What is 1/30 plus 2/9? (Answer: 23/90)

Exact Answer

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Problem: What is 1/30 plus 2/9?
Formula / Expression: 1/30 + 2/9
Final Answer: 23/90
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 1/30 by 3, and multiply the numerator and denominator of 2/9 by 10 so both fractions share the common base 90.
Working: 1 × 3/30 × 3 = 3/90 and 2 × 10/9 × 10 = 20/90

Step 3: Add the Numerators
Now add the numerators (3 + 20 = 23) and keep the common denominator 90 unchanged.
Working: 3 + 20/90 = 23/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 90 is 1, confirming that 23/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 90 produces a repeating decimal (approximately 0.255556, or 25.5556%).
Working: 23 ÷ 90 = 0.255556 (25.5556%)

Key Values:
- Simplified Fraction: 23/90
- Mixed Number Form: 23/90
- Decimal Value: 0.255556
- Percentage: 25.5556%

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1/30 + 2/9 = 23/90

Simplified Fraction

23/90

Mixed Number

Proper (23/90)

Decimal Value

0.255556

Percentage

25.5556%

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Step-by-Step Solution: 1/30 + 2/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(30, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 1/30 by 3, and multiply the numerator and denominator of 2/9 by 10 so both fractions share the common base 90.

1 × 3/30 × 3 = 3/90 and 2 × 10/9 × 10 = 20/90

Step 3

Add the Numerators

Now add the numerators (3 + 20 = 23) and keep the common denominator 90 unchanged.

3 + 20/90 = 23/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 90 is 1, confirming that 23/90 cannot be reduced further—it is already in its simplest irreducible form.

23/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 90 produces a repeating decimal (approximately 0.255556, or 25.5556%).

23 ÷ 90 = 0.255556 (25.5556%)

Visual Representation

The diagram below illustrates 1/30 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/90`
Mixed Number Form	`23/90`
Decimal Form	`0.255556`
Percentage	`25.5556%`

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Frequently Asked Questions

What is 1/30 plus 2/9 as a fraction?

1/30 + 2/9 in simplest fraction form is 23/90.

What is 1/30 plus 2/9 as a decimal?

1/30 + 2/9 converted to a decimal is 0.255556.

What is 1/30 plus 2/9 as a percentage?

1/30 + 2/9 expressed as a percentage is 25.5556%.

Does 1/30 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.255556...) because the denominator contains prime factors other than 2 and 5.