What is 4/17 plus 4/9? (Answer: 104/153)

Exact Answer

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Problem: What is 4/17 plus 4/9?
Formula / Expression: 4/17 + 4/9
Final Answer: 104/153
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 9 = 153.
Working: LCD(17, 9) = 153

Step 2: Convert to Equivalent Fractions with Common Denominator 153
Multiply the numerator and denominator of 4/17 by 9, and multiply the numerator and denominator of 4/9 by 17 so both fractions share the common base 153.
Working: 4 × 9/17 × 9 = 36/153 and 4 × 17/9 × 17 = 68/153

Step 3: Add the Numerators
Now add the numerators (36 + 68 = 104) and keep the common denominator 153 unchanged.
Working: 36 + 68/153 = 104/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 104 and 153 is 1, confirming that 104/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 104/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 104 by denominator 153 produces a repeating decimal (approximately 0.679739, or 67.9739%).
Working: 104 ÷ 153 = 0.679739 (67.9739%)

Key Values:
- Simplified Fraction: 104/153
- Mixed Number Form: 104/153
- Decimal Value: 0.679739
- Percentage: 67.9739%

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Solved with FractionsCalc:
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4/17 + 4/9 = 104/153

Simplified Fraction

104/153

Mixed Number

Proper (104/153)

Decimal Value

0.679739

Percentage

67.9739%

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Step-by-Step Solution: 4/17 + 4/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 9 = 153.

LCD(17, 9) = 153

Step 2

Convert to Equivalent Fractions with Common Denominator 153

Multiply the numerator and denominator of 4/17 by 9, and multiply the numerator and denominator of 4/9 by 17 so both fractions share the common base 153.

4 × 9/17 × 9 = 36/153 and 4 × 17/9 × 17 = 68/153

Step 3

Add the Numerators

Now add the numerators (36 + 68 = 104) and keep the common denominator 153 unchanged.

36 + 68/153 = 104/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 104 and 153 is 1, confirming that 104/153 cannot be reduced further—it is already in its simplest irreducible form.

104/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 104 by denominator 153 produces a repeating decimal (approximately 0.679739, or 67.9739%).

104 ÷ 153 = 0.679739 (67.9739%)

Visual Representation

The diagram below illustrates 4/17 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`104/153`
Mixed Number Form	`104/153`
Decimal Form	`0.679739`
Percentage	`67.9739%`

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Frequently Asked Questions

What is 4/17 plus 4/9 as a fraction?

4/17 + 4/9 in simplest fraction form is 104/153.

What is 4/17 plus 4/9 as a decimal?

4/17 + 4/9 converted to a decimal is 0.679739.

What is 4/17 plus 4/9 as a percentage?

4/17 + 4/9 expressed as a percentage is 67.9739%.

Does 4/17 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.679739...) because the denominator contains prime factors other than 2 and 5.