What is 9/35 plus 2/3? (Answer: 97/105)

Exact Answer

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Problem: What is 9/35 plus 2/3?
Formula / Expression: 9/35 + 2/3
Final Answer: 97/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 3 = 105.
Working: LCD(35, 3) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 9/35 by 3, and multiply the numerator and denominator of 2/3 by 35 so both fractions share the common base 105.
Working: 9 × 3/35 × 3 = 27/105 and 2 × 35/3 × 35 = 70/105

Step 3: Add the Numerators
Now add the numerators (27 + 70 = 97) and keep the common denominator 105 unchanged.
Working: 27 + 70/105 = 97/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 105 is 1, confirming that 97/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 105 produces a repeating decimal (approximately 0.92381, or 92.381%).
Working: 97 ÷ 105 = 0.92381 (92.381%)

Key Values:
- Simplified Fraction: 97/105
- Mixed Number Form: 97/105
- Decimal Value: 0.92381
- Percentage: 92.381%

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Solved with FractionsCalc:
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9/35 + 2/3 = 97/105

Simplified Fraction

97/105

Mixed Number

Proper (97/105)

Decimal Value

0.92381

Percentage

92.381%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 3 = 105.

LCD(35, 3) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 9/35 by 3, and multiply the numerator and denominator of 2/3 by 35 so both fractions share the common base 105.

9 × 3/35 × 3 = 27/105 and 2 × 35/3 × 35 = 70/105

Step 3

Add the Numerators

Now add the numerators (27 + 70 = 97) and keep the common denominator 105 unchanged.

27 + 70/105 = 97/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 105 is 1, confirming that 97/105 cannot be reduced further—it is already in its simplest irreducible form.

97/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 105 produces a repeating decimal (approximately 0.92381, or 92.381%).

97 ÷ 105 = 0.92381 (92.381%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/105`
Mixed Number Form	`97/105`
Decimal Form	`0.92381`
Percentage	`92.381%`

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Frequently Asked Questions

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

9/35 + 2/3 in simplest fraction form is 97/105.

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

9/35 + 2/3 converted to a decimal is 0.92381.

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

9/35 + 2/3 expressed as a percentage is 92.381%.

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

It results in a repeating decimal (approximately 0.92381...) because the denominator contains prime factors other than 2 and 5.