What is 4/9 plus 9/17? (Answer: 149/153)

Exact Answer

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Problem: What is 4/9 plus 9/17?
Formula / Expression: 4/9 + 9/17
Final Answer: 149/153
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 153
Multiply the numerator and denominator of 4/9 by 17, and multiply the numerator and denominator of 9/17 by 9 so both fractions share the common base 153.
Working: 4 × 17/9 × 17 = 68/153 and 9 × 9/17 × 9 = 81/153

Step 3: Add the Numerators
Now add the numerators (68 + 81 = 149) and keep the common denominator 153 unchanged.
Working: 68 + 81/153 = 149/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 149 and 153 is 1, confirming that 149/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 149/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 149 by denominator 153 produces a repeating decimal (approximately 0.973856, or 97.3856%).
Working: 149 ÷ 153 = 0.973856 (97.3856%)

Key Values:
- Simplified Fraction: 149/153
- Mixed Number Form: 149/153
- Decimal Value: 0.973856
- Percentage: 97.3856%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-9-plus-9-17/
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4/9 + 9/17 = 149/153

Simplified Fraction

149/153

Mixed Number

Proper (149/153)

Decimal Value

0.973856

Percentage

97.3856%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 17) = 153

Step 2

Convert to Equivalent Fractions with Common Denominator 153

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

4 × 17/9 × 17 = 68/153 and 9 × 9/17 × 9 = 81/153

Step 3

Add the Numerators

Now add the numerators (68 + 81 = 149) and keep the common denominator 153 unchanged.

68 + 81/153 = 149/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 149 and 153 is 1, confirming that 149/153 cannot be reduced further—it is already in its simplest irreducible form.

149/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 149 by denominator 153 produces a repeating decimal (approximately 0.973856, or 97.3856%).

149 ÷ 153 = 0.973856 (97.3856%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`149/153`
Mixed Number Form	`149/153`
Decimal Form	`0.973856`
Percentage	`97.3856%`

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Frequently Asked Questions

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

4/9 + 9/17 in simplest fraction form is 149/153.

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

4/9 + 9/17 converted to a decimal is 0.973856.

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

4/9 + 9/17 expressed as a percentage is 97.3856%.

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

It results in a repeating decimal (approximately 0.973856...) because the denominator contains prime factors other than 2 and 5.