What is 2/34 plus 5/9? (Answer: 94/153)

Exact Answer

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Problem: What is 2/34 plus 5/9?
Formula / Expression: 2/34 + 5/9
Final Answer: 94/153
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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 5/9 by 34 so both fractions share the common base 306.
Working: 2 × 9/34 × 9 = 18/306 and 5 × 34/9 × 34 = 170/306

Step 3: Add the Numerators
Now add the numerators (18 + 170 = 188) and keep the common denominator 306 unchanged.
Working: 18 + 170/306 = 188/306

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 188 and 306, which is 2. Divide both the numerator and denominator by 2.
Working: 188 ÷ 2/306 ÷ 2 = 94/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 94 by denominator 153 produces a repeating decimal (approximately 0.614379, or 61.4379%).
Working: 94 ÷ 153 = 0.614379 (61.4379%)

Key Values:
- Simplified Fraction: 94/153
- Mixed Number Form: 94/153
- Decimal Value: 0.614379
- Percentage: 61.4379%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-34-plus-5-9/
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2/34 + 5/9 = 94/153

Simplified Fraction

94/153

Mixed Number

Proper (94/153)

Decimal Value

0.614379

Percentage

61.4379%

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

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 5/9 by 34 so both fractions share the common base 306.

2 × 9/34 × 9 = 18/306 and 5 × 34/9 × 34 = 170/306

Step 3

Add the Numerators

Now add the numerators (18 + 170 = 188) and keep the common denominator 306 unchanged.

18 + 170/306 = 188/306

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 188 and 306, which is 2. Divide both the numerator and denominator by 2.

188 ÷ 2/306 ÷ 2 = 94/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 94 by denominator 153 produces a repeating decimal (approximately 0.614379, or 61.4379%).

94 ÷ 153 = 0.614379 (61.4379%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`94/153`
Mixed Number Form	`94/153`
Decimal Form	`0.614379`
Percentage	`61.4379%`

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Frequently Asked Questions

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

2/34 + 5/9 in simplest fraction form is 94/153.

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

2/34 + 5/9 converted to a decimal is 0.614379.

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

2/34 + 5/9 expressed as a percentage is 61.4379%.

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

It results in a repeating decimal (approximately 0.614379...) because the denominator contains prime factors other than 2 and 5.