What is 2/9 plus 4/15? (Answer: 22/45)

Exact Answer

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Problem: What is 2/9 plus 4/15?
Formula / Expression: 2/9 + 4/15
Final Answer: 22/45
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 9 × 15 = 135, keeping the calculation simpler).
Working: LCD(9, 15) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 2/9 by 5, and multiply the numerator and denominator of 4/15 by 3 so both fractions share the common base 45.
Working: 2 × 5/9 × 5 = 10/45 and 4 × 3/15 × 3 = 12/45

Step 3: Add the Numerators
Now add the numerators (10 + 12 = 22) and keep the common denominator 45 unchanged.
Working: 10 + 12/45 = 22/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 22 and 45 is 1, confirming that 22/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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 + 4/15 = 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 + 4/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 9 × 15 = 135, keeping the calculation simpler).

LCD(9, 15) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 2/9 by 5, and multiply the numerator and denominator of 4/15 by 3 so both fractions share the common base 45.

2 × 5/9 × 5 = 10/45 and 4 × 3/15 × 3 = 12/45

Step 3

Add the Numerators

Now add the numerators (10 + 12 = 22) and keep the common denominator 45 unchanged.

10 + 12/45 = 22/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 22 and 45 is 1, confirming that 22/45 cannot be reduced further—it is already in its simplest irreducible form.

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 4/15 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 4/15 as a fraction?

2/9 + 4/15 in simplest fraction form is 22/45.

What is 2/9 plus 4/15 as a decimal?

2/9 + 4/15 converted to a decimal is 0.488889.

What is 2/9 plus 4/15 as a percentage?

2/9 + 4/15 expressed as a percentage is 48.8889%.

Does 2/9 plus 4/15 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.