What is 9/29 plus 10/13?
9/29 plus 10/13 equals 407/377 (or 1 30/377 as a mixed number) (or 1.079576 in decimal form). Learn the step-by-step solution to add 9/29 and 10/13 using Least Common Denominator and simplification.
Exact Answer
9/29 + 10/13 = 407/377
Simplified Fraction
407/377
Mixed Number
1 30/377
Decimal Value
1.079576
Percentage
107.9576%
Step-by-Step Solution: 9/29 + 10/13
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 9/29 by 13, and multiply the numerator and denominator of 10/13 by 29 so both fractions share the common base 377.
9 × 13/29 × 13 = 117/377 and 10 × 29/13 × 29 = 290/377
Step 3
Add the Numerators
Now add the numerators (117 + 290 = 407) and keep the common denominator 377 unchanged.
117 + 290/377 = 407/377
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 407 and 377 is 1, confirming that 407/377 cannot be reduced further—it is already in its simplest irreducible form.
407/377
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (407) is greater than the denominator (377), divide 407 by 377: it goes in 1 whole time(s) with a remainder of 30, giving the mixed number 1 30/377.
407/377 = 130/377
Step 6
Decimal & Percentage Representation
Dividing the numerator 407 by denominator 377 produces a repeating decimal (approximately 1.079576, or 107.9576%).
407 ÷ 377 = 1.079576 (107.9576%)
Visual Representation
The diagram below illustrates 9/29 plus 10/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 407/377 |
| Mixed Number Form | 1 30/377 |
| Decimal Form | 1.079576 |
| Percentage | 107.9576% |
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Frequently Asked Questions
What is 9/29 plus 10/13 as a fraction?
9/29 + 10/13 in simplest fraction form is 407/377 (or 1 30/377 as a mixed number).
What is 9/29 plus 10/13 as a decimal?
9/29 + 10/13 converted to a decimal is 1.079576.
What is 9/29 plus 10/13 as a percentage?
9/29 + 10/13 expressed as a percentage is 107.9576%.
How do you write 9/29 plus 10/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 407/377 can be written as the mixed number 1 30/377.
Does 9/29 plus 10/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.079576...) because the denominator contains prime factors other than 2 and 5.