Would this be never true? both sides of an equation containing fractions can be multiplied by the same number w/o changing the solution of the equation.

Question

I was thinking that this would be never true because it's when you change the denominator. Is that right?

Answer 1

As long as it's an equation, not an inequality, multiplying both sides by the same quantity preserves the equality. So the equation is always true. However, multiplying both sides by zero is not recommended because, if the equation was in fact false, multiplying through by zero would make it appear to be true! So avoid zero multipliers! For example: 2=3 is false but multiplying both sides by zero gives 0=0 which is true. But the equation x=3 is still true if we multiply it by a non-zero quantity, say, 10: 10x=30 is still true. For fractions the same holds true: x/4=5/6. Multiply through by 12 (for example): 3x=10, and x=10/3 and x/4=10/12=5/6, still true.