Sure, I'd be happy to help you with these fraction problems!
1/5 + 1/9 + 1/6:
To add these fractions together, we need to find a common denominator. The least common multiple (LCM) of 5, 9, and 6 is 90.
Now, let's convert each fraction to have a denominator of 90:
1/5 = 18/90
1/9 = 10/90
1/6 = 15/90
Now, we can add the fractions:
18/90 + 10/90 + 15/90 = (18 + 10 + 15)/90 = 43/90
So, 1/5 + 1/9 + 1/6 = 43/90.
3 3/8 + 2 1/4:
To add mixed numbers, we first need to convert them into improper fractions.
3 3/8 = (8 * 3 + 3)/8 = 27/8
2 1/4 = (4 * 2 + 1)/4 = 9/4
Now, let's find a common denominator, which is 8:
27/8 + 9/4
To add these fractions, we need the same denominator. Let's convert 9/4 to have a denominator of 8:
9/4 = 18/8
Now we can add the fractions:
27/8 + 18/8 = 45/8
So, 3 3/8 + 2 1/4 = 45/8.
6 1/3 + 1 1/7 + 3 1/12:
To add these mixed numbers, we first convert them into improper fractions:
6 1/3 = (3 * 6 + 1)/3 = 19/3
1 1/7 = (7 * 1 + 1)/7 = 8/7
3 1/12 = (12 * 3 + 1)/12 = 37/12
Now, let's find a common denominator, which is 84:
19/3 + 8/7 + 37/12
To add these fractions, we need the same denominator. Let's convert each fraction to have a denominator of 84:
19/3 = 532/84
8/7 = 96/84
37/12 = 259/84
Now we can add the fractions:
532/84 + 96/84 + 259/84 = (532 + 96 + 259)/84 = 887/84
So, 6 1/3 + 1 1/7 + 3 1/12 = 887/84.
I hope this helps! Let me know if you have any further questions.