What is 5/26 plus 2/3? (Answer: 67/78)

Exact Answer

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Problem: What is 5/26 plus 2/3?
Formula / Expression: 5/26 + 2/3
Final Answer: 67/78
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 3 = 78.
Working: LCD(26, 3) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 5/26 by 3, and multiply the numerator and denominator of 2/3 by 26 so both fractions share the common base 78.
Working: 5 × 3/26 × 3 = 15/78 and 2 × 26/3 × 26 = 52/78

Step 3: Add the Numerators
Now add the numerators (15 + 52 = 67) and keep the common denominator 78 unchanged.
Working: 15 + 52/78 = 67/78

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 78 is 1, confirming that 67/78 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 78 produces a repeating decimal (approximately 0.858974, or 85.8974%).
Working: 67 ÷ 78 = 0.858974 (85.8974%)

Key Values:
- Simplified Fraction: 67/78
- Mixed Number Form: 67/78
- Decimal Value: 0.858974
- Percentage: 85.8974%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-26-plus-2-3/
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5/26 + 2/3 = 67/78

Simplified Fraction

67/78

Mixed Number

Proper (67/78)

Decimal Value

0.858974

Percentage

85.8974%

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Step-by-Step Solution: 5/26 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 3 = 78.

LCD(26, 3) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 5/26 by 3, and multiply the numerator and denominator of 2/3 by 26 so both fractions share the common base 78.

5 × 3/26 × 3 = 15/78 and 2 × 26/3 × 26 = 52/78

Step 3

Add the Numerators

Now add the numerators (15 + 52 = 67) and keep the common denominator 78 unchanged.

15 + 52/78 = 67/78

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 78 is 1, confirming that 67/78 cannot be reduced further—it is already in its simplest irreducible form.

67/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 78 produces a repeating decimal (approximately 0.858974, or 85.8974%).

67 ÷ 78 = 0.858974 (85.8974%)

Visual Representation

The diagram below illustrates 5/26 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/78`
Mixed Number Form	`67/78`
Decimal Form	`0.858974`
Percentage	`85.8974%`

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Frequently Asked Questions

What is 5/26 plus 2/3 as a fraction?

5/26 + 2/3 in simplest fraction form is 67/78.

What is 5/26 plus 2/3 as a decimal?

5/26 + 2/3 converted to a decimal is 0.858974.

What is 5/26 plus 2/3 as a percentage?

5/26 + 2/3 expressed as a percentage is 85.8974%.

Does 5/26 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.858974...) because the denominator contains prime factors other than 2 and 5.