What is 1/9 plus 8/22? (Answer: 47/99)

Exact Answer

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Problem: What is 1/9 plus 8/22?
Formula / Expression: 1/9 + 8/22
Final Answer: 47/99
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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 1/9 by 22, and multiply the numerator and denominator of 8/22 by 9 so both fractions share the common base 198.
Working: 1 × 22/9 × 22 = 22/198 and 8 × 9/22 × 9 = 72/198

Step 3: Add the Numerators
Now add the numerators (22 + 72 = 94) and keep the common denominator 198 unchanged.
Working: 22 + 72/198 = 94/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 198, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/198 ÷ 2 = 47/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 99 produces a repeating decimal (approximately 0.474747, or 47.4747%).
Working: 47 ÷ 99 = 0.474747 (47.4747%)

Key Values:
- Simplified Fraction: 47/99
- Mixed Number Form: 47/99
- Decimal Value: 0.474747
- Percentage: 47.4747%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-8-22/
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1/9 + 8/22 = 47/99

Simplified Fraction

47/99

Mixed Number

Proper (47/99)

Decimal Value

0.474747

Percentage

47.4747%

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Step-by-Step Solution: 1/9 + 8/22

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 1/9 by 22, and multiply the numerator and denominator of 8/22 by 9 so both fractions share the common base 198.

1 × 22/9 × 22 = 22/198 and 8 × 9/22 × 9 = 72/198

Step 3

Add the Numerators

Now add the numerators (22 + 72 = 94) and keep the common denominator 198 unchanged.

22 + 72/198 = 94/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 198, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/198 ÷ 2 = 47/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 99 produces a repeating decimal (approximately 0.474747, or 47.4747%).

47 ÷ 99 = 0.474747 (47.4747%)

Visual Representation

The diagram below illustrates 1/9 plus 8/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/99`
Mixed Number Form	`47/99`
Decimal Form	`0.474747`
Percentage	`47.4747%`

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Frequently Asked Questions

What is 1/9 plus 8/22 as a fraction?

1/9 + 8/22 in simplest fraction form is 47/99.

What is 1/9 plus 8/22 as a decimal?

1/9 + 8/22 converted to a decimal is 0.474747.

What is 1/9 plus 8/22 as a percentage?

1/9 + 8/22 expressed as a percentage is 47.4747%.

Does 1/9 plus 8/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.474747...) because the denominator contains prime factors other than 2 and 5.