What is 9/34 plus 2/5? (Answer: 113/170)

Exact Answer

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Problem: What is 9/34 plus 2/5?
Formula / Expression: 9/34 + 2/5
Final Answer: 113/170
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 5 = 170.
Working: LCD(34, 5) = 170

Step 2: Convert to Equivalent Fractions with Common Denominator 170
Multiply the numerator and denominator of 9/34 by 5, and multiply the numerator and denominator of 2/5 by 34 so both fractions share the common base 170.
Working: 9 × 5/34 × 5 = 45/170 and 2 × 34/5 × 34 = 68/170

Step 3: Add the Numerators
Now add the numerators (45 + 68 = 113) and keep the common denominator 170 unchanged.
Working: 45 + 68/170 = 113/170

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 170 is 1, confirming that 113/170 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/170

Step 5: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 170 produces a repeating decimal (approximately 0.664706, or 66.4706%).
Working: 113 ÷ 170 = 0.664706 (66.4706%)

Key Values:
- Simplified Fraction: 113/170
- Mixed Number Form: 113/170
- Decimal Value: 0.664706
- Percentage: 66.4706%

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Solved with FractionsCalc:
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9/34 + 2/5 = 113/170

Simplified Fraction

113/170

Mixed Number

Proper (113/170)

Decimal Value

0.664706

Percentage

66.4706%

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Step-by-Step Solution: 9/34 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 5 = 170.

LCD(34, 5) = 170

Step 2

Convert to Equivalent Fractions with Common Denominator 170

Multiply the numerator and denominator of 9/34 by 5, and multiply the numerator and denominator of 2/5 by 34 so both fractions share the common base 170.

9 × 5/34 × 5 = 45/170 and 2 × 34/5 × 34 = 68/170

Step 3

Add the Numerators

Now add the numerators (45 + 68 = 113) and keep the common denominator 170 unchanged.

45 + 68/170 = 113/170

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 170 is 1, confirming that 113/170 cannot be reduced further—it is already in its simplest irreducible form.

113/170

Step 5

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 170 produces a repeating decimal (approximately 0.664706, or 66.4706%).

113 ÷ 170 = 0.664706 (66.4706%)

Visual Representation

The diagram below illustrates 9/34 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/170`
Mixed Number Form	`113/170`
Decimal Form	`0.664706`
Percentage	`66.4706%`

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Frequently Asked Questions

What is 9/34 plus 2/5 as a fraction?

9/34 + 2/5 in simplest fraction form is 113/170.

What is 9/34 plus 2/5 as a decimal?

9/34 + 2/5 converted to a decimal is 0.664706.

What is 9/34 plus 2/5 as a percentage?

9/34 + 2/5 expressed as a percentage is 66.4706%.

Does 9/34 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.664706...) because the denominator contains prime factors other than 2 and 5.