What is 5/22 plus 3/9? (Answer: 37/66)

Exact Answer

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Problem: What is 5/22 plus 3/9?
Formula / Expression: 5/22 + 3/9
Final Answer: 37/66
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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 5/22 by 9, and multiply the numerator and denominator of 3/9 by 22 so both fractions share the common base 198.
Working: 5 × 9/22 × 9 = 45/198 and 3 × 22/9 × 22 = 66/198

Step 3: Add the Numerators
Now add the numerators (45 + 66 = 111) and keep the common denominator 198 unchanged.
Working: 45 + 66/198 = 111/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 111 and 198, which is 3. Divide both the numerator and denominator by 3.
Working: 111 ÷ 3/198 ÷ 3 = 37/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 66 produces a repeating decimal (approximately 0.560606, or 56.0606%).
Working: 37 ÷ 66 = 0.560606 (56.0606%)

Key Values:
- Simplified Fraction: 37/66
- Mixed Number Form: 37/66
- Decimal Value: 0.560606
- Percentage: 56.0606%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-22-plus-3-9/
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5/22 + 3/9 = 37/66

Simplified Fraction

37/66

Mixed Number

Proper (37/66)

Decimal Value

0.560606

Percentage

56.0606%

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Step-by-Step Solution: 5/22 + 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 5/22 by 9, and multiply the numerator and denominator of 3/9 by 22 so both fractions share the common base 198.

5 × 9/22 × 9 = 45/198 and 3 × 22/9 × 22 = 66/198

Step 3

Add the Numerators

Now add the numerators (45 + 66 = 111) and keep the common denominator 198 unchanged.

45 + 66/198 = 111/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 111 and 198, which is 3. Divide both the numerator and denominator by 3.

111 ÷ 3/198 ÷ 3 = 37/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 66 produces a repeating decimal (approximately 0.560606, or 56.0606%).

37 ÷ 66 = 0.560606 (56.0606%)

Visual Representation

The diagram below illustrates 5/22 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/66`
Mixed Number Form	`37/66`
Decimal Form	`0.560606`
Percentage	`56.0606%`

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Frequently Asked Questions

What is 5/22 plus 3/9 as a fraction?

5/22 + 3/9 in simplest fraction form is 37/66.

What is 5/22 plus 3/9 as a decimal?

5/22 + 3/9 converted to a decimal is 0.560606.

What is 5/22 plus 3/9 as a percentage?

5/22 + 3/9 expressed as a percentage is 56.0606%.

Does 5/22 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.560606...) because the denominator contains prime factors other than 2 and 5.