Why 32.5divided by 0.5 is same as 325 divided by 5?

Answer 1

32.5/0.5 = 325/5

The reason for this is with a fraction, you can multiply or divide both the numerator by the same term and the fraction is exactly the same. In this case, we are multiplying both the numerator (top) and denominator (bottom) by 10.

32.5 x 10 = 325

0.5 x 10 = 5

32.5/0.5 < --- original fraction

(32.5 x 10) / (0.5 x 10) = 325/10 <--- multiplied both numerator and denominator by 10

Another way you can think about this is, you can always move a decimal to the left or the right, as long as you do it on both the numerator and denominator of a fraction.

1.0 / 2.0 = 10./20. (moved decimal to the right)

1.0 / 2.0 = .10/.20 (moved decimal to the left)

With fractions, the first step to simplifying them is usually to clear any decimals, so mastering this concept is very important.