1
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4 + 1
_________
4+1
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4 1/4
one over 4 plus (1 over 4 + 1 over 4 1/4)) the numerator in the denominator is 1.
To simplify the given expression, let's break down each step:
1. Start with the expression: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ 4 1/4)
2. The first step is to evaluate the denominator inside the parentheses: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ (4 + 1/4))
3. Next, simplify the numerator inside the parentheses: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ (4 + 1/4))
The numerator is already a simplified expression, so we can move on to the next step.
4. Evaluate the innermost parentheses: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ (4 + 1/4))
In this case, the innermost parentheses contain an addition operation (4 + 1/4), which gives us the sum of 4 1/4.
5. Replace the simplified expression in the parentheses: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ 4 1/4)
So, our expression becomes: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ 4 1/4)
6. Evaluate the denominator: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ 4 1/4)
The denominator contains the sum of 4 and 1/4, which is equal to 4 1/4.
7. Replace the simplified expression for the denominator: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ 4 1/4)
The expression now becomes: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ 4 1/4)
8. Evaluate the remaining addition operation before the division: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ 4 1/4)
The addition operation: 4 + 1 ÷ 4 gives us the sum of 4 1/4.
9. Replace the simplified expression for the addition: 4 + 1 ÷ (4 + 1 ÷ 4 + 1 ÷ 4 1/4)
The expression now becomes: 4 + 1 ÷ (4 1/4 + 1 ÷ 4 1/4)
10. Finally, evaluate the division operation: 1 ÷ (4 1/4 + 1 ÷ 4 1/4)
The division operation: 1 ÷ 4 1/4 is equal to 1/4.
11. Replace the simplified expression for the division: 4 + 1 ÷ (4 1/4 + 1 ÷ 4 1/4)
The expression now becomes: 4 + 1 ÷ (4 1/4 + 1/4)
12. Continue to simplify the expression: 4 + 1 ÷ (4 1/4 + 1/4)
In this case, the addition operation: 4 1/4 + 1/4 is equal to 4 3/4.
13. Replace the simplified expression for the addition: 4 + 1 ÷ (4 3/4)
The expression now becomes: 4 + 1 ÷ 4 3/4
14. Evaluate the division operation: 1 ÷ 4 3/4
To divide by a mixed number, we multiply the numerator by the reciprocal of the denominator. In this case, the reciprocal of 4 3/4 is 4/19.
So, the division becomes: 1 × 4/19 = 4/19
15. Replace the simplified expression for the division: 4 + 4/19
The expression now becomes: 4 + 4/19
16. Finally, combine the terms: 4 + 4/19
To add mixed numbers, we find a common denominator. In this case, we can find the common denominator as 19.
17. Multiply the whole number (4) by the denominator (19) and add the numerator (4) for a new numerator of 76.
The expression becomes: 76/19 + 4/19
18. Add the numerators: 76/19 + 4/19 = 80/19
So, the simplified expression is 80/19.