If photocopiers are compared to see which makes the most errors copier a makes 13 errors out of 250 copies copier b makes 9 out of 180 copies which is the most reliable?

Answer 1

This is a lowest common multiple question

We need to compare two fractions - 13/250 and 9/180

The factors of 250 are 2, 5, 5 and 5

The factors of 180 are 2, 2, 3, 3 and 5

So the denominator of each fraction needs to be made up of two 2s, two 3s and three 5s

2 x 2 x 3 x 3 x 5 x 5 x 5 = 4500

To raise 250 to 4500 we need to multiply it by 18

To raise 180 to 4500 we need to multiply it by 25.

Now, whatever action we do to the denominator of a fraction, we must also do to the numerator, so....

13/250 x 18/18 ---- and ----- 9/180 x 25/25

... will give us fractions which can then be compared.

13/250 x 18/18 = 234/4500

and

9/180 x 25/25 = 225/4500

So we now see that copier B will make 9 fewer errors over the same number of copies as copier A.