What is 4/17 plus 2/5? (Answer: 54/85)

Exact Answer

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Problem: What is 4/17 plus 2/5?
Formula / Expression: 4/17 + 2/5
Final Answer: 54/85
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 5 = 85.
Working: LCD(17, 5) = 85

Step 2: Convert to Equivalent Fractions with Common Denominator 85
Multiply the numerator and denominator of 4/17 by 5, and multiply the numerator and denominator of 2/5 by 17 so both fractions share the common base 85.
Working: 4 × 5/17 × 5 = 20/85 and 2 × 17/5 × 17 = 34/85

Step 3: Add the Numerators
Now add the numerators (20 + 34 = 54) and keep the common denominator 85 unchanged.
Working: 20 + 34/85 = 54/85

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 54 and 85 is 1, confirming that 54/85 cannot be reduced further—it is already in its simplest irreducible form.
Working: 54/85

Step 5: Decimal & Percentage Representation
Dividing the numerator 54 by denominator 85 produces a repeating decimal (approximately 0.635294, or 63.5294%).
Working: 54 ÷ 85 = 0.635294 (63.5294%)

Key Values:
- Simplified Fraction: 54/85
- Mixed Number Form: 54/85
- Decimal Value: 0.635294
- Percentage: 63.5294%

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Solved with FractionsCalc:
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4/17 + 2/5 = 54/85

Simplified Fraction

54/85

Mixed Number

Proper (54/85)

Decimal Value

0.635294

Percentage

63.5294%

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Step-by-Step Solution: 4/17 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 5 = 85.

LCD(17, 5) = 85

Step 2

Convert to Equivalent Fractions with Common Denominator 85

Multiply the numerator and denominator of 4/17 by 5, and multiply the numerator and denominator of 2/5 by 17 so both fractions share the common base 85.

4 × 5/17 × 5 = 20/85 and 2 × 17/5 × 17 = 34/85

Step 3

Add the Numerators

Now add the numerators (20 + 34 = 54) and keep the common denominator 85 unchanged.

20 + 34/85 = 54/85

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 54 and 85 is 1, confirming that 54/85 cannot be reduced further—it is already in its simplest irreducible form.

54/85

Step 5

Decimal & Percentage Representation

Dividing the numerator 54 by denominator 85 produces a repeating decimal (approximately 0.635294, or 63.5294%).

54 ÷ 85 = 0.635294 (63.5294%)

Visual Representation

The diagram below illustrates 4/17 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`54/85`
Mixed Number Form	`54/85`
Decimal Form	`0.635294`
Percentage	`63.5294%`

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Frequently Asked Questions

What is 4/17 plus 2/5 as a fraction?

4/17 + 2/5 in simplest fraction form is 54/85.

What is 4/17 plus 2/5 as a decimal?

4/17 + 2/5 converted to a decimal is 0.635294.

What is 4/17 plus 2/5 as a percentage?

4/17 + 2/5 expressed as a percentage is 63.5294%.

Does 4/17 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.635294...) because the denominator contains prime factors other than 2 and 5.