What is 10/29 plus 9/13?
10/29 plus 9/13 equals 391/377 (or 1 14/377 as a mixed number) (or 1.037135 in decimal form). Learn the step-by-step solution to add 10/29 and 9/13 using Least Common Denominator and simplification.
Exact Answer
10/29 + 9/13 = 391/377
Simplified Fraction
391/377
Mixed Number
1 14/377
Decimal Value
1.037135
Percentage
103.7135%
Step-by-Step Solution: 10/29 + 9/13
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 10/29 by 13, and multiply the numerator and denominator of 9/13 by 29 so both fractions share the common base 377.
10 × 13/29 × 13 = 130/377 and 9 × 29/13 × 29 = 261/377
Step 3
Add the Numerators
Now add the numerators (130 + 261 = 391) and keep the common denominator 377 unchanged.
130 + 261/377 = 391/377
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 391 and 377 is 1, confirming that 391/377 cannot be reduced further—it is already in its simplest irreducible form.
391/377
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (391) is greater than the denominator (377), divide 391 by 377: it goes in 1 whole time(s) with a remainder of 14, giving the mixed number 1 14/377.
391/377 = 114/377
Step 6
Decimal & Percentage Representation
Dividing the numerator 391 by denominator 377 produces a repeating decimal (approximately 1.037135, or 103.7135%).
391 ÷ 377 = 1.037135 (103.7135%)
Visual Representation
The diagram below illustrates 10/29 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 391/377 |
| Mixed Number Form | 1 14/377 |
| Decimal Form | 1.037135 |
| Percentage | 103.7135% |
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Frequently Asked Questions
What is 10/29 plus 9/13 as a fraction?
10/29 + 9/13 in simplest fraction form is 391/377 (or 1 14/377 as a mixed number).
What is 10/29 plus 9/13 as a decimal?
10/29 + 9/13 converted to a decimal is 1.037135.
What is 10/29 plus 9/13 as a percentage?
10/29 + 9/13 expressed as a percentage is 103.7135%.
How do you write 10/29 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 391/377 can be written as the mixed number 1 14/377.
Does 10/29 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.037135...) because the denominator contains prime factors other than 2 and 5.