What is 8/22 plus 4/9? (Answer: 80/99)

Exact Answer

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Problem: What is 8/22 plus 4/9?
Formula / Expression: 8/22 + 4/9
Final Answer: 80/99
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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 8/22 by 9, and multiply the numerator and denominator of 4/9 by 22 so both fractions share the common base 198.
Working: 8 × 9/22 × 9 = 72/198 and 4 × 22/9 × 22 = 88/198

Step 3: Add the Numerators
Now add the numerators (72 + 88 = 160) and keep the common denominator 198 unchanged.
Working: 72 + 88/198 = 160/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 160 and 198, which is 2. Divide both the numerator and denominator by 2.
Working: 160 ÷ 2/198 ÷ 2 = 80/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 80 by denominator 99 produces a repeating decimal (approximately 0.808081, or 80.8081%).
Working: 80 ÷ 99 = 0.808081 (80.8081%)

Key Values:
- Simplified Fraction: 80/99
- Mixed Number Form: 80/99
- Decimal Value: 0.808081
- Percentage: 80.8081%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-22-plus-4-9/
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8/22 + 4/9 = 80/99

Simplified Fraction

80/99

Mixed Number

Proper (80/99)

Decimal Value

0.808081

Percentage

80.8081%

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Step-by-Step Solution: 8/22 + 4/9

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 8/22 by 9, and multiply the numerator and denominator of 4/9 by 22 so both fractions share the common base 198.

8 × 9/22 × 9 = 72/198 and 4 × 22/9 × 22 = 88/198

Step 3

Add the Numerators

Now add the numerators (72 + 88 = 160) and keep the common denominator 198 unchanged.

72 + 88/198 = 160/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 160 and 198, which is 2. Divide both the numerator and denominator by 2.

160 ÷ 2/198 ÷ 2 = 80/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 80 by denominator 99 produces a repeating decimal (approximately 0.808081, or 80.8081%).

80 ÷ 99 = 0.808081 (80.8081%)

Visual Representation

The diagram below illustrates 8/22 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`80/99`
Mixed Number Form	`80/99`
Decimal Form	`0.808081`
Percentage	`80.8081%`

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Frequently Asked Questions

What is 8/22 plus 4/9 as a fraction?

8/22 + 4/9 in simplest fraction form is 80/99.

What is 8/22 plus 4/9 as a decimal?

8/22 + 4/9 converted to a decimal is 0.808081.

What is 8/22 plus 4/9 as a percentage?

8/22 + 4/9 expressed as a percentage is 80.8081%.

Does 8/22 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.808081...) because the denominator contains prime factors other than 2 and 5.