What is 2/12 plus 5/9? (Answer: 13/18)

Exact Answer

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Problem: What is 2/12 plus 5/9?
Formula / Expression: 2/12 + 5/9
Final Answer: 13/18
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 2/12 by 3, and multiply the numerator and denominator of 5/9 by 4 so both fractions share the common base 36.
Working: 2 × 3/12 × 3 = 6/36 and 5 × 4/9 × 4 = 20/36

Step 3: Add the Numerators
Now add the numerators (6 + 20 = 26) and keep the common denominator 36 unchanged.
Working: 6 + 20/36 = 26/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 36, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/36 ÷ 2 = 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:
https://fractionscalc.com/what-is-2-12-plus-5-9/
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2/12 + 5/9 = 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: 2/12 + 5/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(12, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 2/12 by 3, and multiply the numerator and denominator of 5/9 by 4 so both fractions share the common base 36.

2 × 3/12 × 3 = 6/36 and 5 × 4/9 × 4 = 20/36

Step 3

Add the Numerators

Now add the numerators (6 + 20 = 26) and keep the common denominator 36 unchanged.

6 + 20/36 = 26/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 36, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/36 ÷ 2 = 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 2/12 plus 5/9 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 2/12 plus 5/9 as a fraction?

2/12 + 5/9 in simplest fraction form is 13/18.

What is 2/12 plus 5/9 as a decimal?

2/12 + 5/9 converted to a decimal is 0.722222.

What is 2/12 plus 5/9 as a percentage?

2/12 + 5/9 expressed as a percentage is 72.2222%.

Does 2/12 plus 5/9 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.