What is 2/26 plus 2/5? (Answer: 31/65)

Exact Answer

==================================================
Problem: What is 2/26 plus 2/5?
Formula / Expression: 2/26 + 2/5
Final Answer: 31/65
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 5 = 130.
Working: LCD(26, 5) = 130

Step 2: Convert to Equivalent Fractions with Common Denominator 130
Multiply the numerator and denominator of 2/26 by 5, and multiply the numerator and denominator of 2/5 by 26 so both fractions share the common base 130.
Working: 2 × 5/26 × 5 = 10/130 and 2 × 26/5 × 26 = 52/130

Step 3: Add the Numerators
Now add the numerators (10 + 52 = 62) and keep the common denominator 130 unchanged.
Working: 10 + 52/130 = 62/130

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 130, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/130 ÷ 2 = 31/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 65 produces a repeating decimal (approximately 0.476923, or 47.6923%).
Working: 31 ÷ 65 = 0.476923 (47.6923%)

Key Values:
- Simplified Fraction: 31/65
- Mixed Number Form: 31/65
- Decimal Value: 0.476923
- Percentage: 47.6923%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-26-plus-2-5/
==================================================

2/26 + 2/5 = 31/65

Simplified Fraction

31/65

Mixed Number

Proper (31/65)

Decimal Value

0.476923

Percentage

47.6923%

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: 2/26 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 5 = 130.

LCD(26, 5) = 130

Step 2

Convert to Equivalent Fractions with Common Denominator 130

Multiply the numerator and denominator of 2/26 by 5, and multiply the numerator and denominator of 2/5 by 26 so both fractions share the common base 130.

2 × 5/26 × 5 = 10/130 and 2 × 26/5 × 26 = 52/130

Step 3

Add the Numerators

Now add the numerators (10 + 52 = 62) and keep the common denominator 130 unchanged.

10 + 52/130 = 62/130

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 130, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/130 ÷ 2 = 31/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 65 produces a repeating decimal (approximately 0.476923, or 47.6923%).

31 ÷ 65 = 0.476923 (47.6923%)

Visual Representation

The diagram below illustrates 2/26 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/65`
Mixed Number Form	`31/65`
Decimal Form	`0.476923`
Percentage	`47.6923%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/26 plus 2/5 as a fraction?

2/26 + 2/5 in simplest fraction form is 31/65.

What is 2/26 plus 2/5 as a decimal?

2/26 + 2/5 converted to a decimal is 0.476923.

What is 2/26 plus 2/5 as a percentage?

2/26 + 2/5 expressed as a percentage is 47.6923%.

Does 2/26 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.476923...) because the denominator contains prime factors other than 2 and 5.