What is 6/8 plus 11/13? (Answer: 83/52)

Exact Answer

==================================================
Problem: What is 6/8 plus 11/13?
Formula / Expression: 6/8 + 11/13
Final Answer: 1 31/52 (83/52)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.
Working: LCD(8, 13) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 6/8 by 13, and multiply the numerator and denominator of 11/13 by 8 so both fractions share the common base 104.
Working: 6 × 13/8 × 13 = 78/104 and 11 × 8/13 × 8 = 88/104

Step 3: Add the Numerators
Now add the numerators (78 + 88 = 166) and keep the common denominator 104 unchanged.
Working: 78 + 88/104 = 166/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 166 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 166 ÷ 2/104 ÷ 2 = 83/52

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (83) is greater than the denominator (52), divide 83 by 52: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/52.
Working: 83/52 = 1 31/52

Step 6: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 52 produces a repeating decimal (approximately 1.596154, or 159.6154%).
Working: 83 ÷ 52 = 1.596154 (159.6154%)

Key Values:
- Simplified Fraction: 83/52
- Mixed Number Form: 1 31/52
- Decimal Value: 1.596154
- Percentage: 159.6154%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-8-plus-11-13/
==================================================

6/8 + 11/13 = 83/52

Simplified Fraction

83/52

Mixed Number

1 31/52

Decimal Value

1.596154

Percentage

159.6154%

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: 6/8 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.

LCD(8, 13) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 6/8 by 13, and multiply the numerator and denominator of 11/13 by 8 so both fractions share the common base 104.

6 × 13/8 × 13 = 78/104 and 11 × 8/13 × 8 = 88/104

Step 3

Add the Numerators

Now add the numerators (78 + 88 = 166) and keep the common denominator 104 unchanged.

78 + 88/104 = 166/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 166 and 104, which is 2. Divide both the numerator and denominator by 2.

166 ÷ 2/104 ÷ 2 = 83/52

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (83) is greater than the denominator (52), divide 83 by 52: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/52.

83/52 = 131/52

Step 6

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 52 produces a repeating decimal (approximately 1.596154, or 159.6154%).

83 ÷ 52 = 1.596154 (159.6154%)

Visual Representation

The diagram below illustrates 6/8 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/52`
Mixed Number Form	`1 31/52`
Decimal Form	`1.596154`
Percentage	`159.6154%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 6/8 plus 11/13 as a fraction?

6/8 + 11/13 in simplest fraction form is 83/52 (or 1 31/52 as a mixed number).

What is 6/8 plus 11/13 as a decimal?

6/8 + 11/13 converted to a decimal is 1.596154.

What is 6/8 plus 11/13 as a percentage?

6/8 + 11/13 expressed as a percentage is 159.6154%.

How do you write 6/8 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 83/52 can be written as the mixed number 1 31/52.

Does 6/8 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.596154...) because the denominator contains prime factors other than 2 and 5.