What is 5/17 plus 4/9? (Answer: 113/153)

Exact Answer

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Problem: What is 5/17 plus 4/9?
Formula / Expression: 5/17 + 4/9
Final Answer: 113/153
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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 5/17 by 9, and multiply the numerator and denominator of 4/9 by 17 so both fractions share the common base 153.
Working: 5 × 9/17 × 9 = 45/153 and 4 × 17/9 × 17 = 68/153

Step 3: Add the Numerators
Now add the numerators (45 + 68 = 113) and keep the common denominator 153 unchanged.
Working: 45 + 68/153 = 113/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 153 is 1, confirming that 113/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 153 produces a repeating decimal (approximately 0.738562, or 73.8562%).
Working: 113 ÷ 153 = 0.738562 (73.8562%)

Key Values:
- Simplified Fraction: 113/153
- Mixed Number Form: 113/153
- Decimal Value: 0.738562
- Percentage: 73.8562%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-17-plus-4-9/
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5/17 + 4/9 = 113/153

Simplified Fraction

113/153

Mixed Number

Proper (113/153)

Decimal Value

0.738562

Percentage

73.8562%

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Step-by-Step Solution: 5/17 + 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 5/17 by 9, and multiply the numerator and denominator of 4/9 by 17 so both fractions share the common base 153.

5 × 9/17 × 9 = 45/153 and 4 × 17/9 × 17 = 68/153

Step 3

Add the Numerators

Now add the numerators (45 + 68 = 113) and keep the common denominator 153 unchanged.

45 + 68/153 = 113/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 153 is 1, confirming that 113/153 cannot be reduced further—it is already in its simplest irreducible form.

113/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 153 produces a repeating decimal (approximately 0.738562, or 73.8562%).

113 ÷ 153 = 0.738562 (73.8562%)

Visual Representation

The diagram below illustrates 5/17 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/153`
Mixed Number Form	`113/153`
Decimal Form	`0.738562`
Percentage	`73.8562%`

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Frequently Asked Questions

What is 5/17 plus 4/9 as a fraction?

5/17 + 4/9 in simplest fraction form is 113/153.

What is 5/17 plus 4/9 as a decimal?

5/17 + 4/9 converted to a decimal is 0.738562.

What is 5/17 plus 4/9 as a percentage?

5/17 + 4/9 expressed as a percentage is 73.8562%.

Does 5/17 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.738562...) because the denominator contains prime factors other than 2 and 5.