What is 4/29 plus 3/4? (Answer: 103/116)

Exact Answer

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Problem: What is 4/29 plus 3/4?
Formula / Expression: 4/29 + 3/4
Final Answer: 103/116
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 4 = 116.
Working: LCD(29, 4) = 116

Step 2: Convert to Equivalent Fractions with Common Denominator 116
Multiply the numerator and denominator of 4/29 by 4, and multiply the numerator and denominator of 3/4 by 29 so both fractions share the common base 116.
Working: 4 × 4/29 × 4 = 16/116 and 3 × 29/4 × 29 = 87/116

Step 3: Add the Numerators
Now add the numerators (16 + 87 = 103) and keep the common denominator 116 unchanged.
Working: 16 + 87/116 = 103/116

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 116 is 1, confirming that 103/116 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/116

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 116 produces a repeating decimal (approximately 0.887931, or 88.7931%).
Working: 103 ÷ 116 = 0.887931 (88.7931%)

Key Values:
- Simplified Fraction: 103/116
- Mixed Number Form: 103/116
- Decimal Value: 0.887931
- Percentage: 88.7931%

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4/29 + 3/4 = 103/116

Simplified Fraction

103/116

Mixed Number

Proper (103/116)

Decimal Value

0.887931

Percentage

88.7931%

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Step-by-Step Solution: 4/29 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 4 = 116.

LCD(29, 4) = 116

Step 2

Convert to Equivalent Fractions with Common Denominator 116

Multiply the numerator and denominator of 4/29 by 4, and multiply the numerator and denominator of 3/4 by 29 so both fractions share the common base 116.

4 × 4/29 × 4 = 16/116 and 3 × 29/4 × 29 = 87/116

Step 3

Add the Numerators

Now add the numerators (16 + 87 = 103) and keep the common denominator 116 unchanged.

16 + 87/116 = 103/116

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 116 is 1, confirming that 103/116 cannot be reduced further—it is already in its simplest irreducible form.

103/116

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 116 produces a repeating decimal (approximately 0.887931, or 88.7931%).

103 ÷ 116 = 0.887931 (88.7931%)

Visual Representation

The diagram below illustrates 4/29 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/116`
Mixed Number Form	`103/116`
Decimal Form	`0.887931`
Percentage	`88.7931%`

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Frequently Asked Questions

What is 4/29 plus 3/4 as a fraction?

4/29 + 3/4 in simplest fraction form is 103/116.

What is 4/29 plus 3/4 as a decimal?

4/29 + 3/4 converted to a decimal is 0.887931.

What is 4/29 plus 3/4 as a percentage?

4/29 + 3/4 expressed as a percentage is 88.7931%.

Does 4/29 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.887931...) because the denominator contains prime factors other than 2 and 5.