What is 2/9 plus 1/3? (Answer: 5/9)

Exact Answer

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Problem: What is 2/9 plus 1/3?
Formula / Expression: 2/9 + 1/3
Final Answer: 5/9
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.
Working: LCD(9, 3) = 9

Step 2: Convert to Equivalent Fractions with Common Denominator 9
Multiply the numerator and denominator of 2/9 by 1, and multiply the numerator and denominator of 1/3 by 3 so both fractions share the common base 9.
Working: 2 × 1/9 × 1 = 2/9 and 1 × 3/3 × 3 = 3/9

Step 3: Add the Numerators
Now add the numerators (2 + 3 = 5) and keep the common denominator 9 unchanged.
Working: 2 + 3/9 = 5/9

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 9 is 1, confirming that 5/9 cannot be reduced further—it is already in its simplest irreducible form.
Working: 5/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).
Working: 5 ÷ 9 = 0.555556 (55.5556%)

Key Values:
- Simplified Fraction: 5/9
- Mixed Number Form: 5/9
- Decimal Value: 0.555556
- Percentage: 55.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-1-3/
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2/9 + 1/3 = 5/9

Simplified Fraction

5/9

Mixed Number

Proper (5/9)

Decimal Value

0.555556

Percentage

55.5556%

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Step-by-Step Solution: 2/9 + 1/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.

LCD(9, 3) = 9

Step 2

Convert to Equivalent Fractions with Common Denominator 9

Multiply the numerator and denominator of 2/9 by 1, and multiply the numerator and denominator of 1/3 by 3 so both fractions share the common base 9.

2 × 1/9 × 1 = 2/9 and 1 × 3/3 × 3 = 3/9

Step 3

Add the Numerators

Now add the numerators (2 + 3 = 5) and keep the common denominator 9 unchanged.

2 + 3/9 = 5/9

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 9 is 1, confirming that 5/9 cannot be reduced further—it is already in its simplest irreducible form.

5/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).

5 ÷ 9 = 0.555556 (55.5556%)

Visual Representation

The diagram below illustrates 2/9 plus 1/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/9`
Mixed Number Form	`5/9`
Decimal Form	`0.555556`
Percentage	`55.5556%`

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Frequently Asked Questions

What is 2/9 plus 1/3 as a fraction?

2/9 + 1/3 in simplest fraction form is 5/9.

What is 2/9 plus 1/3 as a decimal?

2/9 + 1/3 converted to a decimal is 0.555556.

What is 2/9 plus 1/3 as a percentage?

2/9 + 1/3 expressed as a percentage is 55.5556%.

Does 2/9 plus 1/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.555556...) because the denominator contains prime factors other than 2 and 5.