What is 4/34 plus 2/9? (Answer: 52/153)

Exact Answer

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Problem: What is 4/34 plus 2/9?
Formula / Expression: 4/34 + 2/9
Final Answer: 52/153
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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 4/34 by 9, and multiply the numerator and denominator of 2/9 by 34 so both fractions share the common base 306.
Working: 4 × 9/34 × 9 = 36/306 and 2 × 34/9 × 34 = 68/306

Step 3: Add the Numerators
Now add the numerators (36 + 68 = 104) and keep the common denominator 306 unchanged.
Working: 36 + 68/306 = 104/306

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 104 and 306, which is 2. Divide both the numerator and denominator by 2.
Working: 104 ÷ 2/306 ÷ 2 = 52/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 153 produces a repeating decimal (approximately 0.339869, or 33.9869%).
Working: 52 ÷ 153 = 0.339869 (33.9869%)

Key Values:
- Simplified Fraction: 52/153
- Mixed Number Form: 52/153
- Decimal Value: 0.339869
- Percentage: 33.9869%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-34-plus-2-9/
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4/34 + 2/9 = 52/153

Simplified Fraction

52/153

Mixed Number

Proper (52/153)

Decimal Value

0.339869

Percentage

33.9869%

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Step-by-Step Solution: 4/34 + 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 4/34 by 9, and multiply the numerator and denominator of 2/9 by 34 so both fractions share the common base 306.

4 × 9/34 × 9 = 36/306 and 2 × 34/9 × 34 = 68/306

Step 3

Add the Numerators

Now add the numerators (36 + 68 = 104) and keep the common denominator 306 unchanged.

36 + 68/306 = 104/306

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 104 and 306, which is 2. Divide both the numerator and denominator by 2.

104 ÷ 2/306 ÷ 2 = 52/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 153 produces a repeating decimal (approximately 0.339869, or 33.9869%).

52 ÷ 153 = 0.339869 (33.9869%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/153`
Mixed Number Form	`52/153`
Decimal Form	`0.339869`
Percentage	`33.9869%`

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Frequently Asked Questions

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

4/34 + 2/9 in simplest fraction form is 52/153.

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

4/34 + 2/9 converted to a decimal is 0.339869.

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

4/34 + 2/9 expressed as a percentage is 33.9869%.

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

It results in a repeating decimal (approximately 0.339869...) because the denominator contains prime factors other than 2 and 5.