What is 4/29 plus 3/13?
4/29 plus 3/13 equals 139/377 (or 0.3687 in decimal form). Learn the step-by-step solution to add 4/29 and 3/13 using Least Common Denominator and simplification.
Exact Answer
4/29 + 3/13 = 139/377
Simplified Fraction
139/377
Mixed Number
Proper (139/377)
Decimal Value
0.3687
Percentage
36.87%
Step-by-Step Solution: 4/29 + 3/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 29 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 13 = 377.
LCD(29, 13) = 377
Step 2
Convert to Equivalent Fractions with Common Denominator 377
Multiply the numerator and denominator of 4/29 by 13, and multiply the numerator and denominator of 3/13 by 29 so both fractions share the common base 377.
4 × 13/29 × 13 = 52/377 and 3 × 29/13 × 29 = 87/377
Step 3
Add the Numerators
Now add the numerators (52 + 87 = 139) and keep the common denominator 377 unchanged.
52 + 87/377 = 139/377
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 139 and 377 is 1, confirming that 139/377 cannot be reduced further—it is already in its simplest irreducible form.
139/377
Step 5
Decimal & Percentage Representation
Dividing the numerator 139 by denominator 377 produces a repeating decimal (approximately 0.3687, or 36.87%).
139 ÷ 377 = 0.3687 (36.87%)
Visual Representation
The diagram below illustrates 4/29 plus 3/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 139/377 |
| Mixed Number Form | 139/377 |
| Decimal Form | 0.3687 |
| Percentage | 36.87% |
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Frequently Asked Questions
What is 4/29 plus 3/13 as a fraction?
4/29 + 3/13 in simplest fraction form is 139/377.
What is 4/29 plus 3/13 as a decimal?
4/29 + 3/13 converted to a decimal is 0.3687.
What is 4/29 plus 3/13 as a percentage?
4/29 + 3/13 expressed as a percentage is 36.87%.
Does 4/29 plus 3/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.3687...) because the denominator contains prime factors other than 2 and 5.