What is 2/9 plus 9/18? (Answer: 13/18)

Exact Answer

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Problem: What is 2/9 plus 9/18?
Formula / Expression: 2/9 + 9/18
Final Answer: 13/18
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 18 is an exact multiple of 9 (9 × 2 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.
Working: LCD(9, 18) = 18

Step 2: Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 2/9 by 2, and multiply the numerator and denominator of 9/18 by 1 so both fractions share the common base 18.
Working: 2 × 2/9 × 2 = 4/18 and 9 × 1/18 × 1 = 9/18

Step 3: Add the Numerators
Now add the numerators (4 + 9 = 13) and keep the common denominator 18 unchanged.
Working: 4 + 9/18 = 13/18

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 18 is 1, confirming that 13/18 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 18 produces a repeating decimal (approximately 0.722222, or 72.2222%).
Working: 13 ÷ 18 = 0.722222 (72.2222%)

Key Values:
- Simplified Fraction: 13/18
- Mixed Number Form: 13/18
- Decimal Value: 0.722222
- Percentage: 72.2222%

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Solved with FractionsCalc:
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2/9 + 9/18 = 13/18

Simplified Fraction

13/18

Mixed Number

Proper (13/18)

Decimal Value

0.722222

Percentage

72.2222%

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Step-by-Step Solution: 2/9 + 9/18

Step 1

Find the Least Common Denominator (LCD)

Notice that 18 is an exact multiple of 9 (9 × 2 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.

LCD(9, 18) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

Multiply the numerator and denominator of 2/9 by 2, and multiply the numerator and denominator of 9/18 by 1 so both fractions share the common base 18.

2 × 2/9 × 2 = 4/18 and 9 × 1/18 × 1 = 9/18

Step 3

Add the Numerators

Now add the numerators (4 + 9 = 13) and keep the common denominator 18 unchanged.

4 + 9/18 = 13/18

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 18 is 1, confirming that 13/18 cannot be reduced further—it is already in its simplest irreducible form.

13/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 18 produces a repeating decimal (approximately 0.722222, or 72.2222%).

13 ÷ 18 = 0.722222 (72.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 9/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/18`
Mixed Number Form	`13/18`
Decimal Form	`0.722222`
Percentage	`72.2222%`

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Frequently Asked Questions

What is 2/9 plus 9/18 as a fraction?

2/9 + 9/18 in simplest fraction form is 13/18.

What is 2/9 plus 9/18 as a decimal?

2/9 + 9/18 converted to a decimal is 0.722222.

What is 2/9 plus 9/18 as a percentage?

2/9 + 9/18 expressed as a percentage is 72.2222%.

Does 2/9 plus 9/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.722222...) because the denominator contains prime factors other than 2 and 5.