Explain why all of these expressions have the same value. 4500÷90 450÷9 45÷0.9 4.5÷0.09

Both sides of the  first equation are divided by 10 to get the 2nd question so on and so forth...

As the cycle continues, you will always get 50 as the answer since you are dividing both the numerator and the denominator with 10 in each expression. In other words; the ten you divide the numerator with cancels out with the ten you divide the denominator with. So the answer will always be 50 in each next expression.

Step-by-step explanation:

(i) 4500 ÷ 90 = = 50

(ii) 450 ÷ 9 = = 50

(iii) 45 ÷ 0.9 = = 50

(iv) 4.5 ÷ 0.09 = = 50

Starting with: (i) 4500 ÷ 90 = = 50

You divide the numerator and the denominator by 10 to get;

(ii) 450 ÷ 9 = = 50

Then you divide the both the numerator and denominator in (ii) with 10 to get;

(iii) 45 ÷ 0.9 = = 50

As the cycle continues, you will always get 50 as the answer since you are dividing both the numerator and the denominator with 10 in each expression. In other words; the ten you divide the numerator with cancels out with the ten you divide the denominator with. So the answer will always be 50 in each next expression.