9 = 3/7 x 21/1 = 63/7
36
5/7 * 63 315/7 = 45 ----------
1 29/63
To determine if 3/7 is greater than 4/9, we need to find a common denominator. The least common multiple of 7 and 9 is 63. Converting 3/7 to have a denominator of 63 gives us 27/63, and converting 4/9 to have a denominator of 63 gives us 28/63. Comparing these fractions, we see that 28/63 (4/9) is indeed greater than 27/63 (3/7).
It is: 3/7 of 63 = 27
28/63
It is: 1/7 of 63 = 9
9 = 3/7 x 21/1 = 63/7
We can convert both ninths and sevenths into a common fraction, by multiplying nine by seven, to get 63. So, 4/9 = 28/63 and 3/7 = 27/63. You can then easily see that 28/63 is exactly 1/63 larger than 27/63. So it is true, 4/9 is indeed greater than 3/7. Not much greater, but slightly greater.
36
27
63
2/7 of 63 = 63*2/7 = 9*2 = 18
28/63 + 36/63 = 64/63 = 1 and 1/63
63/7 * 21 = 45/7 * 21 = 45*3 = 135
5/7 * 63 315/7 = 45 ----------