What is 2/34 plus 3/9? (Answer: 20/51)

Exact Answer

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Problem: What is 2/34 plus 3/9?
Formula / Expression: 2/34 + 3/9
Final Answer: 20/51
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 9 = 306.
Working: LCD(34, 9) = 306

Step 2: Convert to Equivalent Fractions with Common Denominator 306
Multiply the numerator and denominator of 2/34 by 9, and multiply the numerator and denominator of 3/9 by 34 so both fractions share the common base 306.
Working: 2 × 9/34 × 9 = 18/306 and 3 × 34/9 × 34 = 102/306

Step 3: Add the Numerators
Now add the numerators (18 + 102 = 120) and keep the common denominator 306 unchanged.
Working: 18 + 102/306 = 120/306

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 306, which is 6. Divide both the numerator and denominator by 6.
Working: 120 ÷ 6/306 ÷ 6 = 20/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 51 produces a repeating decimal (approximately 0.392157, or 39.2157%).
Working: 20 ÷ 51 = 0.392157 (39.2157%)

Key Values:
- Simplified Fraction: 20/51
- Mixed Number Form: 20/51
- Decimal Value: 0.392157
- Percentage: 39.2157%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-34-plus-3-9/
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2/34 + 3/9 = 20/51

Simplified Fraction

20/51

Mixed Number

Proper (20/51)

Decimal Value

0.392157

Percentage

39.2157%

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Step-by-Step Solution: 2/34 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 9 = 306.

LCD(34, 9) = 306

Step 2

Convert to Equivalent Fractions with Common Denominator 306

Multiply the numerator and denominator of 2/34 by 9, and multiply the numerator and denominator of 3/9 by 34 so both fractions share the common base 306.

2 × 9/34 × 9 = 18/306 and 3 × 34/9 × 34 = 102/306

Step 3

Add the Numerators

Now add the numerators (18 + 102 = 120) and keep the common denominator 306 unchanged.

18 + 102/306 = 120/306

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 306, which is 6. Divide both the numerator and denominator by 6.

120 ÷ 6/306 ÷ 6 = 20/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 51 produces a repeating decimal (approximately 0.392157, or 39.2157%).

20 ÷ 51 = 0.392157 (39.2157%)

Visual Representation

The diagram below illustrates 2/34 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/51`
Mixed Number Form	`20/51`
Decimal Form	`0.392157`
Percentage	`39.2157%`

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Frequently Asked Questions

What is 2/34 plus 3/9 as a fraction?

2/34 + 3/9 in simplest fraction form is 20/51.

What is 2/34 plus 3/9 as a decimal?

2/34 + 3/9 converted to a decimal is 0.392157.

What is 2/34 plus 3/9 as a percentage?

2/34 + 3/9 expressed as a percentage is 39.2157%.

Does 2/34 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.392157...) because the denominator contains prime factors other than 2 and 5.