What is 2/34 plus 2/3? (Answer: 37/51)

Exact Answer

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Problem: What is 2/34 plus 2/3?
Formula / Expression: 2/34 + 2/3
Final Answer: 37/51
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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 2/34 by 3, and multiply the numerator and denominator of 2/3 by 34 so both fractions share the common base 102.
Working: 2 × 3/34 × 3 = 6/102 and 2 × 34/3 × 34 = 68/102

Step 3: Add the Numerators
Now add the numerators (6 + 68 = 74) and keep the common denominator 102 unchanged.
Working: 6 + 68/102 = 74/102

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 102, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/102 ÷ 2 = 37/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 51 produces a repeating decimal (approximately 0.72549, or 72.549%).
Working: 37 ÷ 51 = 0.72549 (72.549%)

Key Values:
- Simplified Fraction: 37/51
- Mixed Number Form: 37/51
- Decimal Value: 0.72549
- Percentage: 72.549%

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Solved with FractionsCalc:
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2/34 + 2/3 = 37/51

Simplified Fraction

37/51

Mixed Number

Proper (37/51)

Decimal Value

0.72549

Percentage

72.549%

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Step-by-Step Solution: 2/34 + 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 2/34 by 3, and multiply the numerator and denominator of 2/3 by 34 so both fractions share the common base 102.

2 × 3/34 × 3 = 6/102 and 2 × 34/3 × 34 = 68/102

Step 3

Add the Numerators

Now add the numerators (6 + 68 = 74) and keep the common denominator 102 unchanged.

6 + 68/102 = 74/102

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 102, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/102 ÷ 2 = 37/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 51 produces a repeating decimal (approximately 0.72549, or 72.549%).

37 ÷ 51 = 0.72549 (72.549%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/51`
Mixed Number Form	`37/51`
Decimal Form	`0.72549`
Percentage	`72.549%`

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Frequently Asked Questions

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

2/34 + 2/3 in simplest fraction form is 37/51.

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

2/34 + 2/3 converted to a decimal is 0.72549.

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

2/34 + 2/3 expressed as a percentage is 72.549%.

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

It results in a repeating decimal (approximately 0.72549...) because the denominator contains prime factors other than 2 and 5.