What is 2/22 plus 7/9? (Answer: 86/99)

Exact Answer

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Problem: What is 2/22 plus 7/9?
Formula / Expression: 2/22 + 7/9
Final Answer: 86/99
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 198
Multiply the numerator and denominator of 2/22 by 9, and multiply the numerator and denominator of 7/9 by 22 so both fractions share the common base 198.
Working: 2 × 9/22 × 9 = 18/198 and 7 × 22/9 × 22 = 154/198

Step 3: Add the Numerators
Now add the numerators (18 + 154 = 172) and keep the common denominator 198 unchanged.
Working: 18 + 154/198 = 172/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 172 and 198, which is 2. Divide both the numerator and denominator by 2.
Working: 172 ÷ 2/198 ÷ 2 = 86/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 99 produces a repeating decimal (approximately 0.868687, or 86.8687%).
Working: 86 ÷ 99 = 0.868687 (86.8687%)

Key Values:
- Simplified Fraction: 86/99
- Mixed Number Form: 86/99
- Decimal Value: 0.868687
- Percentage: 86.8687%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-22-plus-7-9/
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2/22 + 7/9 = 86/99

Simplified Fraction

86/99

Mixed Number

Proper (86/99)

Decimal Value

0.868687

Percentage

86.8687%

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Step-by-Step Solution: 2/22 + 7/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(22, 9) = 198

Step 2

Convert to Equivalent Fractions with Common Denominator 198

Multiply the numerator and denominator of 2/22 by 9, and multiply the numerator and denominator of 7/9 by 22 so both fractions share the common base 198.

2 × 9/22 × 9 = 18/198 and 7 × 22/9 × 22 = 154/198

Step 3

Add the Numerators

Now add the numerators (18 + 154 = 172) and keep the common denominator 198 unchanged.

18 + 154/198 = 172/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 172 and 198, which is 2. Divide both the numerator and denominator by 2.

172 ÷ 2/198 ÷ 2 = 86/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 99 produces a repeating decimal (approximately 0.868687, or 86.8687%).

86 ÷ 99 = 0.868687 (86.8687%)

Visual Representation

The diagram below illustrates 2/22 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/99`
Mixed Number Form	`86/99`
Decimal Form	`0.868687`
Percentage	`86.8687%`

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Frequently Asked Questions

What is 2/22 plus 7/9 as a fraction?

2/22 + 7/9 in simplest fraction form is 86/99.

What is 2/22 plus 7/9 as a decimal?

2/22 + 7/9 converted to a decimal is 0.868687.

What is 2/22 plus 7/9 as a percentage?

2/22 + 7/9 expressed as a percentage is 86.8687%.

Does 2/22 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.868687...) because the denominator contains prime factors other than 2 and 5.