What is 3/34 plus 2/3? (Answer: 77/102)

Exact Answer

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Problem: What is 3/34 plus 2/3?
Formula / Expression: 3/34 + 2/3
Final Answer: 77/102
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 3 = 102.
Working: LCD(34, 3) = 102

Step 2: Convert to Equivalent Fractions with Common Denominator 102
Multiply the numerator and denominator of 3/34 by 3, and multiply the numerator and denominator of 2/3 by 34 so both fractions share the common base 102.
Working: 3 × 3/34 × 3 = 9/102 and 2 × 34/3 × 34 = 68/102

Step 3: Add the Numerators
Now add the numerators (9 + 68 = 77) and keep the common denominator 102 unchanged.
Working: 9 + 68/102 = 77/102

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 102 is 1, confirming that 77/102 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/102

Step 5: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 102 produces a repeating decimal (approximately 0.754902, or 75.4902%).
Working: 77 ÷ 102 = 0.754902 (75.4902%)

Key Values:
- Simplified Fraction: 77/102
- Mixed Number Form: 77/102
- Decimal Value: 0.754902
- Percentage: 75.4902%

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Solved with FractionsCalc:
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3/34 + 2/3 = 77/102

Simplified Fraction

77/102

Mixed Number

Proper (77/102)

Decimal Value

0.754902

Percentage

75.4902%

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Step-by-Step Solution: 3/34 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 3 = 102.

LCD(34, 3) = 102

Step 2

Convert to Equivalent Fractions with Common Denominator 102

Multiply the numerator and denominator of 3/34 by 3, and multiply the numerator and denominator of 2/3 by 34 so both fractions share the common base 102.

3 × 3/34 × 3 = 9/102 and 2 × 34/3 × 34 = 68/102

Step 3

Add the Numerators

Now add the numerators (9 + 68 = 77) and keep the common denominator 102 unchanged.

9 + 68/102 = 77/102

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 102 is 1, confirming that 77/102 cannot be reduced further—it is already in its simplest irreducible form.

77/102

Step 5

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 102 produces a repeating decimal (approximately 0.754902, or 75.4902%).

77 ÷ 102 = 0.754902 (75.4902%)

Visual Representation

The diagram below illustrates 3/34 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/102`
Mixed Number Form	`77/102`
Decimal Form	`0.754902`
Percentage	`75.4902%`

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Frequently Asked Questions

What is 3/34 plus 2/3 as a fraction?

3/34 + 2/3 in simplest fraction form is 77/102.

What is 3/34 plus 2/3 as a decimal?

3/34 + 2/3 converted to a decimal is 0.754902.

What is 3/34 plus 2/3 as a percentage?

3/34 + 2/3 expressed as a percentage is 75.4902%.

Does 3/34 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.754902...) because the denominator contains prime factors other than 2 and 5.