What is 2/17 plus 4/5? (Answer: 78/85)

Exact Answer

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Problem: What is 2/17 plus 4/5?
Formula / Expression: 2/17 + 4/5
Final Answer: 78/85
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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 2/17 by 5, and multiply the numerator and denominator of 4/5 by 17 so both fractions share the common base 85.
Working: 2 × 5/17 × 5 = 10/85 and 4 × 17/5 × 17 = 68/85

Step 3: Add the Numerators
Now add the numerators (10 + 68 = 78) and keep the common denominator 85 unchanged.
Working: 10 + 68/85 = 78/85

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 78 and 85 is 1, confirming that 78/85 cannot be reduced further—it is already in its simplest irreducible form.
Working: 78/85

Step 5: Decimal & Percentage Representation
Dividing the numerator 78 by denominator 85 produces a repeating decimal (approximately 0.917647, or 91.7647%).
Working: 78 ÷ 85 = 0.917647 (91.7647%)

Key Values:
- Simplified Fraction: 78/85
- Mixed Number Form: 78/85
- Decimal Value: 0.917647
- Percentage: 91.7647%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-17-plus-4-5/
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2/17 + 4/5 = 78/85

Simplified Fraction

78/85

Mixed Number

Proper (78/85)

Decimal Value

0.917647

Percentage

91.7647%

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

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

2 × 5/17 × 5 = 10/85 and 4 × 17/5 × 17 = 68/85

Step 3

Add the Numerators

Now add the numerators (10 + 68 = 78) and keep the common denominator 85 unchanged.

10 + 68/85 = 78/85

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 78 and 85 is 1, confirming that 78/85 cannot be reduced further—it is already in its simplest irreducible form.

78/85

Step 5

Decimal & Percentage Representation

Dividing the numerator 78 by denominator 85 produces a repeating decimal (approximately 0.917647, or 91.7647%).

78 ÷ 85 = 0.917647 (91.7647%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`78/85`
Mixed Number Form	`78/85`
Decimal Form	`0.917647`
Percentage	`91.7647%`

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Frequently Asked Questions

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

2/17 + 4/5 in simplest fraction form is 78/85.

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

2/17 + 4/5 converted to a decimal is 0.917647.

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

2/17 + 4/5 expressed as a percentage is 91.7647%.

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

It results in a repeating decimal (approximately 0.917647...) because the denominator contains prime factors other than 2 and 5.