What is 4/31 plus 5/13?
4/31 plus 5/13 equals 207/403 (or 0.513648 in decimal form). Learn the step-by-step solution to add 4/31 and 5/13 using Least Common Denominator and simplification.
Exact Answer
4/31 + 5/13 = 207/403
Simplified Fraction
207/403
Mixed Number
Proper (207/403)
Decimal Value
0.513648
Percentage
51.3648%
Step-by-Step Solution: 4/31 + 5/13
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 4/31 by 13, and multiply the numerator and denominator of 5/13 by 31 so both fractions share the common base 403.
4 × 13/31 × 13 = 52/403 and 5 × 31/13 × 31 = 155/403
Step 3
Add the Numerators
Now add the numerators (52 + 155 = 207) and keep the common denominator 403 unchanged.
52 + 155/403 = 207/403
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 207 and 403 is 1, confirming that 207/403 cannot be reduced further—it is already in its simplest irreducible form.
207/403
Step 5
Decimal & Percentage Representation
Dividing the numerator 207 by denominator 403 produces a repeating decimal (approximately 0.513648, or 51.3648%).
207 ÷ 403 = 0.513648 (51.3648%)
Visual Representation
The diagram below illustrates 4/31 plus 5/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 207/403 |
| Mixed Number Form | 207/403 |
| Decimal Form | 0.513648 |
| Percentage | 51.3648% |
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Frequently Asked Questions
What is 4/31 plus 5/13 as a fraction?
4/31 + 5/13 in simplest fraction form is 207/403.
What is 4/31 plus 5/13 as a decimal?
4/31 + 5/13 converted to a decimal is 0.513648.
What is 4/31 plus 5/13 as a percentage?
4/31 + 5/13 expressed as a percentage is 51.3648%.
Does 4/31 plus 5/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.513648...) because the denominator contains prime factors other than 2 and 5.