What is 9/35 plus 2/5? (Answer: 23/35)

Exact Answer

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Problem: What is 9/35 plus 2/5?
Formula / Expression: 9/35 + 2/5
Final Answer: 23/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 35 is an exact multiple of 5 (5 × 7 = 35). The Least Common Denominator (LCD) is simply 35, meaning we only need to scale one fraction.
Working: LCD(35, 5) = 35

Step 2: Convert to Equivalent Fractions with Common Denominator 35
Multiply the numerator and denominator of 9/35 by 1, and multiply the numerator and denominator of 2/5 by 7 so both fractions share the common base 35.
Working: 9 × 1/35 × 1 = 9/35 and 2 × 7/5 × 7 = 14/35

Step 3: Add the Numerators
Now add the numerators (9 + 14 = 23) and keep the common denominator 35 unchanged.
Working: 9 + 14/35 = 23/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 35 is 1, confirming that 23/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 35 produces a repeating decimal (approximately 0.657143, or 65.7143%).
Working: 23 ÷ 35 = 0.657143 (65.7143%)

Key Values:
- Simplified Fraction: 23/35
- Mixed Number Form: 23/35
- Decimal Value: 0.657143
- Percentage: 65.7143%

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Solved with FractionsCalc:
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9/35 + 2/5 = 23/35

Simplified Fraction

23/35

Mixed Number

Proper (23/35)

Decimal Value

0.657143

Percentage

65.7143%

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Step-by-Step Solution: 9/35 + 2/5

Step 1

Find the Least Common Denominator (LCD)

Notice that 35 is an exact multiple of 5 (5 × 7 = 35). The Least Common Denominator (LCD) is simply 35, meaning we only need to scale one fraction.

LCD(35, 5) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

Multiply the numerator and denominator of 9/35 by 1, and multiply the numerator and denominator of 2/5 by 7 so both fractions share the common base 35.

9 × 1/35 × 1 = 9/35 and 2 × 7/5 × 7 = 14/35

Step 3

Add the Numerators

Now add the numerators (9 + 14 = 23) and keep the common denominator 35 unchanged.

9 + 14/35 = 23/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 35 is 1, confirming that 23/35 cannot be reduced further—it is already in its simplest irreducible form.

23/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 35 produces a repeating decimal (approximately 0.657143, or 65.7143%).

23 ÷ 35 = 0.657143 (65.7143%)

Visual Representation

The diagram below illustrates 9/35 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/35`
Mixed Number Form	`23/35`
Decimal Form	`0.657143`
Percentage	`65.7143%`

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Frequently Asked Questions

What is 9/35 plus 2/5 as a fraction?

9/35 + 2/5 in simplest fraction form is 23/35.

What is 9/35 plus 2/5 as a decimal?

9/35 + 2/5 converted to a decimal is 0.657143.

What is 9/35 plus 2/5 as a percentage?

9/35 + 2/5 expressed as a percentage is 65.7143%.

Does 9/35 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.657143...) because the denominator contains prime factors other than 2 and 5.