What is 2/13 plus 5/31? (Answer: 127/403)

Exact Answer

==================================================
Problem: What is 2/13 plus 5/31?
Formula / Expression: 2/13 + 5/31
Final Answer: 127/403
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 31 = 403.
Working: LCD(13, 31) = 403

Step 2: Convert to Equivalent Fractions with Common Denominator 403
Multiply the numerator and denominator of 2/13 by 31, and multiply the numerator and denominator of 5/31 by 13 so both fractions share the common base 403.
Working: 2 × 31/13 × 31 = 62/403 and 5 × 13/31 × 13 = 65/403

Step 3: Add the Numerators
Now add the numerators (62 + 65 = 127) and keep the common denominator 403 unchanged.
Working: 62 + 65/403 = 127/403

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 127 and 403 is 1, confirming that 127/403 cannot be reduced further—it is already in its simplest irreducible form.
Working: 127/403

Step 5: Decimal & Percentage Representation
Dividing the numerator 127 by denominator 403 produces a repeating decimal (approximately 0.315136, or 31.5136%).
Working: 127 ÷ 403 = 0.315136 (31.5136%)

Key Values:
- Simplified Fraction: 127/403
- Mixed Number Form: 127/403
- Decimal Value: 0.315136
- Percentage: 31.5136%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-5-31/
==================================================

2/13 + 5/31 = 127/403

Simplified Fraction

127/403

Mixed Number

Proper (127/403)

Decimal Value

0.315136

Percentage

31.5136%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 2/13 + 5/31

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 31 = 403.

LCD(13, 31) = 403

Step 2

Convert to Equivalent Fractions with Common Denominator 403

Multiply the numerator and denominator of 2/13 by 31, and multiply the numerator and denominator of 5/31 by 13 so both fractions share the common base 403.

2 × 31/13 × 31 = 62/403 and 5 × 13/31 × 13 = 65/403

Step 3

Add the Numerators

Now add the numerators (62 + 65 = 127) and keep the common denominator 403 unchanged.

62 + 65/403 = 127/403

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 127 and 403 is 1, confirming that 127/403 cannot be reduced further—it is already in its simplest irreducible form.

127/403

Step 5

Decimal & Percentage Representation

Dividing the numerator 127 by denominator 403 produces a repeating decimal (approximately 0.315136, or 31.5136%).

127 ÷ 403 = 0.315136 (31.5136%)

Visual Representation

The diagram below illustrates 2/13 plus 5/31 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`127/403`
Mixed Number Form	`127/403`
Decimal Form	`0.315136`
Percentage	`31.5136%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/13 plus 5/31 as a fraction?

2/13 + 5/31 in simplest fraction form is 127/403.

What is 2/13 plus 5/31 as a decimal?

2/13 + 5/31 converted to a decimal is 0.315136.

What is 2/13 plus 5/31 as a percentage?

2/13 + 5/31 expressed as a percentage is 31.5136%.

Does 2/13 plus 5/31 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.315136...) because the denominator contains prime factors other than 2 and 5.