What is 5/34 plus 2/9? (Answer: 113/306)

Exact Answer

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Problem: What is 5/34 plus 2/9?
Formula / Expression: 5/34 + 2/9
Final Answer: 113/306
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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 5/34 by 9, and multiply the numerator and denominator of 2/9 by 34 so both fractions share the common base 306.
Working: 5 × 9/34 × 9 = 45/306 and 2 × 34/9 × 34 = 68/306

Step 3: Add the Numerators
Now add the numerators (45 + 68 = 113) and keep the common denominator 306 unchanged.
Working: 45 + 68/306 = 113/306

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 306 is 1, confirming that 113/306 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/306

Step 5: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 306 produces a repeating decimal (approximately 0.369281, or 36.9281%).
Working: 113 ÷ 306 = 0.369281 (36.9281%)

Key Values:
- Simplified Fraction: 113/306
- Mixed Number Form: 113/306
- Decimal Value: 0.369281
- Percentage: 36.9281%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-34-plus-2-9/
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5/34 + 2/9 = 113/306

Simplified Fraction

113/306

Mixed Number

Proper (113/306)

Decimal Value

0.369281

Percentage

36.9281%

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Step-by-Step Solution: 5/34 + 2/9

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 5/34 by 9, and multiply the numerator and denominator of 2/9 by 34 so both fractions share the common base 306.

5 × 9/34 × 9 = 45/306 and 2 × 34/9 × 34 = 68/306

Step 3

Add the Numerators

Now add the numerators (45 + 68 = 113) and keep the common denominator 306 unchanged.

45 + 68/306 = 113/306

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 306 is 1, confirming that 113/306 cannot be reduced further—it is already in its simplest irreducible form.

113/306

Step 5

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 306 produces a repeating decimal (approximately 0.369281, or 36.9281%).

113 ÷ 306 = 0.369281 (36.9281%)

Visual Representation

The diagram below illustrates 5/34 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/306`
Mixed Number Form	`113/306`
Decimal Form	`0.369281`
Percentage	`36.9281%`

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Frequently Asked Questions

What is 5/34 plus 2/9 as a fraction?

5/34 + 2/9 in simplest fraction form is 113/306.

What is 5/34 plus 2/9 as a decimal?

5/34 + 2/9 converted to a decimal is 0.369281.

What is 5/34 plus 2/9 as a percentage?

5/34 + 2/9 expressed as a percentage is 36.9281%.

Does 5/34 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.369281...) because the denominator contains prime factors other than 2 and 5.