What is 4/23 plus 3/9? (Answer: 35/69)

Exact Answer

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Problem: What is 4/23 plus 3/9?
Formula / Expression: 4/23 + 3/9
Final Answer: 35/69
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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 4/23 by 9, and multiply the numerator and denominator of 3/9 by 23 so both fractions share the common base 207.
Working: 4 × 9/23 × 9 = 36/207 and 3 × 23/9 × 23 = 69/207

Step 3: Add the Numerators
Now add the numerators (36 + 69 = 105) and keep the common denominator 207 unchanged.
Working: 36 + 69/207 = 105/207

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 105 and 207, which is 3. Divide both the numerator and denominator by 3.
Working: 105 ÷ 3/207 ÷ 3 = 35/69

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 69 produces a repeating decimal (approximately 0.507246, or 50.7246%).
Working: 35 ÷ 69 = 0.507246 (50.7246%)

Key Values:
- Simplified Fraction: 35/69
- Mixed Number Form: 35/69
- Decimal Value: 0.507246
- Percentage: 50.7246%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-23-plus-3-9/
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4/23 + 3/9 = 35/69

Simplified Fraction

35/69

Mixed Number

Proper (35/69)

Decimal Value

0.507246

Percentage

50.7246%

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Step-by-Step Solution: 4/23 + 3/9

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 4/23 by 9, and multiply the numerator and denominator of 3/9 by 23 so both fractions share the common base 207.

4 × 9/23 × 9 = 36/207 and 3 × 23/9 × 23 = 69/207

Step 3

Add the Numerators

Now add the numerators (36 + 69 = 105) and keep the common denominator 207 unchanged.

36 + 69/207 = 105/207

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 105 and 207, which is 3. Divide both the numerator and denominator by 3.

105 ÷ 3/207 ÷ 3 = 35/69

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 69 produces a repeating decimal (approximately 0.507246, or 50.7246%).

35 ÷ 69 = 0.507246 (50.7246%)

Visual Representation

The diagram below illustrates 4/23 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/69`
Mixed Number Form	`35/69`
Decimal Form	`0.507246`
Percentage	`50.7246%`

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Frequently Asked Questions

What is 4/23 plus 3/9 as a fraction?

4/23 + 3/9 in simplest fraction form is 35/69.

What is 4/23 plus 3/9 as a decimal?

4/23 + 3/9 converted to a decimal is 0.507246.

What is 4/23 plus 3/9 as a percentage?

4/23 + 3/9 expressed as a percentage is 50.7246%.

Does 4/23 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.507246...) because the denominator contains prime factors other than 2 and 5.