What is 3/17 plus 4/9? (Answer: 95/153)

Exact Answer

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Problem: What is 3/17 plus 4/9?
Formula / Expression: 3/17 + 4/9
Final Answer: 95/153
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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 3/17 by 9, and multiply the numerator and denominator of 4/9 by 17 so both fractions share the common base 153.
Working: 3 × 9/17 × 9 = 27/153 and 4 × 17/9 × 17 = 68/153

Step 3: Add the Numerators
Now add the numerators (27 + 68 = 95) and keep the common denominator 153 unchanged.
Working: 27 + 68/153 = 95/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 95 and 153 is 1, confirming that 95/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 95/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 95 by denominator 153 produces a repeating decimal (approximately 0.620915, or 62.0915%).
Working: 95 ÷ 153 = 0.620915 (62.0915%)

Key Values:
- Simplified Fraction: 95/153
- Mixed Number Form: 95/153
- Decimal Value: 0.620915
- Percentage: 62.0915%

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Solved with FractionsCalc:
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3/17 + 4/9 = 95/153

Simplified Fraction

95/153

Mixed Number

Proper (95/153)

Decimal Value

0.620915

Percentage

62.0915%

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Step-by-Step Solution: 3/17 + 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 3/17 by 9, and multiply the numerator and denominator of 4/9 by 17 so both fractions share the common base 153.

3 × 9/17 × 9 = 27/153 and 4 × 17/9 × 17 = 68/153

Step 3

Add the Numerators

Now add the numerators (27 + 68 = 95) and keep the common denominator 153 unchanged.

27 + 68/153 = 95/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 95 and 153 is 1, confirming that 95/153 cannot be reduced further—it is already in its simplest irreducible form.

95/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 95 by denominator 153 produces a repeating decimal (approximately 0.620915, or 62.0915%).

95 ÷ 153 = 0.620915 (62.0915%)

Visual Representation

The diagram below illustrates 3/17 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`95/153`
Mixed Number Form	`95/153`
Decimal Form	`0.620915`
Percentage	`62.0915%`

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Frequently Asked Questions

What is 3/17 plus 4/9 as a fraction?

3/17 + 4/9 in simplest fraction form is 95/153.

What is 3/17 plus 4/9 as a decimal?

3/17 + 4/9 converted to a decimal is 0.620915.

What is 3/17 plus 4/9 as a percentage?

3/17 + 4/9 expressed as a percentage is 62.0915%.

Does 3/17 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.620915...) because the denominator contains prime factors other than 2 and 5.