What is 8/23 plus 4/9? (Answer: 164/207)

Exact Answer

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Problem: What is 8/23 plus 4/9?
Formula / Expression: 8/23 + 4/9
Final Answer: 164/207
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 9 = 207.
Working: LCD(23, 9) = 207

Step 2: Convert to Equivalent Fractions with Common Denominator 207
Multiply the numerator and denominator of 8/23 by 9, and multiply the numerator and denominator of 4/9 by 23 so both fractions share the common base 207.
Working: 8 × 9/23 × 9 = 72/207 and 4 × 23/9 × 23 = 92/207

Step 3: Add the Numerators
Now add the numerators (72 + 92 = 164) and keep the common denominator 207 unchanged.
Working: 72 + 92/207 = 164/207

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 164 and 207 is 1, confirming that 164/207 cannot be reduced further—it is already in its simplest irreducible form.
Working: 164/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 164 by denominator 207 produces a repeating decimal (approximately 0.792271, or 79.2271%).
Working: 164 ÷ 207 = 0.792271 (79.2271%)

Key Values:
- Simplified Fraction: 164/207
- Mixed Number Form: 164/207
- Decimal Value: 0.792271
- Percentage: 79.2271%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-23-plus-4-9/
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8/23 + 4/9 = 164/207

Simplified Fraction

164/207

Mixed Number

Proper (164/207)

Decimal Value

0.792271

Percentage

79.2271%

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Step-by-Step Solution: 8/23 + 4/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 9 = 207.

LCD(23, 9) = 207

Step 2

Convert to Equivalent Fractions with Common Denominator 207

Multiply the numerator and denominator of 8/23 by 9, and multiply the numerator and denominator of 4/9 by 23 so both fractions share the common base 207.

8 × 9/23 × 9 = 72/207 and 4 × 23/9 × 23 = 92/207

Step 3

Add the Numerators

Now add the numerators (72 + 92 = 164) and keep the common denominator 207 unchanged.

72 + 92/207 = 164/207

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 164 and 207 is 1, confirming that 164/207 cannot be reduced further—it is already in its simplest irreducible form.

164/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 164 by denominator 207 produces a repeating decimal (approximately 0.792271, or 79.2271%).

164 ÷ 207 = 0.792271 (79.2271%)

Visual Representation

The diagram below illustrates 8/23 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`164/207`
Mixed Number Form	`164/207`
Decimal Form	`0.792271`
Percentage	`79.2271%`

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Frequently Asked Questions

What is 8/23 plus 4/9 as a fraction?

8/23 + 4/9 in simplest fraction form is 164/207.

What is 8/23 plus 4/9 as a decimal?

8/23 + 4/9 converted to a decimal is 0.792271.

What is 8/23 plus 4/9 as a percentage?

8/23 + 4/9 expressed as a percentage is 79.2271%.

Does 8/23 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.792271...) because the denominator contains prime factors other than 2 and 5.