%2F(5%2B2-1%2F3)-in-fraction.jpeg "(6/4+5 1/6 Of 3/7)/(5+2 1/3) In Fraction")
Solving the Fraction Problem: (6/4+5 1/6 of 3/7)/(5+2 1/3)
This problem involves a combination of fractions, mixed numbers, and operations. Let's break it down step-by-step:
Step 1: Convert mixed numbers to improper fractions.
- 5 1/6: (5 * 6 + 1) / 6 = 31/6
- 2 1/3: (2 * 3 + 1) / 3 = 7/3
Step 2: Calculate "5 1/6 of 3/7".
- This means multiplying 31/6 by 3/7: (31/6) * (3/7) = 93/42
Step 3: Simplify the numerator.
- (6/4 + 93/42): Find a common denominator (84)
- (6/4) * (21/21) = 126/84
- (93/42) * (2/2) = 186/84
- Add the fractions: 126/84 + 186/84 = 312/84
Step 4: Simplify the denominator.
- (5 + 7/3): Find a common denominator (3)
- (5 * 3/3) = 15/3
- Add the fractions: 15/3 + 7/3 = 22/3
Step 5: Divide the numerator by the denominator.
- (312/84) / (22/3): Dividing by a fraction is the same as multiplying by its reciprocal.
- (312/84) * (3/22) = 936/1848
Step 6: Simplify the final fraction.
- Both the numerator and denominator are divisible by 12:
- (936/12) / (1848/12) = 78/154
Final Answer:
The simplified fraction for (6/4+5 1/6 of 3/7)/(5+2 1/3) is 78/154.