What is 2/29 plus 2/3? (Answer: 64/87)

Exact Answer

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Problem: What is 2/29 plus 2/3?
Formula / Expression: 2/29 + 2/3
Final Answer: 64/87
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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 2/29 by 3, and multiply the numerator and denominator of 2/3 by 29 so both fractions share the common base 87.
Working: 2 × 3/29 × 3 = 6/87 and 2 × 29/3 × 29 = 58/87

Step 3: Add the Numerators
Now add the numerators (6 + 58 = 64) and keep the common denominator 87 unchanged.
Working: 6 + 58/87 = 64/87

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 64 and 87 is 1, confirming that 64/87 cannot be reduced further—it is already in its simplest irreducible form.
Working: 64/87

Step 5: Decimal & Percentage Representation
Dividing the numerator 64 by denominator 87 produces a repeating decimal (approximately 0.735632, or 73.5632%).
Working: 64 ÷ 87 = 0.735632 (73.5632%)

Key Values:
- Simplified Fraction: 64/87
- Mixed Number Form: 64/87
- Decimal Value: 0.735632
- Percentage: 73.5632%

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Solved with FractionsCalc:
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2/29 + 2/3 = 64/87

Simplified Fraction

64/87

Mixed Number

Proper (64/87)

Decimal Value

0.735632

Percentage

73.5632%

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Step-by-Step Solution: 2/29 + 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 2/29 by 3, and multiply the numerator and denominator of 2/3 by 29 so both fractions share the common base 87.

2 × 3/29 × 3 = 6/87 and 2 × 29/3 × 29 = 58/87

Step 3

Add the Numerators

Now add the numerators (6 + 58 = 64) and keep the common denominator 87 unchanged.

6 + 58/87 = 64/87

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 64 and 87 is 1, confirming that 64/87 cannot be reduced further—it is already in its simplest irreducible form.

64/87

Step 5

Decimal & Percentage Representation

Dividing the numerator 64 by denominator 87 produces a repeating decimal (approximately 0.735632, or 73.5632%).

64 ÷ 87 = 0.735632 (73.5632%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`64/87`
Mixed Number Form	`64/87`
Decimal Form	`0.735632`
Percentage	`73.5632%`

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Frequently Asked Questions

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

2/29 + 2/3 in simplest fraction form is 64/87.

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

2/29 + 2/3 converted to a decimal is 0.735632.

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

2/29 + 2/3 expressed as a percentage is 73.5632%.

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

It results in a repeating decimal (approximately 0.735632...) because the denominator contains prime factors other than 2 and 5.