What is 2/26 plus 2/12? (Answer: 19/78)

Exact Answer

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Problem: What is 2/26 plus 2/12?
Formula / Expression: 2/26 + 2/12
Final Answer: 19/78
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 12 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 156 (which is smaller than their product 26 × 12 = 312, keeping the calculation simpler).
Working: LCD(26, 12) = 156

Step 2: Convert to Equivalent Fractions with Common Denominator 156
Multiply the numerator and denominator of 2/26 by 6, and multiply the numerator and denominator of 2/12 by 13 so both fractions share the common base 156.
Working: 2 × 6/26 × 6 = 12/156 and 2 × 13/12 × 13 = 26/156

Step 3: Add the Numerators
Now add the numerators (12 + 26 = 38) and keep the common denominator 156 unchanged.
Working: 12 + 26/156 = 38/156

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 156, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/156 ÷ 2 = 19/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 78 produces a repeating decimal (approximately 0.24359, or 24.359%).
Working: 19 ÷ 78 = 0.24359 (24.359%)

Key Values:
- Simplified Fraction: 19/78
- Mixed Number Form: 19/78
- Decimal Value: 0.24359
- Percentage: 24.359%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-26-plus-2-12/
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2/26 + 2/12 = 19/78

Simplified Fraction

19/78

Mixed Number

Proper (19/78)

Decimal Value

0.24359

Percentage

24.359%

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Step-by-Step Solution: 2/26 + 2/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 12 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 156 (which is smaller than their product 26 × 12 = 312, keeping the calculation simpler).

LCD(26, 12) = 156

Step 2

Convert to Equivalent Fractions with Common Denominator 156

Multiply the numerator and denominator of 2/26 by 6, and multiply the numerator and denominator of 2/12 by 13 so both fractions share the common base 156.

2 × 6/26 × 6 = 12/156 and 2 × 13/12 × 13 = 26/156

Step 3

Add the Numerators

Now add the numerators (12 + 26 = 38) and keep the common denominator 156 unchanged.

12 + 26/156 = 38/156

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 156, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/156 ÷ 2 = 19/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 78 produces a repeating decimal (approximately 0.24359, or 24.359%).

19 ÷ 78 = 0.24359 (24.359%)

Visual Representation

The diagram below illustrates 2/26 plus 2/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/78`
Mixed Number Form	`19/78`
Decimal Form	`0.24359`
Percentage	`24.359%`

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Frequently Asked Questions

What is 2/26 plus 2/12 as a fraction?

2/26 + 2/12 in simplest fraction form is 19/78.

What is 2/26 plus 2/12 as a decimal?

2/26 + 2/12 converted to a decimal is 0.24359.

What is 2/26 plus 2/12 as a percentage?

2/26 + 2/12 expressed as a percentage is 24.359%.

Does 2/26 plus 2/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.24359...) because the denominator contains prime factors other than 2 and 5.