What is 2/34 plus 3/7? (Answer: 58/119)

Exact Answer

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Problem: What is 2/34 plus 3/7?
Formula / Expression: 2/34 + 3/7
Final Answer: 58/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 7 = 238.
Working: LCD(34, 7) = 238

Step 2: Convert to Equivalent Fractions with Common Denominator 238
Multiply the numerator and denominator of 2/34 by 7, and multiply the numerator and denominator of 3/7 by 34 so both fractions share the common base 238.
Working: 2 × 7/34 × 7 = 14/238 and 3 × 34/7 × 34 = 102/238

Step 3: Add the Numerators
Now add the numerators (14 + 102 = 116) and keep the common denominator 238 unchanged.
Working: 14 + 102/238 = 116/238

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 116 and 238, which is 2. Divide both the numerator and denominator by 2.
Working: 116 ÷ 2/238 ÷ 2 = 58/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 119 produces a repeating decimal (approximately 0.487395, or 48.7395%).
Working: 58 ÷ 119 = 0.487395 (48.7395%)

Key Values:
- Simplified Fraction: 58/119
- Mixed Number Form: 58/119
- Decimal Value: 0.487395
- Percentage: 48.7395%

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Solved with FractionsCalc:
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2/34 + 3/7 = 58/119

Simplified Fraction

58/119

Mixed Number

Proper (58/119)

Decimal Value

0.487395

Percentage

48.7395%

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Step-by-Step Solution: 2/34 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 7 = 238.

LCD(34, 7) = 238

Step 2

Convert to Equivalent Fractions with Common Denominator 238

Multiply the numerator and denominator of 2/34 by 7, and multiply the numerator and denominator of 3/7 by 34 so both fractions share the common base 238.

2 × 7/34 × 7 = 14/238 and 3 × 34/7 × 34 = 102/238

Step 3

Add the Numerators

Now add the numerators (14 + 102 = 116) and keep the common denominator 238 unchanged.

14 + 102/238 = 116/238

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 116 and 238, which is 2. Divide both the numerator and denominator by 2.

116 ÷ 2/238 ÷ 2 = 58/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 119 produces a repeating decimal (approximately 0.487395, or 48.7395%).

58 ÷ 119 = 0.487395 (48.7395%)

Visual Representation

The diagram below illustrates 2/34 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/119`
Mixed Number Form	`58/119`
Decimal Form	`0.487395`
Percentage	`48.7395%`

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Frequently Asked Questions

What is 2/34 plus 3/7 as a fraction?

2/34 + 3/7 in simplest fraction form is 58/119.

What is 2/34 plus 3/7 as a decimal?

2/34 + 3/7 converted to a decimal is 0.487395.

What is 2/34 plus 3/7 as a percentage?

2/34 + 3/7 expressed as a percentage is 48.7395%.

Does 2/34 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.487395...) because the denominator contains prime factors other than 2 and 5.