What is 9/34 plus 3/9? (Answer: 61/102)

Exact Answer

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Problem: What is 9/34 plus 3/9?
Formula / Expression: 9/34 + 3/9
Final Answer: 61/102
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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 9/34 by 9, and multiply the numerator and denominator of 3/9 by 34 so both fractions share the common base 306.
Working: 9 × 9/34 × 9 = 81/306 and 3 × 34/9 × 34 = 102/306

Step 3: Add the Numerators
Now add the numerators (81 + 102 = 183) and keep the common denominator 306 unchanged.
Working: 81 + 102/306 = 183/306

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 183 and 306, which is 3. Divide both the numerator and denominator by 3.
Working: 183 ÷ 3/306 ÷ 3 = 61/102

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 102 produces a repeating decimal (approximately 0.598039, or 59.8039%).
Working: 61 ÷ 102 = 0.598039 (59.8039%)

Key Values:
- Simplified Fraction: 61/102
- Mixed Number Form: 61/102
- Decimal Value: 0.598039
- Percentage: 59.8039%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-34-plus-3-9/
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9/34 + 3/9 = 61/102

Simplified Fraction

61/102

Mixed Number

Proper (61/102)

Decimal Value

0.598039

Percentage

59.8039%

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Step-by-Step Solution: 9/34 + 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 9/34 by 9, and multiply the numerator and denominator of 3/9 by 34 so both fractions share the common base 306.

9 × 9/34 × 9 = 81/306 and 3 × 34/9 × 34 = 102/306

Step 3

Add the Numerators

Now add the numerators (81 + 102 = 183) and keep the common denominator 306 unchanged.

81 + 102/306 = 183/306

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 183 and 306, which is 3. Divide both the numerator and denominator by 3.

183 ÷ 3/306 ÷ 3 = 61/102

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 102 produces a repeating decimal (approximately 0.598039, or 59.8039%).

61 ÷ 102 = 0.598039 (59.8039%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/102`
Mixed Number Form	`61/102`
Decimal Form	`0.598039`
Percentage	`59.8039%`

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Frequently Asked Questions

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

9/34 + 3/9 in simplest fraction form is 61/102.

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

9/34 + 3/9 converted to a decimal is 0.598039.

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

9/34 + 3/9 expressed as a percentage is 59.8039%.

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

It results in a repeating decimal (approximately 0.598039...) because the denominator contains prime factors other than 2 and 5.