What is 4/17 plus 3/4? (Answer: 67/68)

Exact Answer

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Problem: What is 4/17 plus 3/4?
Formula / Expression: 4/17 + 3/4
Final Answer: 67/68
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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 4/17 by 4, and multiply the numerator and denominator of 3/4 by 17 so both fractions share the common base 68.
Working: 4 × 4/17 × 4 = 16/68 and 3 × 17/4 × 17 = 51/68

Step 3: Add the Numerators
Now add the numerators (16 + 51 = 67) and keep the common denominator 68 unchanged.
Working: 16 + 51/68 = 67/68

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 68 is 1, confirming that 67/68 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/68

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 68 produces a repeating decimal (approximately 0.985294, or 98.5294%).
Working: 67 ÷ 68 = 0.985294 (98.5294%)

Key Values:
- Simplified Fraction: 67/68
- Mixed Number Form: 67/68
- Decimal Value: 0.985294
- Percentage: 98.5294%

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Solved with FractionsCalc:
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4/17 + 3/4 = 67/68

Simplified Fraction

67/68

Mixed Number

Proper (67/68)

Decimal Value

0.985294

Percentage

98.5294%

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Step-by-Step Solution: 4/17 + 3/4

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 4/17 by 4, and multiply the numerator and denominator of 3/4 by 17 so both fractions share the common base 68.

4 × 4/17 × 4 = 16/68 and 3 × 17/4 × 17 = 51/68

Step 3

Add the Numerators

Now add the numerators (16 + 51 = 67) and keep the common denominator 68 unchanged.

16 + 51/68 = 67/68

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 68 is 1, confirming that 67/68 cannot be reduced further—it is already in its simplest irreducible form.

67/68

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 68 produces a repeating decimal (approximately 0.985294, or 98.5294%).

67 ÷ 68 = 0.985294 (98.5294%)

Visual Representation

The diagram below illustrates 4/17 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/68`
Mixed Number Form	`67/68`
Decimal Form	`0.985294`
Percentage	`98.5294%`

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Frequently Asked Questions

What is 4/17 plus 3/4 as a fraction?

4/17 + 3/4 in simplest fraction form is 67/68.

What is 4/17 plus 3/4 as a decimal?

4/17 + 3/4 converted to a decimal is 0.985294.

What is 4/17 plus 3/4 as a percentage?

4/17 + 3/4 expressed as a percentage is 98.5294%.

Does 4/17 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.985294...) because the denominator contains prime factors other than 2 and 5.