What is 2/8 plus 7/26? (Answer: 27/52)

Exact Answer

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Problem: What is 2/8 plus 7/26?
Formula / Expression: 2/8 + 7/26
Final Answer: 27/52
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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 7/26 by 4 so both fractions share the common base 104.
Working: 2 × 13/8 × 13 = 26/104 and 7 × 4/26 × 4 = 28/104

Step 3: Add the Numerators
Now add the numerators (26 + 28 = 54) and keep the common denominator 104 unchanged.
Working: 26 + 28/104 = 54/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 54 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 54 ÷ 2/104 ÷ 2 = 27/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 52 produces a repeating decimal (approximately 0.519231, or 51.9231%).
Working: 27 ÷ 52 = 0.519231 (51.9231%)

Key Values:
- Simplified Fraction: 27/52
- Mixed Number Form: 27/52
- Decimal Value: 0.519231
- Percentage: 51.9231%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-7-26/
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2/8 + 7/26 = 27/52

Simplified Fraction

27/52

Mixed Number

Proper (27/52)

Decimal Value

0.519231

Percentage

51.9231%

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Step-by-Step Solution: 2/8 + 7/26

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 7/26 by 4 so both fractions share the common base 104.

2 × 13/8 × 13 = 26/104 and 7 × 4/26 × 4 = 28/104

Step 3

Add the Numerators

Now add the numerators (26 + 28 = 54) and keep the common denominator 104 unchanged.

26 + 28/104 = 54/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 54 and 104, which is 2. Divide both the numerator and denominator by 2.

54 ÷ 2/104 ÷ 2 = 27/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 52 produces a repeating decimal (approximately 0.519231, or 51.9231%).

27 ÷ 52 = 0.519231 (51.9231%)

Visual Representation

The diagram below illustrates 2/8 plus 7/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/52`
Mixed Number Form	`27/52`
Decimal Form	`0.519231`
Percentage	`51.9231%`

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Frequently Asked Questions

What is 2/8 plus 7/26 as a fraction?

2/8 + 7/26 in simplest fraction form is 27/52.

What is 2/8 plus 7/26 as a decimal?

2/8 + 7/26 converted to a decimal is 0.519231.

What is 2/8 plus 7/26 as a percentage?

2/8 + 7/26 expressed as a percentage is 51.9231%.

Does 2/8 plus 7/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.519231...) because the denominator contains prime factors other than 2 and 5.