To solve this problem, we will first convert all mixed numbers to improper fractions.
17 16/19 = (19*17+16)/19 = 323/19
5 16/19 = (19*5+16)/19 = 111/19
4 43/5 = (5*4+43)/5 = 63/5
Now, we can rewrite the expression:
30 / (323/19 - 111/19) + (7 3/5 - 63/5) / 7
30 / (212/19) + (7 3/5 - 63/5) / 7
30 / (212/19) + (38/5) / 7
30 * (19/212) + (38/5) / 7
570/212 + 38/5 / 7
570/212 + 38/5 * 1/7
570/212 + 38/35
To add these two fractions, we need to find a common denominator:
570/212 = (3190)/(3106) = 190/106
38/35
Now, we add the fractions:
190/106 + 38/35
To add fractions, we need a common denominator which is 106*35 = 3710
So, the expression becomes:
(19035)/(10635) + (38106)/(35106)
6650/3710 + 4028/3710
(6650 + 4028) / 3710
10678 / 3710
Therefore, the simplified answer is:
10678 / 3710 or approximately 2.8798.
To solve this problem, we will first convert all mixed numbers to improper fractions.
17 16/19 = (19*17+16)/19 = 323/19
5 16/19 = (19*5+16)/19 = 111/19
4 43/5 = (5*4+43)/5 = 63/5
Now, we can rewrite the expression:
30 / (323/19 - 111/19) + (7 3/5 - 63/5) / 7
30 / (212/19) + (7 3/5 - 63/5) / 7
30 / (212/19) + (7 3/5 - 63/5) / 7
30 / (212/19) + (38/5) / 7
30 / (212/19) + (38/5) / 7
30 * (19/212) + (38/5) / 7
570/212 + 38/5 / 7
570/212 + 38/5 * 1/7
570/212 + 38/35
To add these two fractions, we need to find a common denominator:
570/212 = (3190)/(3106) = 190/106
38/35
Now, we add the fractions:
190/106 + 38/35
To add fractions, we need a common denominator which is 106*35 = 3710
So, the expression becomes:
(19035)/(10635) + (38106)/(35106)
6650/3710 + 4028/3710
(6650 + 4028) / 3710
10678 / 3710
Therefore, the simplified answer is:
10678 / 3710 or approximately 2.8798.