What is 3/29 plus 2/3? (Answer: 67/87)

Exact Answer

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Problem: What is 3/29 plus 2/3?
Formula / Expression: 3/29 + 2/3
Final Answer: 67/87
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 3 = 87.
Working: LCD(29, 3) = 87

Step 2: Convert to Equivalent Fractions with Common Denominator 87
Multiply the numerator and denominator of 3/29 by 3, and multiply the numerator and denominator of 2/3 by 29 so both fractions share the common base 87.
Working: 3 × 3/29 × 3 = 9/87 and 2 × 29/3 × 29 = 58/87

Step 3: Add the Numerators
Now add the numerators (9 + 58 = 67) and keep the common denominator 87 unchanged.
Working: 9 + 58/87 = 67/87

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 87 is 1, confirming that 67/87 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/87

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 87 produces a repeating decimal (approximately 0.770115, or 77.0115%).
Working: 67 ÷ 87 = 0.770115 (77.0115%)

Key Values:
- Simplified Fraction: 67/87
- Mixed Number Form: 67/87
- Decimal Value: 0.770115
- Percentage: 77.0115%

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Solved with FractionsCalc:
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3/29 + 2/3 = 67/87

Simplified Fraction

67/87

Mixed Number

Proper (67/87)

Decimal Value

0.770115

Percentage

77.0115%

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Step-by-Step Solution: 3/29 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 3 = 87.

LCD(29, 3) = 87

Step 2

Convert to Equivalent Fractions with Common Denominator 87

Multiply the numerator and denominator of 3/29 by 3, and multiply the numerator and denominator of 2/3 by 29 so both fractions share the common base 87.

3 × 3/29 × 3 = 9/87 and 2 × 29/3 × 29 = 58/87

Step 3

Add the Numerators

Now add the numerators (9 + 58 = 67) and keep the common denominator 87 unchanged.

9 + 58/87 = 67/87

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 87 is 1, confirming that 67/87 cannot be reduced further—it is already in its simplest irreducible form.

67/87

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 87 produces a repeating decimal (approximately 0.770115, or 77.0115%).

67 ÷ 87 = 0.770115 (77.0115%)

Visual Representation

The diagram below illustrates 3/29 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/87`
Mixed Number Form	`67/87`
Decimal Form	`0.770115`
Percentage	`77.0115%`

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Frequently Asked Questions

What is 3/29 plus 2/3 as a fraction?

3/29 + 2/3 in simplest fraction form is 67/87.

What is 3/29 plus 2/3 as a decimal?

3/29 + 2/3 converted to a decimal is 0.770115.

What is 3/29 plus 2/3 as a percentage?

3/29 + 2/3 expressed as a percentage is 77.0115%.

Does 3/29 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.770115...) because the denominator contains prime factors other than 2 and 5.