What is 6/31 plus 7/13?
6/31 plus 7/13 equals 295/403 (or 0.73201 in decimal form). Learn the step-by-step solution to add 6/31 and 7/13 using Least Common Denominator and simplification.
Exact Answer
6/31 + 7/13 = 295/403
Simplified Fraction
295/403
Mixed Number
Proper (295/403)
Decimal Value
0.73201
Percentage
73.201%
Step-by-Step Solution: 6/31 + 7/13
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 6/31 by 13, and multiply the numerator and denominator of 7/13 by 31 so both fractions share the common base 403.
6 × 13/31 × 13 = 78/403 and 7 × 31/13 × 31 = 217/403
Step 3
Add the Numerators
Now add the numerators (78 + 217 = 295) and keep the common denominator 403 unchanged.
78 + 217/403 = 295/403
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 295 and 403 is 1, confirming that 295/403 cannot be reduced further—it is already in its simplest irreducible form.
295/403
Step 5
Decimal & Percentage Representation
Dividing the numerator 295 by denominator 403 produces a repeating decimal (approximately 0.73201, or 73.201%).
295 ÷ 403 = 0.73201 (73.201%)
Visual Representation
The diagram below illustrates 6/31 plus 7/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 295/403 |
| Mixed Number Form | 295/403 |
| Decimal Form | 0.73201 |
| Percentage | 73.201% |
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Frequently Asked Questions
What is 6/31 plus 7/13 as a fraction?
6/31 + 7/13 in simplest fraction form is 295/403.
What is 6/31 plus 7/13 as a decimal?
6/31 + 7/13 converted to a decimal is 0.73201.
What is 6/31 plus 7/13 as a percentage?
6/31 + 7/13 expressed as a percentage is 73.201%.
Does 6/31 plus 7/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.73201...) because the denominator contains prime factors other than 2 and 5.