What is 8/13 plus 2/3? (Answer: 50/39)

Exact Answer

==================================================
Problem: What is 8/13 plus 2/3?
Formula / Expression: 8/13 + 2/3
Final Answer: 1 11/39 (50/39)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.
Working: LCD(13, 3) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 8/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.
Working: 8 × 3/13 × 3 = 24/39 and 2 × 13/3 × 13 = 26/39

Step 3: Add the Numerators
Now add the numerators (24 + 26 = 50) and keep the common denominator 39 unchanged.
Working: 24 + 26/39 = 50/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 50 and 39 is 1, confirming that 50/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 50/39

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (50) is greater than the denominator (39), divide 50 by 39: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/39.
Working: 50/39 = 1 11/39

Step 6: Decimal & Percentage Representation
Dividing the numerator 50 by denominator 39 produces a repeating decimal (approximately 1.282051, or 128.2051%).
Working: 50 ÷ 39 = 1.282051 (128.2051%)

Key Values:
- Simplified Fraction: 50/39
- Mixed Number Form: 1 11/39
- Decimal Value: 1.282051
- Percentage: 128.2051%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-13-plus-2-3/
==================================================

8/13 + 2/3 = 50/39

Simplified Fraction

50/39

Mixed Number

1 11/39

Decimal Value

1.282051

Percentage

128.2051%

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: 8/13 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.

LCD(13, 3) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 8/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.

8 × 3/13 × 3 = 24/39 and 2 × 13/3 × 13 = 26/39

Step 3

Add the Numerators

Now add the numerators (24 + 26 = 50) and keep the common denominator 39 unchanged.

24 + 26/39 = 50/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 50 and 39 is 1, confirming that 50/39 cannot be reduced further—it is already in its simplest irreducible form.

50/39

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (50) is greater than the denominator (39), divide 50 by 39: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/39.

50/39 = 111/39

Step 6

Decimal & Percentage Representation

Dividing the numerator 50 by denominator 39 produces a repeating decimal (approximately 1.282051, or 128.2051%).

50 ÷ 39 = 1.282051 (128.2051%)

Visual Representation

The diagram below illustrates 8/13 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`50/39`
Mixed Number Form	`1 11/39`
Decimal Form	`1.282051`
Percentage	`128.2051%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 8/13 plus 2/3 as a fraction?

8/13 + 2/3 in simplest fraction form is 50/39 (or 1 11/39 as a mixed number).

What is 8/13 plus 2/3 as a decimal?

8/13 + 2/3 converted to a decimal is 1.282051.

What is 8/13 plus 2/3 as a percentage?

8/13 + 2/3 expressed as a percentage is 128.2051%.

How do you write 8/13 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 50/39 can be written as the mixed number 1 11/39.

Does 8/13 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.282051...) because the denominator contains prime factors other than 2 and 5.