What is 2/9 plus 12/22? (Answer: 76/99)

Exact Answer

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Problem: What is 2/9 plus 12/22?
Formula / Expression: 2/9 + 12/22
Final Answer: 76/99
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 22 = 198.
Working: LCD(9, 22) = 198

Step 2: Convert to Equivalent Fractions with Common Denominator 198
Multiply the numerator and denominator of 2/9 by 22, and multiply the numerator and denominator of 12/22 by 9 so both fractions share the common base 198.
Working: 2 × 22/9 × 22 = 44/198 and 12 × 9/22 × 9 = 108/198

Step 3: Add the Numerators
Now add the numerators (44 + 108 = 152) and keep the common denominator 198 unchanged.
Working: 44 + 108/198 = 152/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 152 and 198, which is 2. Divide both the numerator and denominator by 2.
Working: 152 ÷ 2/198 ÷ 2 = 76/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 99 produces a repeating decimal (approximately 0.767677, or 76.7677%).
Working: 76 ÷ 99 = 0.767677 (76.7677%)

Key Values:
- Simplified Fraction: 76/99
- Mixed Number Form: 76/99
- Decimal Value: 0.767677
- Percentage: 76.7677%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-12-22/
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2/9 + 12/22 = 76/99

Simplified Fraction

76/99

Mixed Number

Proper (76/99)

Decimal Value

0.767677

Percentage

76.7677%

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Step-by-Step Solution: 2/9 + 12/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 22 = 198.

LCD(9, 22) = 198

Step 2

Convert to Equivalent Fractions with Common Denominator 198

Multiply the numerator and denominator of 2/9 by 22, and multiply the numerator and denominator of 12/22 by 9 so both fractions share the common base 198.

2 × 22/9 × 22 = 44/198 and 12 × 9/22 × 9 = 108/198

Step 3

Add the Numerators

Now add the numerators (44 + 108 = 152) and keep the common denominator 198 unchanged.

44 + 108/198 = 152/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 152 and 198, which is 2. Divide both the numerator and denominator by 2.

152 ÷ 2/198 ÷ 2 = 76/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 99 produces a repeating decimal (approximately 0.767677, or 76.7677%).

76 ÷ 99 = 0.767677 (76.7677%)

Visual Representation

The diagram below illustrates 2/9 plus 12/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/99`
Mixed Number Form	`76/99`
Decimal Form	`0.767677`
Percentage	`76.7677%`

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Frequently Asked Questions

What is 2/9 plus 12/22 as a fraction?

2/9 + 12/22 in simplest fraction form is 76/99.

What is 2/9 plus 12/22 as a decimal?

2/9 + 12/22 converted to a decimal is 0.767677.

What is 2/9 plus 12/22 as a percentage?

2/9 + 12/22 expressed as a percentage is 76.7677%.

Does 2/9 plus 12/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.767677...) because the denominator contains prime factors other than 2 and 5.