Step 1: Understand the Expression
To simplify the expression 4÷3 + 13÷4 ÷ 37÷7 + 3÷7, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Step 2: Simplify Each Division
- Calculate 4 ÷ 3:
- 4 ÷ 3 = 1.3333 (approximately)
- Calculate 37 ÷ 7:
- 37 ÷ 7 = 5.2857 (approximately)
- Calculate 13 ÷ 4 ÷ 37 ÷ 7:
- First, calculate 13 ÷ 4 = 3.25
- Then, divide by the result from 37 ÷ 7:
- 3.25 ÷ 5.2857 = 0.6143 (approximately)
- Calculate 3 ÷ 7:
- 3 ÷ 7 = 0.4286 (approximately)
Step 3: Combine All Results
Now we sum up all the results:
- 1.3333 (from 4 ÷ 3)
- 0.6143 (from 13 ÷ 4 ÷ 37 ÷ 7)
- 0.4286 (from 3 ÷ 7)
Step 4: Final Calculation
- Total = 1.3333 + 0.6143 + 0.4286
- Total ≈ 2.3762 (approximately)
Conclusion
The simplified result of the expression 4 ÷ 3 + 13 ÷ 4 ÷ 37 ÷ 7 + 3 ÷ 7 is approximately 2.3762.