What is 2/34 plus 4/9? (Answer: 77/153)

Exact Answer

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Problem: What is 2/34 plus 4/9?
Formula / Expression: 2/34 + 4/9
Final Answer: 77/153
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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 4/9 by 34 so both fractions share the common base 306.
Working: 2 × 9/34 × 9 = 18/306 and 4 × 34/9 × 34 = 136/306

Step 3: Add the Numerators
Now add the numerators (18 + 136 = 154) and keep the common denominator 306 unchanged.
Working: 18 + 136/306 = 154/306

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 154 and 306, which is 2. Divide both the numerator and denominator by 2.
Working: 154 ÷ 2/306 ÷ 2 = 77/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 153 produces a repeating decimal (approximately 0.503268, or 50.3268%).
Working: 77 ÷ 153 = 0.503268 (50.3268%)

Key Values:
- Simplified Fraction: 77/153
- Mixed Number Form: 77/153
- Decimal Value: 0.503268
- Percentage: 50.3268%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-34-plus-4-9/
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2/34 + 4/9 = 77/153

Simplified Fraction

77/153

Mixed Number

Proper (77/153)

Decimal Value

0.503268

Percentage

50.3268%

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Step-by-Step Solution: 2/34 + 4/9

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 4/9 by 34 so both fractions share the common base 306.

2 × 9/34 × 9 = 18/306 and 4 × 34/9 × 34 = 136/306

Step 3

Add the Numerators

Now add the numerators (18 + 136 = 154) and keep the common denominator 306 unchanged.

18 + 136/306 = 154/306

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 154 and 306, which is 2. Divide both the numerator and denominator by 2.

154 ÷ 2/306 ÷ 2 = 77/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 153 produces a repeating decimal (approximately 0.503268, or 50.3268%).

77 ÷ 153 = 0.503268 (50.3268%)

Visual Representation

The diagram below illustrates 2/34 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/153`
Mixed Number Form	`77/153`
Decimal Form	`0.503268`
Percentage	`50.3268%`

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Frequently Asked Questions

What is 2/34 plus 4/9 as a fraction?

2/34 + 4/9 in simplest fraction form is 77/153.

What is 2/34 plus 4/9 as a decimal?

2/34 + 4/9 converted to a decimal is 0.503268.

What is 2/34 plus 4/9 as a percentage?

2/34 + 4/9 expressed as a percentage is 50.3268%.

Does 2/34 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.503268...) because the denominator contains prime factors other than 2 and 5.