What is 4/22 plus 3/9? (Answer: 17/33)

Exact Answer

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Problem: What is 4/22 plus 3/9?
Formula / Expression: 4/22 + 3/9
Final Answer: 17/33
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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 4/22 by 9, and multiply the numerator and denominator of 3/9 by 22 so both fractions share the common base 198.
Working: 4 × 9/22 × 9 = 36/198 and 3 × 22/9 × 22 = 66/198

Step 3: Add the Numerators
Now add the numerators (36 + 66 = 102) and keep the common denominator 198 unchanged.
Working: 36 + 66/198 = 102/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 198, which is 6. Divide both the numerator and denominator by 6.
Working: 102 ÷ 6/198 ÷ 6 = 17/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 33 produces a repeating decimal (approximately 0.515152, or 51.5152%).
Working: 17 ÷ 33 = 0.515152 (51.5152%)

Key Values:
- Simplified Fraction: 17/33
- Mixed Number Form: 17/33
- Decimal Value: 0.515152
- Percentage: 51.5152%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-22-plus-3-9/
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4/22 + 3/9 = 17/33

Simplified Fraction

17/33

Mixed Number

Proper (17/33)

Decimal Value

0.515152

Percentage

51.5152%

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Step-by-Step Solution: 4/22 + 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 4/22 by 9, and multiply the numerator and denominator of 3/9 by 22 so both fractions share the common base 198.

4 × 9/22 × 9 = 36/198 and 3 × 22/9 × 22 = 66/198

Step 3

Add the Numerators

Now add the numerators (36 + 66 = 102) and keep the common denominator 198 unchanged.

36 + 66/198 = 102/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 198, which is 6. Divide both the numerator and denominator by 6.

102 ÷ 6/198 ÷ 6 = 17/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 33 produces a repeating decimal (approximately 0.515152, or 51.5152%).

17 ÷ 33 = 0.515152 (51.5152%)

Visual Representation

The diagram below illustrates 4/22 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/33`
Mixed Number Form	`17/33`
Decimal Form	`0.515152`
Percentage	`51.5152%`

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Frequently Asked Questions

What is 4/22 plus 3/9 as a fraction?

4/22 + 3/9 in simplest fraction form is 17/33.

What is 4/22 plus 3/9 as a decimal?

4/22 + 3/9 converted to a decimal is 0.515152.

What is 4/22 plus 3/9 as a percentage?

4/22 + 3/9 expressed as a percentage is 51.5152%.

Does 4/22 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.515152...) because the denominator contains prime factors other than 2 and 5.