of prime Factorization ,prime factors are those factors which only divide by itself or by one we will do the same example with prime factor let’s see what is the difference?

243 can be factorized by prime factors as 3*3*3*3*3,

126 can be factorized by prime factors as 7*3*3*2,

81 can be factorize by prime factors as 3*3*3*3,

49 can be factorize by prime factors as 7*7,

Now on combing we get,

3*3*3*3*3*7*7/3*3*3*3*7*3*3*2,

3*3*3*3*3 gets cancel by 3*3*3*3*3 and 7 gets cancel by 7,

So remaining result is,

7/6,

With the help of prime factorization we can minimize the expression but with the help of simple factorization but with the help of prime factorization we can minimize it up to its last limit so we can use prime factorization.