What is 1/26 plus 3/13? (Answer: 7/26)

Exact Answer

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Problem: What is 1/26 plus 3/13?
Formula / Expression: 1/26 + 3/13
Final Answer: 7/26
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 26 is an exact multiple of 13 (13 × 2 = 26). The Least Common Denominator (LCD) is simply 26, meaning we only need to scale one fraction.
Working: LCD(26, 13) = 26

Step 2: Convert to Equivalent Fractions with Common Denominator 26
Multiply the numerator and denominator of 1/26 by 1, and multiply the numerator and denominator of 3/13 by 2 so both fractions share the common base 26.
Working: 1 × 1/26 × 1 = 1/26 and 3 × 2/13 × 2 = 6/26

Step 3: Add the Numerators
Now add the numerators (1 + 6 = 7) and keep the common denominator 26 unchanged.
Working: 1 + 6/26 = 7/26

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 26 is 1, confirming that 7/26 cannot be reduced further—it is already in its simplest irreducible form.
Working: 7/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 26 produces a repeating decimal (approximately 0.269231, or 26.9231%).
Working: 7 ÷ 26 = 0.269231 (26.9231%)

Key Values:
- Simplified Fraction: 7/26
- Mixed Number Form: 7/26
- Decimal Value: 0.269231
- Percentage: 26.9231%

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Solved with FractionsCalc:
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1/26 + 3/13 = 7/26

Simplified Fraction

7/26

Mixed Number

Proper (7/26)

Decimal Value

0.269231

Percentage

26.9231%

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Step-by-Step Solution: 1/26 + 3/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 26 is an exact multiple of 13 (13 × 2 = 26). The Least Common Denominator (LCD) is simply 26, meaning we only need to scale one fraction.

LCD(26, 13) = 26

Step 2

Convert to Equivalent Fractions with Common Denominator 26

Multiply the numerator and denominator of 1/26 by 1, and multiply the numerator and denominator of 3/13 by 2 so both fractions share the common base 26.

1 × 1/26 × 1 = 1/26 and 3 × 2/13 × 2 = 6/26

Step 3

Add the Numerators

Now add the numerators (1 + 6 = 7) and keep the common denominator 26 unchanged.

1 + 6/26 = 7/26

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 7 and 26 is 1, confirming that 7/26 cannot be reduced further—it is already in its simplest irreducible form.

7/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 26 produces a repeating decimal (approximately 0.269231, or 26.9231%).

7 ÷ 26 = 0.269231 (26.9231%)

Visual Representation

The diagram below illustrates 1/26 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/26`
Mixed Number Form	`7/26`
Decimal Form	`0.269231`
Percentage	`26.9231%`

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Frequently Asked Questions

What is 1/26 plus 3/13 as a fraction?

1/26 + 3/13 in simplest fraction form is 7/26.

What is 1/26 plus 3/13 as a decimal?

1/26 + 3/13 converted to a decimal is 0.269231.

What is 1/26 plus 3/13 as a percentage?

1/26 + 3/13 expressed as a percentage is 26.9231%.

Does 1/26 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.269231...) because the denominator contains prime factors other than 2 and 5.