What is 3/35 plus 2/9? (Answer: 97/315)

Exact Answer

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Problem: What is 3/35 plus 2/9?
Formula / Expression: 3/35 + 2/9
Final Answer: 97/315
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 9 = 315.
Working: LCD(35, 9) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 3/35 by 9, and multiply the numerator and denominator of 2/9 by 35 so both fractions share the common base 315.
Working: 3 × 9/35 × 9 = 27/315 and 2 × 35/9 × 35 = 70/315

Step 3: Add the Numerators
Now add the numerators (27 + 70 = 97) and keep the common denominator 315 unchanged.
Working: 27 + 70/315 = 97/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 315 is 1, confirming that 97/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 315 produces a repeating decimal (approximately 0.307937, or 30.7937%).
Working: 97 ÷ 315 = 0.307937 (30.7937%)

Key Values:
- Simplified Fraction: 97/315
- Mixed Number Form: 97/315
- Decimal Value: 0.307937
- Percentage: 30.7937%

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Solved with FractionsCalc:
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3/35 + 2/9 = 97/315

Simplified Fraction

97/315

Mixed Number

Proper (97/315)

Decimal Value

0.307937

Percentage

30.7937%

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Step-by-Step Solution: 3/35 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 9 = 315.

LCD(35, 9) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 3/35 by 9, and multiply the numerator and denominator of 2/9 by 35 so both fractions share the common base 315.

3 × 9/35 × 9 = 27/315 and 2 × 35/9 × 35 = 70/315

Step 3

Add the Numerators

Now add the numerators (27 + 70 = 97) and keep the common denominator 315 unchanged.

27 + 70/315 = 97/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 315 is 1, confirming that 97/315 cannot be reduced further—it is already in its simplest irreducible form.

97/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 315 produces a repeating decimal (approximately 0.307937, or 30.7937%).

97 ÷ 315 = 0.307937 (30.7937%)

Visual Representation

The diagram below illustrates 3/35 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/315`
Mixed Number Form	`97/315`
Decimal Form	`0.307937`
Percentage	`30.7937%`

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Frequently Asked Questions

What is 3/35 plus 2/9 as a fraction?

3/35 + 2/9 in simplest fraction form is 97/315.

What is 3/35 plus 2/9 as a decimal?

3/35 + 2/9 converted to a decimal is 0.307937.

What is 3/35 plus 2/9 as a percentage?

3/35 + 2/9 expressed as a percentage is 30.7937%.

Does 3/35 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.307937...) because the denominator contains prime factors other than 2 and 5.