What is 2/9 plus 10/22? (Answer: 67/99)

Exact Answer

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Problem: What is 2/9 plus 10/22?
Formula / Expression: 2/9 + 10/22
Final Answer: 67/99
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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 10/22 by 9 so both fractions share the common base 198.
Working: 2 × 22/9 × 22 = 44/198 and 10 × 9/22 × 9 = 90/198

Step 3: Add the Numerators
Now add the numerators (44 + 90 = 134) and keep the common denominator 198 unchanged.
Working: 44 + 90/198 = 134/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 134 and 198, which is 2. Divide both the numerator and denominator by 2.
Working: 134 ÷ 2/198 ÷ 2 = 67/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 99 produces a repeating decimal (approximately 0.676768, or 67.6768%).
Working: 67 ÷ 99 = 0.676768 (67.6768%)

Key Values:
- Simplified Fraction: 67/99
- Mixed Number Form: 67/99
- Decimal Value: 0.676768
- Percentage: 67.6768%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-10-22/
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2/9 + 10/22 = 67/99

Simplified Fraction

67/99

Mixed Number

Proper (67/99)

Decimal Value

0.676768

Percentage

67.6768%

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Step-by-Step Solution: 2/9 + 10/22

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 10/22 by 9 so both fractions share the common base 198.

2 × 22/9 × 22 = 44/198 and 10 × 9/22 × 9 = 90/198

Step 3

Add the Numerators

Now add the numerators (44 + 90 = 134) and keep the common denominator 198 unchanged.

44 + 90/198 = 134/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 134 and 198, which is 2. Divide both the numerator and denominator by 2.

134 ÷ 2/198 ÷ 2 = 67/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 99 produces a repeating decimal (approximately 0.676768, or 67.6768%).

67 ÷ 99 = 0.676768 (67.6768%)

Visual Representation

The diagram below illustrates 2/9 plus 10/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/99`
Mixed Number Form	`67/99`
Decimal Form	`0.676768`
Percentage	`67.6768%`

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Frequently Asked Questions

What is 2/9 plus 10/22 as a fraction?

2/9 + 10/22 in simplest fraction form is 67/99.

What is 2/9 plus 10/22 as a decimal?

2/9 + 10/22 converted to a decimal is 0.676768.

What is 2/9 plus 10/22 as a percentage?

2/9 + 10/22 expressed as a percentage is 67.6768%.

Does 2/9 plus 10/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.676768...) because the denominator contains prime factors other than 2 and 5.