What is 3/23 plus 2/9? (Answer: 73/207)

Exact Answer

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Problem: What is 3/23 plus 2/9?
Formula / Expression: 3/23 + 2/9
Final Answer: 73/207
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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 3/23 by 9, and multiply the numerator and denominator of 2/9 by 23 so both fractions share the common base 207.
Working: 3 × 9/23 × 9 = 27/207 and 2 × 23/9 × 23 = 46/207

Step 3: Add the Numerators
Now add the numerators (27 + 46 = 73) and keep the common denominator 207 unchanged.
Working: 27 + 46/207 = 73/207

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 207 is 1, confirming that 73/207 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 207 produces a repeating decimal (approximately 0.352657, or 35.2657%).
Working: 73 ÷ 207 = 0.352657 (35.2657%)

Key Values:
- Simplified Fraction: 73/207
- Mixed Number Form: 73/207
- Decimal Value: 0.352657
- Percentage: 35.2657%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-23-plus-2-9/
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3/23 + 2/9 = 73/207

Simplified Fraction

73/207

Mixed Number

Proper (73/207)

Decimal Value

0.352657

Percentage

35.2657%

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Step-by-Step Solution: 3/23 + 2/9

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 3/23 by 9, and multiply the numerator and denominator of 2/9 by 23 so both fractions share the common base 207.

3 × 9/23 × 9 = 27/207 and 2 × 23/9 × 23 = 46/207

Step 3

Add the Numerators

Now add the numerators (27 + 46 = 73) and keep the common denominator 207 unchanged.

27 + 46/207 = 73/207

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 207 is 1, confirming that 73/207 cannot be reduced further—it is already in its simplest irreducible form.

73/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 207 produces a repeating decimal (approximately 0.352657, or 35.2657%).

73 ÷ 207 = 0.352657 (35.2657%)

Visual Representation

The diagram below illustrates 3/23 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/207`
Mixed Number Form	`73/207`
Decimal Form	`0.352657`
Percentage	`35.2657%`

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Frequently Asked Questions

What is 3/23 plus 2/9 as a fraction?

3/23 + 2/9 in simplest fraction form is 73/207.

What is 3/23 plus 2/9 as a decimal?

3/23 + 2/9 converted to a decimal is 0.352657.

What is 3/23 plus 2/9 as a percentage?

3/23 + 2/9 expressed as a percentage is 35.2657%.

Does 3/23 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.352657...) because the denominator contains prime factors other than 2 and 5.