What is 3/26 plus 5/13? (Answer: 1/2)

Exact Answer

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Problem: What is 3/26 plus 5/13?
Formula / Expression: 3/26 + 5/13
Final Answer: 1/2
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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 3/26 by 1, and multiply the numerator and denominator of 5/13 by 2 so both fractions share the common base 26.
Working: 3 × 1/26 × 1 = 3/26 and 5 × 2/13 × 2 = 10/26

Step 3: Add the Numerators
Now add the numerators (3 + 10 = 13) and keep the common denominator 26 unchanged.
Working: 3 + 10/26 = 13/26

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 13 and 26, which is 13. Divide both the numerator and denominator by 13.
Working: 13 ÷ 13/26 ÷ 13 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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Solved with FractionsCalc:
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3/26 + 5/13 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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Step-by-Step Solution: 3/26 + 5/13

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 3/26 by 1, and multiply the numerator and denominator of 5/13 by 2 so both fractions share the common base 26.

3 × 1/26 × 1 = 3/26 and 5 × 2/13 × 2 = 10/26

Step 3

Add the Numerators

Now add the numerators (3 + 10 = 13) and keep the common denominator 26 unchanged.

3 + 10/26 = 13/26

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 13 and 26, which is 13. Divide both the numerator and denominator by 13.

13 ÷ 13/26 ÷ 13 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 3/26 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

What is 3/26 plus 5/13 as a fraction?

3/26 + 5/13 in simplest fraction form is 1/2.

What is 3/26 plus 5/13 as a decimal?

3/26 + 5/13 converted to a decimal is 0.5.

What is 3/26 plus 5/13 as a percentage?

3/26 + 5/13 expressed as a percentage is 50%.

Does 3/26 plus 5/13 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.