What is 1/9 plus 2/12? (Answer: 5/18)

Exact Answer

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Problem: What is 1/9 plus 2/12?
Formula / Expression: 1/9 + 2/12
Final Answer: 5/18
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).
Working: LCD(9, 12) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 1/9 by 4, and multiply the numerator and denominator of 2/12 by 3 so both fractions share the common base 36.
Working: 1 × 4/9 × 4 = 4/36 and 2 × 3/12 × 3 = 6/36

Step 3: Add the Numerators
Now add the numerators (4 + 6 = 10) and keep the common denominator 36 unchanged.
Working: 4 + 6/36 = 10/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 10 and 36, which is 2. Divide both the numerator and denominator by 2.
Working: 10 ÷ 2/36 ÷ 2 = 5/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 18 produces a repeating decimal (approximately 0.277778, or 27.7778%).
Working: 5 ÷ 18 = 0.277778 (27.7778%)

Key Values:
- Simplified Fraction: 5/18
- Mixed Number Form: 5/18
- Decimal Value: 0.277778
- Percentage: 27.7778%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-2-12/
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1/9 + 2/12 = 5/18

Simplified Fraction

5/18

Mixed Number

Proper (5/18)

Decimal Value

0.277778

Percentage

27.7778%

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Step-by-Step Solution: 1/9 + 2/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).

LCD(9, 12) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 1/9 by 4, and multiply the numerator and denominator of 2/12 by 3 so both fractions share the common base 36.

1 × 4/9 × 4 = 4/36 and 2 × 3/12 × 3 = 6/36

Step 3

Add the Numerators

Now add the numerators (4 + 6 = 10) and keep the common denominator 36 unchanged.

4 + 6/36 = 10/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 10 and 36, which is 2. Divide both the numerator and denominator by 2.

10 ÷ 2/36 ÷ 2 = 5/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 18 produces a repeating decimal (approximately 0.277778, or 27.7778%).

5 ÷ 18 = 0.277778 (27.7778%)

Visual Representation

The diagram below illustrates 1/9 plus 2/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/18`
Mixed Number Form	`5/18`
Decimal Form	`0.277778`
Percentage	`27.7778%`

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Frequently Asked Questions

What is 1/9 plus 2/12 as a fraction?

1/9 + 2/12 in simplest fraction form is 5/18.

What is 1/9 plus 2/12 as a decimal?

1/9 + 2/12 converted to a decimal is 0.277778.

What is 1/9 plus 2/12 as a percentage?

1/9 + 2/12 expressed as a percentage is 27.7778%.

Does 1/9 plus 2/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.277778...) because the denominator contains prime factors other than 2 and 5.