What is 3/17 plus 5/9? (Answer: 112/153)

Exact Answer

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Problem: What is 3/17 plus 5/9?
Formula / Expression: 3/17 + 5/9
Final Answer: 112/153
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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 5/9 by 17 so both fractions share the common base 153.
Working: 3 × 9/17 × 9 = 27/153 and 5 × 17/9 × 17 = 85/153

Step 3: Add the Numerators
Now add the numerators (27 + 85 = 112) and keep the common denominator 153 unchanged.
Working: 27 + 85/153 = 112/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 112 and 153 is 1, confirming that 112/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 112/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 112 by denominator 153 produces a repeating decimal (approximately 0.732026, or 73.2026%).
Working: 112 ÷ 153 = 0.732026 (73.2026%)

Key Values:
- Simplified Fraction: 112/153
- Mixed Number Form: 112/153
- Decimal Value: 0.732026
- Percentage: 73.2026%

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Solved with FractionsCalc:
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3/17 + 5/9 = 112/153

Simplified Fraction

112/153

Mixed Number

Proper (112/153)

Decimal Value

0.732026

Percentage

73.2026%

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Step-by-Step Solution: 3/17 + 5/9

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 5/9 by 17 so both fractions share the common base 153.

3 × 9/17 × 9 = 27/153 and 5 × 17/9 × 17 = 85/153

Step 3

Add the Numerators

Now add the numerators (27 + 85 = 112) and keep the common denominator 153 unchanged.

27 + 85/153 = 112/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 112 and 153 is 1, confirming that 112/153 cannot be reduced further—it is already in its simplest irreducible form.

112/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 112 by denominator 153 produces a repeating decimal (approximately 0.732026, or 73.2026%).

112 ÷ 153 = 0.732026 (73.2026%)

Visual Representation

The diagram below illustrates 3/17 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`112/153`
Mixed Number Form	`112/153`
Decimal Form	`0.732026`
Percentage	`73.2026%`

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Frequently Asked Questions

What is 3/17 plus 5/9 as a fraction?

3/17 + 5/9 in simplest fraction form is 112/153.

What is 3/17 plus 5/9 as a decimal?

3/17 + 5/9 converted to a decimal is 0.732026.

What is 3/17 plus 5/9 as a percentage?

3/17 + 5/9 expressed as a percentage is 73.2026%.

Does 3/17 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.732026...) because the denominator contains prime factors other than 2 and 5.