What is 2/17 plus 1/4? (Answer: 25/68)

Exact Answer

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Problem: What is 2/17 plus 1/4?
Formula / Expression: 2/17 + 1/4
Final Answer: 25/68
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 4 = 68.
Working: LCD(17, 4) = 68

Step 2: Convert to Equivalent Fractions with Common Denominator 68
Multiply the numerator and denominator of 2/17 by 4, and multiply the numerator and denominator of 1/4 by 17 so both fractions share the common base 68.
Working: 2 × 4/17 × 4 = 8/68 and 1 × 17/4 × 17 = 17/68

Step 3: Add the Numerators
Now add the numerators (8 + 17 = 25) and keep the common denominator 68 unchanged.
Working: 8 + 17/68 = 25/68

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 68 is 1, confirming that 25/68 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/68

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 68 produces a repeating decimal (approximately 0.367647, or 36.7647%).
Working: 25 ÷ 68 = 0.367647 (36.7647%)

Key Values:
- Simplified Fraction: 25/68
- Mixed Number Form: 25/68
- Decimal Value: 0.367647
- Percentage: 36.7647%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-17-plus-1-4/
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2/17 + 1/4 = 25/68

Simplified Fraction

25/68

Mixed Number

Proper (25/68)

Decimal Value

0.367647

Percentage

36.7647%

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Step-by-Step Solution: 2/17 + 1/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 4 = 68.

LCD(17, 4) = 68

Step 2

Convert to Equivalent Fractions with Common Denominator 68

Multiply the numerator and denominator of 2/17 by 4, and multiply the numerator and denominator of 1/4 by 17 so both fractions share the common base 68.

2 × 4/17 × 4 = 8/68 and 1 × 17/4 × 17 = 17/68

Step 3

Add the Numerators

Now add the numerators (8 + 17 = 25) and keep the common denominator 68 unchanged.

8 + 17/68 = 25/68

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 68 is 1, confirming that 25/68 cannot be reduced further—it is already in its simplest irreducible form.

25/68

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 68 produces a repeating decimal (approximately 0.367647, or 36.7647%).

25 ÷ 68 = 0.367647 (36.7647%)

Visual Representation

The diagram below illustrates 2/17 plus 1/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/68`
Mixed Number Form	`25/68`
Decimal Form	`0.367647`
Percentage	`36.7647%`

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Frequently Asked Questions

What is 2/17 plus 1/4 as a fraction?

2/17 + 1/4 in simplest fraction form is 25/68.

What is 2/17 plus 1/4 as a decimal?

2/17 + 1/4 converted to a decimal is 0.367647.

What is 2/17 plus 1/4 as a percentage?

2/17 + 1/4 expressed as a percentage is 36.7647%.

Does 2/17 plus 1/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.367647...) because the denominator contains prime factors other than 2 and 5.