What is 2/9 plus 6/26? (Answer: 53/117)

Exact Answer

==================================================
Problem: What is 2/9 plus 6/26?
Formula / Expression: 2/9 + 6/26
Final Answer: 53/117
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 26 = 234.
Working: LCD(9, 26) = 234

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 2/9 by 26, and multiply the numerator and denominator of 6/26 by 9 so both fractions share the common base 234.
Working: 2 × 26/9 × 26 = 52/234 and 6 × 9/26 × 9 = 54/234

Step 3: Add the Numerators
Now add the numerators (52 + 54 = 106) and keep the common denominator 234 unchanged.
Working: 52 + 54/234 = 106/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 106 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 106 ÷ 2/234 ÷ 2 = 53/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 117 produces a repeating decimal (approximately 0.452991, or 45.2991%).
Working: 53 ÷ 117 = 0.452991 (45.2991%)

Key Values:
- Simplified Fraction: 53/117
- Mixed Number Form: 53/117
- Decimal Value: 0.452991
- Percentage: 45.2991%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-6-26/
==================================================

2/9 + 6/26 = 53/117

Simplified Fraction

53/117

Mixed Number

Proper (53/117)

Decimal Value

0.452991

Percentage

45.2991%

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: 2/9 + 6/26

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 26 = 234.

LCD(9, 26) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 2/9 by 26, and multiply the numerator and denominator of 6/26 by 9 so both fractions share the common base 234.

2 × 26/9 × 26 = 52/234 and 6 × 9/26 × 9 = 54/234

Step 3

Add the Numerators

Now add the numerators (52 + 54 = 106) and keep the common denominator 234 unchanged.

52 + 54/234 = 106/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 106 and 234, which is 2. Divide both the numerator and denominator by 2.

106 ÷ 2/234 ÷ 2 = 53/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 117 produces a repeating decimal (approximately 0.452991, or 45.2991%).

53 ÷ 117 = 0.452991 (45.2991%)

Visual Representation

The diagram below illustrates 2/9 plus 6/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/117`
Mixed Number Form	`53/117`
Decimal Form	`0.452991`
Percentage	`45.2991%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/9 plus 6/26 as a fraction?

2/9 + 6/26 in simplest fraction form is 53/117.

What is 2/9 plus 6/26 as a decimal?

2/9 + 6/26 converted to a decimal is 0.452991.

What is 2/9 plus 6/26 as a percentage?

2/9 + 6/26 expressed as a percentage is 45.2991%.

Does 2/9 plus 6/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452991...) because the denominator contains prime factors other than 2 and 5.