What is 2/8 plus 7/13? (Answer: 41/52)

Exact Answer

==================================================
Problem: What is 2/8 plus 7/13?
Formula / Expression: 2/8 + 7/13
Final Answer: 41/52
==================================================

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 2/8 by 13, and multiply the numerator and denominator of 7/13 by 8 so both fractions share the common base 104.
Working: 2 × 13/8 × 13 = 26/104 and 7 × 8/13 × 8 = 56/104

Step 3: Add the Numerators
Now add the numerators (26 + 56 = 82) and keep the common denominator 104 unchanged.
Working: 26 + 56/104 = 82/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/104 ÷ 2 = 41/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 52 produces a repeating decimal (approximately 0.788462, or 78.8462%).
Working: 41 ÷ 52 = 0.788462 (78.8462%)

Key Values:
- Simplified Fraction: 41/52
- Mixed Number Form: 41/52
- Decimal Value: 0.788462
- Percentage: 78.8462%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-7-13/
==================================================

2/8 + 7/13 = 41/52

Simplified Fraction

41/52

Mixed Number

Proper (41/52)

Decimal Value

0.788462

Percentage

78.8462%

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: 2/8 + 7/13

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 2/8 by 13, and multiply the numerator and denominator of 7/13 by 8 so both fractions share the common base 104.

2 × 13/8 × 13 = 26/104 and 7 × 8/13 × 8 = 56/104

Step 3

Add the Numerators

Now add the numerators (26 + 56 = 82) and keep the common denominator 104 unchanged.

26 + 56/104 = 82/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 104, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/104 ÷ 2 = 41/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 52 produces a repeating decimal (approximately 0.788462, or 78.8462%).

41 ÷ 52 = 0.788462 (78.8462%)

Visual Representation

The diagram below illustrates 2/8 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/52`
Mixed Number Form	`41/52`
Decimal Form	`0.788462`
Percentage	`78.8462%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/8 plus 7/13 as a fraction?

2/8 + 7/13 in simplest fraction form is 41/52.

What is 2/8 plus 7/13 as a decimal?

2/8 + 7/13 converted to a decimal is 0.788462.

What is 2/8 plus 7/13 as a percentage?

2/8 + 7/13 expressed as a percentage is 78.8462%.

Does 2/8 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.788462...) because the denominator contains prime factors other than 2 and 5.