What is 2/26 plus 7/9? (Answer: 100/117)

Exact Answer

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Problem: What is 2/26 plus 7/9?
Formula / Expression: 2/26 + 7/9
Final Answer: 100/117
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 2/26 by 9, and multiply the numerator and denominator of 7/9 by 26 so both fractions share the common base 234.
Working: 2 × 9/26 × 9 = 18/234 and 7 × 26/9 × 26 = 182/234

Step 3: Add the Numerators
Now add the numerators (18 + 182 = 200) and keep the common denominator 234 unchanged.
Working: 18 + 182/234 = 200/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 200 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 200 ÷ 2/234 ÷ 2 = 100/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 100 by denominator 117 produces a repeating decimal (approximately 0.854701, or 85.4701%).
Working: 100 ÷ 117 = 0.854701 (85.4701%)

Key Values:
- Simplified Fraction: 100/117
- Mixed Number Form: 100/117
- Decimal Value: 0.854701
- Percentage: 85.4701%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-26-plus-7-9/
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2/26 + 7/9 = 100/117

Simplified Fraction

100/117

Mixed Number

Proper (100/117)

Decimal Value

0.854701

Percentage

85.4701%

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Step-by-Step Solution: 2/26 + 7/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(26, 9) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 2/26 by 9, and multiply the numerator and denominator of 7/9 by 26 so both fractions share the common base 234.

2 × 9/26 × 9 = 18/234 and 7 × 26/9 × 26 = 182/234

Step 3

Add the Numerators

Now add the numerators (18 + 182 = 200) and keep the common denominator 234 unchanged.

18 + 182/234 = 200/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 200 and 234, which is 2. Divide both the numerator and denominator by 2.

200 ÷ 2/234 ÷ 2 = 100/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 100 by denominator 117 produces a repeating decimal (approximately 0.854701, or 85.4701%).

100 ÷ 117 = 0.854701 (85.4701%)

Visual Representation

The diagram below illustrates 2/26 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`100/117`
Mixed Number Form	`100/117`
Decimal Form	`0.854701`
Percentage	`85.4701%`

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Frequently Asked Questions

What is 2/26 plus 7/9 as a fraction?

2/26 + 7/9 in simplest fraction form is 100/117.

What is 2/26 plus 7/9 as a decimal?

2/26 + 7/9 converted to a decimal is 0.854701.

What is 2/26 plus 7/9 as a percentage?

2/26 + 7/9 expressed as a percentage is 85.4701%.

Does 2/26 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.854701...) because the denominator contains prime factors other than 2 and 5.