What is 2/8 plus 9/26? (Answer: 31/52)

Exact Answer

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Problem: What is 2/8 plus 9/26?
Formula / Expression: 2/8 + 9/26
Final Answer: 31/52
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 26 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 104 (which is smaller than their product 8 × 26 = 208, keeping the calculation simpler).
Working: LCD(8, 26) = 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 9/26 by 4 so both fractions share the common base 104.
Working: 2 × 13/8 × 13 = 26/104 and 9 × 4/26 × 4 = 36/104

Step 3: Add the Numerators
Now add the numerators (26 + 36 = 62) and keep the common denominator 104 unchanged.
Working: 26 + 36/104 = 62/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/104 ÷ 2 = 31/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 52 produces a repeating decimal (approximately 0.596154, or 59.6154%).
Working: 31 ÷ 52 = 0.596154 (59.6154%)

Key Values:
- Simplified Fraction: 31/52
- Mixed Number Form: 31/52
- Decimal Value: 0.596154
- Percentage: 59.6154%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-9-26/
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2/8 + 9/26 = 31/52

Simplified Fraction

31/52

Mixed Number

Proper (31/52)

Decimal Value

0.596154

Percentage

59.6154%

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Step-by-Step Solution: 2/8 + 9/26

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 26 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 104 (which is smaller than their product 8 × 26 = 208, keeping the calculation simpler).

LCD(8, 26) = 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 9/26 by 4 so both fractions share the common base 104.

2 × 13/8 × 13 = 26/104 and 9 × 4/26 × 4 = 36/104

Step 3

Add the Numerators

Now add the numerators (26 + 36 = 62) and keep the common denominator 104 unchanged.

26 + 36/104 = 62/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 104, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/104 ÷ 2 = 31/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 52 produces a repeating decimal (approximately 0.596154, or 59.6154%).

31 ÷ 52 = 0.596154 (59.6154%)

Visual Representation

The diagram below illustrates 2/8 plus 9/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/52`
Mixed Number Form	`31/52`
Decimal Form	`0.596154`
Percentage	`59.6154%`

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Frequently Asked Questions

What is 2/8 plus 9/26 as a fraction?

2/8 + 9/26 in simplest fraction form is 31/52.

What is 2/8 plus 9/26 as a decimal?

2/8 + 9/26 converted to a decimal is 0.596154.

What is 2/8 plus 9/26 as a percentage?

2/8 + 9/26 expressed as a percentage is 59.6154%.

Does 2/8 plus 9/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.596154...) because the denominator contains prime factors other than 2 and 5.