What is 2/13 plus 3/6? (Answer: 17/26)

Exact Answer

==================================================
Problem: What is 2/13 plus 3/6?
Formula / Expression: 2/13 + 3/6
Final Answer: 17/26
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 6 = 78.
Working: LCD(13, 6) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 2/13 by 6, and multiply the numerator and denominator of 3/6 by 13 so both fractions share the common base 78.
Working: 2 × 6/13 × 6 = 12/78 and 3 × 13/6 × 13 = 39/78

Step 3: Add the Numerators
Now add the numerators (12 + 39 = 51) and keep the common denominator 78 unchanged.
Working: 12 + 39/78 = 51/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 51 and 78, which is 3. Divide both the numerator and denominator by 3.
Working: 51 ÷ 3/78 ÷ 3 = 17/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 26 produces a repeating decimal (approximately 0.653846, or 65.3846%).
Working: 17 ÷ 26 = 0.653846 (65.3846%)

Key Values:
- Simplified Fraction: 17/26
- Mixed Number Form: 17/26
- Decimal Value: 0.653846
- Percentage: 65.3846%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-3-6/
==================================================

2/13 + 3/6 = 17/26

Simplified Fraction

17/26

Mixed Number

Proper (17/26)

Decimal Value

0.653846

Percentage

65.3846%

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 + 3/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 6 = 78.

LCD(13, 6) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 2/13 by 6, and multiply the numerator and denominator of 3/6 by 13 so both fractions share the common base 78.

2 × 6/13 × 6 = 12/78 and 3 × 13/6 × 13 = 39/78

Step 3

Add the Numerators

Now add the numerators (12 + 39 = 51) and keep the common denominator 78 unchanged.

12 + 39/78 = 51/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 51 and 78, which is 3. Divide both the numerator and denominator by 3.

51 ÷ 3/78 ÷ 3 = 17/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 26 produces a repeating decimal (approximately 0.653846, or 65.3846%).

17 ÷ 26 = 0.653846 (65.3846%)

Visual Representation

The diagram below illustrates 2/13 plus 3/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/26`
Mixed Number Form	`17/26`
Decimal Form	`0.653846`
Percentage	`65.3846%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/13 plus 3/6 as a fraction?

2/13 + 3/6 in simplest fraction form is 17/26.

What is 2/13 plus 3/6 as a decimal?

2/13 + 3/6 converted to a decimal is 0.653846.

What is 2/13 plus 3/6 as a percentage?

2/13 + 3/6 expressed as a percentage is 65.3846%.

Does 2/13 plus 3/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.653846...) because the denominator contains prime factors other than 2 and 5.