What is 6/22 plus 4/9? (Answer: 71/99)

Exact Answer

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Problem: What is 6/22 plus 4/9?
Formula / Expression: 6/22 + 4/9
Final Answer: 71/99
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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 6/22 by 9, and multiply the numerator and denominator of 4/9 by 22 so both fractions share the common base 198.
Working: 6 × 9/22 × 9 = 54/198 and 4 × 22/9 × 22 = 88/198

Step 3: Add the Numerators
Now add the numerators (54 + 88 = 142) and keep the common denominator 198 unchanged.
Working: 54 + 88/198 = 142/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 142 and 198, which is 2. Divide both the numerator and denominator by 2.
Working: 142 ÷ 2/198 ÷ 2 = 71/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 99 produces a repeating decimal (approximately 0.717172, or 71.7172%).
Working: 71 ÷ 99 = 0.717172 (71.7172%)

Key Values:
- Simplified Fraction: 71/99
- Mixed Number Form: 71/99
- Decimal Value: 0.717172
- Percentage: 71.7172%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-22-plus-4-9/
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6/22 + 4/9 = 71/99

Simplified Fraction

71/99

Mixed Number

Proper (71/99)

Decimal Value

0.717172

Percentage

71.7172%

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Step-by-Step Solution: 6/22 + 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 6/22 by 9, and multiply the numerator and denominator of 4/9 by 22 so both fractions share the common base 198.

6 × 9/22 × 9 = 54/198 and 4 × 22/9 × 22 = 88/198

Step 3

Add the Numerators

Now add the numerators (54 + 88 = 142) and keep the common denominator 198 unchanged.

54 + 88/198 = 142/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 142 and 198, which is 2. Divide both the numerator and denominator by 2.

142 ÷ 2/198 ÷ 2 = 71/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 99 produces a repeating decimal (approximately 0.717172, or 71.7172%).

71 ÷ 99 = 0.717172 (71.7172%)

Visual Representation

The diagram below illustrates 6/22 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/99`
Mixed Number Form	`71/99`
Decimal Form	`0.717172`
Percentage	`71.7172%`

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Frequently Asked Questions

What is 6/22 plus 4/9 as a fraction?

6/22 + 4/9 in simplest fraction form is 71/99.

What is 6/22 plus 4/9 as a decimal?

6/22 + 4/9 converted to a decimal is 0.717172.

What is 6/22 plus 4/9 as a percentage?

6/22 + 4/9 expressed as a percentage is 71.7172%.

Does 6/22 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.717172...) because the denominator contains prime factors other than 2 and 5.