What is 9/22 plus 6/9? (Answer: 71/66)

Exact Answer

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Problem: What is 9/22 plus 6/9?
Formula / Expression: 9/22 + 6/9
Final Answer: 1 5/66 (71/66)
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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 9/22 by 9, and multiply the numerator and denominator of 6/9 by 22 so both fractions share the common base 198.
Working: 9 × 9/22 × 9 = 81/198 and 6 × 22/9 × 22 = 132/198

Step 3: Add the Numerators
Now add the numerators (81 + 132 = 213) and keep the common denominator 198 unchanged.
Working: 81 + 132/198 = 213/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 213 and 198, which is 3. Divide both the numerator and denominator by 3.
Working: 213 ÷ 3/198 ÷ 3 = 71/66

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (66), divide 71 by 66: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/66.
Working: 71/66 = 1 5/66

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 66 produces a repeating decimal (approximately 1.075758, or 107.5758%).
Working: 71 ÷ 66 = 1.075758 (107.5758%)

Key Values:
- Simplified Fraction: 71/66
- Mixed Number Form: 1 5/66
- Decimal Value: 1.075758
- Percentage: 107.5758%

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Solved with FractionsCalc:
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9/22 + 6/9 = 71/66

Simplified Fraction

71/66

Mixed Number

1 5/66

Decimal Value

1.075758

Percentage

107.5758%

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Step-by-Step Solution: 9/22 + 6/9

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 9/22 by 9, and multiply the numerator and denominator of 6/9 by 22 so both fractions share the common base 198.

9 × 9/22 × 9 = 81/198 and 6 × 22/9 × 22 = 132/198

Step 3

Add the Numerators

Now add the numerators (81 + 132 = 213) and keep the common denominator 198 unchanged.

81 + 132/198 = 213/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 213 and 198, which is 3. Divide both the numerator and denominator by 3.

213 ÷ 3/198 ÷ 3 = 71/66

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (66), divide 71 by 66: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/66.

71/66 = 15/66

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 66 produces a repeating decimal (approximately 1.075758, or 107.5758%).

71 ÷ 66 = 1.075758 (107.5758%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/66`
Mixed Number Form	`1 5/66`
Decimal Form	`1.075758`
Percentage	`107.5758%`

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Frequently Asked Questions

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

9/22 + 6/9 in simplest fraction form is 71/66 (or 1 5/66 as a mixed number).

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

9/22 + 6/9 converted to a decimal is 1.075758.

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

9/22 + 6/9 expressed as a percentage is 107.5758%.

How do you write 9/22 plus 6/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/66 can be written as the mixed number 1 5/66.

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

It results in a repeating decimal (approximately 1.075758...) because the denominator contains prime factors other than 2 and 5.