a) To add fractions, we need to have a common denominator. The common denominator for 2/3 and 2/9 is 9.
To make the denominators equal, we can multiply the numerator and denominator of 2/3 by 3, and the numerator and denominator of 2/9 by 1:
2/3 * 3/3 = 6/9
2/9 * 1/1 = 2/9
Now that the fractions have a common denominator, we can add them:
6/9 + 2/9 = 8/9
So, 2/3 + 2/9 equals 8/9.
b) The common denominator for 1/3 and 2/5 is 15.
To make the denominators equal, we can multiply the numerator and denominator of 1/3 by 5, and the numerator and denominator of 2/5 by 3:
1/3 * 5/5 = 5/15
2/5 * 3/3 = 6/15
Now that the fractions have a common denominator, we can add them:
5/15 + 6/15 = 11/15
Therefore, 1/3 + 2/5 equals 11/15.
c) The common denominator for 1/2 and 3/8 is 8.
To make the denominators equal, we can multiply the numerator and denominator of 1/2 by 4, and the numerator and denominator of 3/8 by 1:
1/2 * 4/4 = 4/8
3/8 * 1/1 = 3/8
Now that the fractions have a common denominator, we can add them:
4/8 + 3/8 = 7/8
Therefore, 1/2 + 3/8 equals 7/8.
I hope this helps.