No, it does not.
Yes because the numerator will not be right if the denominator doesn't have the same as the other denominator which will mess up the answer
Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.
YES.
by multiplying the denominator with the whole number and adding the numerator. the denominator will remain the same.
Multiply the numerator and the denominator by the same number.
because of mathematical equivalence: it doesn't change the result
It is finding an equivalent fraction.
Adding and subtracting fractions can ONLY be done if the denominators are the same; then the calculation is done by adding or subtracting the numerators. Multiplying (and dividing) fractions does not require the denominators to be the same. To divide by a fraction the divisor is inverted (the original numerator becomes the new denominator and the original denominator becomes the new numerator) and then the fractions are multiplied. Multiplying fractions is achieved by multiplying the numerators together AND multiplying the denominators together. A whole number is the same as a fraction with the whole number as the numerator and a denominator of 1, so when multiplying by a whole number the denominator is multiplied by 1 (leaving it the same) and the is multiplication is effectively just multiplying the numerator by the whole number.
Because doing so is equivalent to multiplying or dividing by x/x, which can be cancelled down to 1.
This is because dividing by a number is the same as multiplying by its reciprocal.
If you mean multiplying numerator and denominator by different numbers, the result is then a different ratio. If you mean variously multiplying the numerator and denominator by the same number on different occasions, the result is unchanged.
Note: numerator is the top part of the fraction, denominator is the bottom part. 1) Find a common denominator. It may be the least common denominator, but it need not be; just multiplying the denominators also gives you a common denominator, not necessarily the smallest one. 2) Convert each fraction so that it has this common denominator. This means multiplying numerator and denominator by the same number.