What is 1/9 plus 2/15? (Answer: 11/45)

Exact Answer

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Problem: What is 1/9 plus 2/15?
Formula / Expression: 1/9 + 2/15
Final Answer: 11/45
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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 1/9 by 5, and multiply the numerator and denominator of 2/15 by 3 so both fractions share the common base 45.
Working: 1 × 5/9 × 5 = 5/45 and 2 × 3/15 × 3 = 6/45

Step 3: Add the Numerators
Now add the numerators (5 + 6 = 11) and keep the common denominator 45 unchanged.
Working: 5 + 6/45 = 11/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 45 is 1, confirming that 11/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 45 produces a repeating decimal (approximately 0.244444, or 24.4444%).
Working: 11 ÷ 45 = 0.244444 (24.4444%)

Key Values:
- Simplified Fraction: 11/45
- Mixed Number Form: 11/45
- Decimal Value: 0.244444
- Percentage: 24.4444%

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Solved with FractionsCalc:
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1/9 + 2/15 = 11/45

Simplified Fraction

11/45

Mixed Number

Proper (11/45)

Decimal Value

0.244444

Percentage

24.4444%

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Step-by-Step Solution: 1/9 + 2/15

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 1/9 by 5, and multiply the numerator and denominator of 2/15 by 3 so both fractions share the common base 45.

1 × 5/9 × 5 = 5/45 and 2 × 3/15 × 3 = 6/45

Step 3

Add the Numerators

Now add the numerators (5 + 6 = 11) and keep the common denominator 45 unchanged.

5 + 6/45 = 11/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 45 is 1, confirming that 11/45 cannot be reduced further—it is already in its simplest irreducible form.

11/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 45 produces a repeating decimal (approximately 0.244444, or 24.4444%).

11 ÷ 45 = 0.244444 (24.4444%)

Visual Representation

The diagram below illustrates 1/9 plus 2/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/45`
Mixed Number Form	`11/45`
Decimal Form	`0.244444`
Percentage	`24.4444%`

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Frequently Asked Questions

What is 1/9 plus 2/15 as a fraction?

1/9 + 2/15 in simplest fraction form is 11/45.

What is 1/9 plus 2/15 as a decimal?

1/9 + 2/15 converted to a decimal is 0.244444.

What is 1/9 plus 2/15 as a percentage?

1/9 + 2/15 expressed as a percentage is 24.4444%.

Does 1/9 plus 2/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.244444...) because the denominator contains prime factors other than 2 and 5.