What is 4/9 plus 8/17? (Answer: 140/153)

Exact Answer

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Problem: What is 4/9 plus 8/17?
Formula / Expression: 4/9 + 8/17
Final Answer: 140/153
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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 8/17 by 9 so both fractions share the common base 153.
Working: 4 × 17/9 × 17 = 68/153 and 8 × 9/17 × 9 = 72/153

Step 3: Add the Numerators
Now add the numerators (68 + 72 = 140) and keep the common denominator 153 unchanged.
Working: 68 + 72/153 = 140/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 140 and 153 is 1, confirming that 140/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 140/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 140 by denominator 153 produces a repeating decimal (approximately 0.915033, or 91.5033%).
Working: 140 ÷ 153 = 0.915033 (91.5033%)

Key Values:
- Simplified Fraction: 140/153
- Mixed Number Form: 140/153
- Decimal Value: 0.915033
- Percentage: 91.5033%

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Solved with FractionsCalc:
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4/9 + 8/17 = 140/153

Simplified Fraction

140/153

Mixed Number

Proper (140/153)

Decimal Value

0.915033

Percentage

91.5033%

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Step-by-Step Solution: 4/9 + 8/17

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 8/17 by 9 so both fractions share the common base 153.

4 × 17/9 × 17 = 68/153 and 8 × 9/17 × 9 = 72/153

Step 3

Add the Numerators

Now add the numerators (68 + 72 = 140) and keep the common denominator 153 unchanged.

68 + 72/153 = 140/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 140 and 153 is 1, confirming that 140/153 cannot be reduced further—it is already in its simplest irreducible form.

140/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 140 by denominator 153 produces a repeating decimal (approximately 0.915033, or 91.5033%).

140 ÷ 153 = 0.915033 (91.5033%)

Visual Representation

The diagram below illustrates 4/9 plus 8/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`140/153`
Mixed Number Form	`140/153`
Decimal Form	`0.915033`
Percentage	`91.5033%`

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Frequently Asked Questions

What is 4/9 plus 8/17 as a fraction?

4/9 + 8/17 in simplest fraction form is 140/153.

What is 4/9 plus 8/17 as a decimal?

4/9 + 8/17 converted to a decimal is 0.915033.

What is 4/9 plus 8/17 as a percentage?

4/9 + 8/17 expressed as a percentage is 91.5033%.

Does 4/9 plus 8/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.915033...) because the denominator contains prime factors other than 2 and 5.