What is 2/9 plus 9/30? (Answer: 47/90)

Exact Answer

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Problem: What is 2/9 plus 9/30?
Formula / Expression: 2/9 + 9/30
Final Answer: 47/90
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 30 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 9 × 30 = 270, keeping the calculation simpler).
Working: LCD(9, 30) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/9 by 10, and multiply the numerator and denominator of 9/30 by 3 so both fractions share the common base 90.
Working: 2 × 10/9 × 10 = 20/90 and 9 × 3/30 × 3 = 27/90

Step 3: Add the Numerators
Now add the numerators (20 + 27 = 47) and keep the common denominator 90 unchanged.
Working: 20 + 27/90 = 47/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 90 is 1, confirming that 47/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 90 produces a repeating decimal (approximately 0.522222, or 52.2222%).
Working: 47 ÷ 90 = 0.522222 (52.2222%)

Key Values:
- Simplified Fraction: 47/90
- Mixed Number Form: 47/90
- Decimal Value: 0.522222
- Percentage: 52.2222%

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Solved with FractionsCalc:
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2/9 + 9/30 = 47/90

Simplified Fraction

47/90

Mixed Number

Proper (47/90)

Decimal Value

0.522222

Percentage

52.2222%

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Step-by-Step Solution: 2/9 + 9/30

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 30 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 9 × 30 = 270, keeping the calculation simpler).

LCD(9, 30) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 2/9 by 10, and multiply the numerator and denominator of 9/30 by 3 so both fractions share the common base 90.

2 × 10/9 × 10 = 20/90 and 9 × 3/30 × 3 = 27/90

Step 3

Add the Numerators

Now add the numerators (20 + 27 = 47) and keep the common denominator 90 unchanged.

20 + 27/90 = 47/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 90 is 1, confirming that 47/90 cannot be reduced further—it is already in its simplest irreducible form.

47/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 90 produces a repeating decimal (approximately 0.522222, or 52.2222%).

47 ÷ 90 = 0.522222 (52.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 9/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/90`
Mixed Number Form	`47/90`
Decimal Form	`0.522222`
Percentage	`52.2222%`

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Frequently Asked Questions

What is 2/9 plus 9/30 as a fraction?

2/9 + 9/30 in simplest fraction form is 47/90.

What is 2/9 plus 9/30 as a decimal?

2/9 + 9/30 converted to a decimal is 0.522222.

What is 2/9 plus 9/30 as a percentage?

2/9 + 9/30 expressed as a percentage is 52.2222%.

Does 2/9 plus 9/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.522222...) because the denominator contains prime factors other than 2 and 5.