What is 1/22 plus 3/9? (Answer: 25/66)

Exact Answer

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Problem: What is 1/22 plus 3/9?
Formula / Expression: 1/22 + 3/9
Final Answer: 25/66
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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 1/22 by 9, and multiply the numerator and denominator of 3/9 by 22 so both fractions share the common base 198.
Working: 1 × 9/22 × 9 = 9/198 and 3 × 22/9 × 22 = 66/198

Step 3: Add the Numerators
Now add the numerators (9 + 66 = 75) and keep the common denominator 198 unchanged.
Working: 9 + 66/198 = 75/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 198, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/198 ÷ 3 = 25/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 66 produces a repeating decimal (approximately 0.378788, or 37.8788%).
Working: 25 ÷ 66 = 0.378788 (37.8788%)

Key Values:
- Simplified Fraction: 25/66
- Mixed Number Form: 25/66
- Decimal Value: 0.378788
- Percentage: 37.8788%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-22-plus-3-9/
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1/22 + 3/9 = 25/66

Simplified Fraction

25/66

Mixed Number

Proper (25/66)

Decimal Value

0.378788

Percentage

37.8788%

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Step-by-Step Solution: 1/22 + 3/9

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 1/22 by 9, and multiply the numerator and denominator of 3/9 by 22 so both fractions share the common base 198.

1 × 9/22 × 9 = 9/198 and 3 × 22/9 × 22 = 66/198

Step 3

Add the Numerators

Now add the numerators (9 + 66 = 75) and keep the common denominator 198 unchanged.

9 + 66/198 = 75/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 198, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/198 ÷ 3 = 25/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 66 produces a repeating decimal (approximately 0.378788, or 37.8788%).

25 ÷ 66 = 0.378788 (37.8788%)

Visual Representation

The diagram below illustrates 1/22 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/66`
Mixed Number Form	`25/66`
Decimal Form	`0.378788`
Percentage	`37.8788%`

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Frequently Asked Questions

What is 1/22 plus 3/9 as a fraction?

1/22 + 3/9 in simplest fraction form is 25/66.

What is 1/22 plus 3/9 as a decimal?

1/22 + 3/9 converted to a decimal is 0.378788.

What is 1/22 plus 3/9 as a percentage?

1/22 + 3/9 expressed as a percentage is 37.8788%.

Does 1/22 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.378788...) because the denominator contains prime factors other than 2 and 5.