What is 5/13 plus 2/5? (Answer: 51/65)

Exact Answer

==================================================
Problem: What is 5/13 plus 2/5?
Formula / Expression: 5/13 + 2/5
Final Answer: 51/65
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 5 = 65.
Working: LCD(13, 5) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 5/13 by 5, and multiply the numerator and denominator of 2/5 by 13 so both fractions share the common base 65.
Working: 5 × 5/13 × 5 = 25/65 and 2 × 13/5 × 13 = 26/65

Step 3: Add the Numerators
Now add the numerators (25 + 26 = 51) and keep the common denominator 65 unchanged.
Working: 25 + 26/65 = 51/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 51 and 65 is 1, confirming that 51/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 51/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 65 produces a repeating decimal (approximately 0.784615, or 78.4615%).
Working: 51 ÷ 65 = 0.784615 (78.4615%)

Key Values:
- Simplified Fraction: 51/65
- Mixed Number Form: 51/65
- Decimal Value: 0.784615
- Percentage: 78.4615%

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

5/13 + 2/5 = 51/65

Simplified Fraction

51/65

Mixed Number

Proper (51/65)

Decimal Value

0.784615

Percentage

78.4615%

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: 5/13 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 5 = 65.

LCD(13, 5) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 5/13 by 5, and multiply the numerator and denominator of 2/5 by 13 so both fractions share the common base 65.

5 × 5/13 × 5 = 25/65 and 2 × 13/5 × 13 = 26/65

Step 3

Add the Numerators

Now add the numerators (25 + 26 = 51) and keep the common denominator 65 unchanged.

25 + 26/65 = 51/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 51 and 65 is 1, confirming that 51/65 cannot be reduced further—it is already in its simplest irreducible form.

51/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 65 produces a repeating decimal (approximately 0.784615, or 78.4615%).

51 ÷ 65 = 0.784615 (78.4615%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/65`
Mixed Number Form	`51/65`
Decimal Form	`0.784615`
Percentage	`78.4615%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

5/13 + 2/5 in simplest fraction form is 51/65.

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

5/13 + 2/5 converted to a decimal is 0.784615.

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

5/13 + 2/5 expressed as a percentage is 78.4615%.

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

It results in a repeating decimal (approximately 0.784615...) because the denominator contains prime factors other than 2 and 5.