What is 1/6 plus 2/9? (Answer: 7/18)

Exact Answer

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Problem: What is 1/6 plus 2/9?
Formula / Expression: 1/6 + 2/9
Final Answer: 7/18
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 18 (which is smaller than their product 6 × 9 = 54, keeping the calculation simpler).
Working: LCD(6, 9) = 18

Step 2: Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 1/6 by 3, and multiply the numerator and denominator of 2/9 by 2 so both fractions share the common base 18.
Working: 1 × 3/6 × 3 = 3/18 and 2 × 2/9 × 2 = 4/18

Step 3: Add the Numerators
Now add the numerators (3 + 4 = 7) and keep the common denominator 18 unchanged.
Working: 3 + 4/18 = 7/18

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 18 is 1, confirming that 7/18 cannot be reduced further—it is already in its simplest irreducible form.
Working: 7/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 18 produces a repeating decimal (approximately 0.388889, or 38.8889%).
Working: 7 ÷ 18 = 0.388889 (38.8889%)

Key Values:
- Simplified Fraction: 7/18
- Mixed Number Form: 7/18
- Decimal Value: 0.388889
- Percentage: 38.8889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-6-plus-2-9/
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1/6 + 2/9 = 7/18

Simplified Fraction

7/18

Mixed Number

Proper (7/18)

Decimal Value

0.388889

Percentage

38.8889%

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Step-by-Step Solution: 1/6 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 18 (which is smaller than their product 6 × 9 = 54, keeping the calculation simpler).

LCD(6, 9) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

Multiply the numerator and denominator of 1/6 by 3, and multiply the numerator and denominator of 2/9 by 2 so both fractions share the common base 18.

1 × 3/6 × 3 = 3/18 and 2 × 2/9 × 2 = 4/18

Step 3

Add the Numerators

Now add the numerators (3 + 4 = 7) and keep the common denominator 18 unchanged.

3 + 4/18 = 7/18

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 7 and 18 is 1, confirming that 7/18 cannot be reduced further—it is already in its simplest irreducible form.

7/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 18 produces a repeating decimal (approximately 0.388889, or 38.8889%).

7 ÷ 18 = 0.388889 (38.8889%)

Visual Representation

The diagram below illustrates 1/6 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/18`
Mixed Number Form	`7/18`
Decimal Form	`0.388889`
Percentage	`38.8889%`

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Frequently Asked Questions

What is 1/6 plus 2/9 as a fraction?

1/6 + 2/9 in simplest fraction form is 7/18.

What is 1/6 plus 2/9 as a decimal?

1/6 + 2/9 converted to a decimal is 0.388889.

What is 1/6 plus 2/9 as a percentage?

1/6 + 2/9 expressed as a percentage is 38.8889%.

Does 1/6 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.388889...) because the denominator contains prime factors other than 2 and 5.