What is 9/31 plus 10/13?
9/31 plus 10/13 equals 427/403 (or 1 24/403 as a mixed number) (or 1.059553 in decimal form). Learn the step-by-step solution to add 9/31 and 10/13 using Least Common Denominator and simplification.
Exact Answer
9/31 + 10/13 = 427/403
Simplified Fraction
427/403
Mixed Number
1 24/403
Decimal Value
1.059553
Percentage
105.9553%
Step-by-Step Solution: 9/31 + 10/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 31 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 13 = 403.
LCD(31, 13) = 403
Step 2
Convert to Equivalent Fractions with Common Denominator 403
Multiply the numerator and denominator of 9/31 by 13, and multiply the numerator and denominator of 10/13 by 31 so both fractions share the common base 403.
9 × 13/31 × 13 = 117/403 and 10 × 31/13 × 31 = 310/403
Step 3
Add the Numerators
Now add the numerators (117 + 310 = 427) and keep the common denominator 403 unchanged.
117 + 310/403 = 427/403
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 427 and 403 is 1, confirming that 427/403 cannot be reduced further—it is already in its simplest irreducible form.
427/403
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (427) is greater than the denominator (403), divide 427 by 403: it goes in 1 whole time(s) with a remainder of 24, giving the mixed number 1 24/403.
427/403 = 124/403
Step 6
Decimal & Percentage Representation
Dividing the numerator 427 by denominator 403 produces a repeating decimal (approximately 1.059553, or 105.9553%).
427 ÷ 403 = 1.059553 (105.9553%)
Visual Representation
The diagram below illustrates 9/31 plus 10/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 427/403 |
| Mixed Number Form | 1 24/403 |
| Decimal Form | 1.059553 |
| Percentage | 105.9553% |
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Frequently Asked Questions
What is 9/31 plus 10/13 as a fraction?
9/31 + 10/13 in simplest fraction form is 427/403 (or 1 24/403 as a mixed number).
What is 9/31 plus 10/13 as a decimal?
9/31 + 10/13 converted to a decimal is 1.059553.
What is 9/31 plus 10/13 as a percentage?
9/31 + 10/13 expressed as a percentage is 105.9553%.
How do you write 9/31 plus 10/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 427/403 can be written as the mixed number 1 24/403.
Does 9/31 plus 10/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.059553...) because the denominator contains prime factors other than 2 and 5.