Understanding the Problem
To solve the expression 3/5 × [1/7 + 8/2], we need to follow the order of operations, which involves simplifying the expression inside the brackets first.
Step 1: Simplify Inside the Brackets
- We have the expression inside the brackets: 1/7 + 8/2.
- First, calculate 8/2:
- 8 divided by 2 equals 4.
- Now, we can rewrite the expression:
- 1/7 + 4.
Step 2: Convert 4 to a Fraction
- To add 1/7 and 4, we need a common denominator.
- We can express 4 as a fraction:
- 4 = 4/1.
- The least common denominator of 7 and 1 is 7.
- Convert 4/1 to a fraction with a denominator of 7:
- 4/1 = 28/7.
Step 3: Add the Fractions
- Now we can add:
- 1/7 + 28/7 = (1 + 28)/7 = 29/7.
Step 4: Multiply by 3/5
- Now we have:
- 3/5 × 29/7.
- Multiply the numerators and the denominators:
- (3 × 29) / (5 × 7) = 87/35.
Step 5: Final Result
- The final simplified answer is:
- 87/35.
This fraction cannot be simplified further, and it can also be expressed as a mixed number if needed.