Question

How do you know that 21 over 30 is greater than 2 over 3

Answer 1

The problem deals with fractions comparison, lets do it:
21/30 > 2/3
we begin solving:
21 > (2/3)*30
21 > 2*10
21 > 20
therefore the proposed inequality is true, 21/30 > 2/3

You can solve as well getting same denominator for both fractions and comparing directly, in this case we need to get 2/3 to be divided by 30:
2/3 = (10/10)(2/3) = 20/30
So we have:
21/30 > 2/3
which is equal to:
21/30 > 20/30
and we compare directly because both fractions are divided by the same number, and we can see that the inequality is true.