What is 2/9 plus 8/30? (Answer: 22/45)

Exact Answer

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Problem: What is 2/9 plus 8/30?
Formula / Expression: 2/9 + 8/30
Final Answer: 22/45
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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 8/30 by 3 so both fractions share the common base 90.
Working: 2 × 10/9 × 10 = 20/90 and 8 × 3/30 × 3 = 24/90

Step 3: Add the Numerators
Now add the numerators (20 + 24 = 44) and keep the common denominator 90 unchanged.
Working: 20 + 24/90 = 44/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 44 and 90, which is 2. Divide both the numerator and denominator by 2.
Working: 44 ÷ 2/90 ÷ 2 = 22/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 45 produces a repeating decimal (approximately 0.488889, or 48.8889%).
Working: 22 ÷ 45 = 0.488889 (48.8889%)

Key Values:
- Simplified Fraction: 22/45
- Mixed Number Form: 22/45
- Decimal Value: 0.488889
- Percentage: 48.8889%

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Solved with FractionsCalc:
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2/9 + 8/30 = 22/45

Simplified Fraction

22/45

Mixed Number

Proper (22/45)

Decimal Value

0.488889

Percentage

48.8889%

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Step-by-Step Solution: 2/9 + 8/30

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 8/30 by 3 so both fractions share the common base 90.

2 × 10/9 × 10 = 20/90 and 8 × 3/30 × 3 = 24/90

Step 3

Add the Numerators

Now add the numerators (20 + 24 = 44) and keep the common denominator 90 unchanged.

20 + 24/90 = 44/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 44 and 90, which is 2. Divide both the numerator and denominator by 2.

44 ÷ 2/90 ÷ 2 = 22/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 45 produces a repeating decimal (approximately 0.488889, or 48.8889%).

22 ÷ 45 = 0.488889 (48.8889%)

Visual Representation

The diagram below illustrates 2/9 plus 8/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/45`
Mixed Number Form	`22/45`
Decimal Form	`0.488889`
Percentage	`48.8889%`

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Frequently Asked Questions

What is 2/9 plus 8/30 as a fraction?

2/9 + 8/30 in simplest fraction form is 22/45.

What is 2/9 plus 8/30 as a decimal?

2/9 + 8/30 converted to a decimal is 0.488889.

What is 2/9 plus 8/30 as a percentage?

2/9 + 8/30 expressed as a percentage is 48.8889%.

Does 2/9 plus 8/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.488889...) because the denominator contains prime factors other than 2 and 5.