What is 1/3 plus 5/11? (Answer: 26/33)

Exact Answer

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Problem: What is 1/3 plus 5/11?
Formula / Expression: 1/3 + 5/11
Final Answer: 26/33
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 11 = 33.
Working: LCD(3, 11) = 33

Step 2: Convert to Equivalent Fractions with Common Denominator 33
Multiply the numerator and denominator of 1/3 by 11, and multiply the numerator and denominator of 5/11 by 3 so both fractions share the common base 33.
Working: 1 × 11/3 × 11 = 11/33 and 5 × 3/11 × 3 = 15/33

Step 3: Add the Numerators
Now add the numerators (11 + 15 = 26) and keep the common denominator 33 unchanged.
Working: 11 + 15/33 = 26/33

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 26 and 33 is 1, confirming that 26/33 cannot be reduced further—it is already in its simplest irreducible form.
Working: 26/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 33 produces a repeating decimal (approximately 0.787879, or 78.7879%).
Working: 26 ÷ 33 = 0.787879 (78.7879%)

Key Values:
- Simplified Fraction: 26/33
- Mixed Number Form: 26/33
- Decimal Value: 0.787879
- Percentage: 78.7879%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-3-plus-5-11/
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1/3 + 5/11 = 26/33

Simplified Fraction

26/33

Mixed Number

Proper (26/33)

Decimal Value

0.787879

Percentage

78.7879%

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Step-by-Step Solution: 1/3 + 5/11

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 11 = 33.

LCD(3, 11) = 33

Step 2

Convert to Equivalent Fractions with Common Denominator 33

Multiply the numerator and denominator of 1/3 by 11, and multiply the numerator and denominator of 5/11 by 3 so both fractions share the common base 33.

1 × 11/3 × 11 = 11/33 and 5 × 3/11 × 3 = 15/33

Step 3

Add the Numerators

Now add the numerators (11 + 15 = 26) and keep the common denominator 33 unchanged.

11 + 15/33 = 26/33

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 26 and 33 is 1, confirming that 26/33 cannot be reduced further—it is already in its simplest irreducible form.

26/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 33 produces a repeating decimal (approximately 0.787879, or 78.7879%).

26 ÷ 33 = 0.787879 (78.7879%)

Visual Representation

The diagram below illustrates 1/3 plus 5/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/33`
Mixed Number Form	`26/33`
Decimal Form	`0.787879`
Percentage	`78.7879%`

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Frequently Asked Questions

What is 1/3 plus 5/11 as a fraction?

1/3 + 5/11 in simplest fraction form is 26/33.

What is 1/3 plus 5/11 as a decimal?

1/3 + 5/11 converted to a decimal is 0.787879.

What is 1/3 plus 5/11 as a percentage?

1/3 + 5/11 expressed as a percentage is 78.7879%.

Does 1/3 plus 5/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.787879...) because the denominator contains prime factors other than 2 and 5.