What is 2/15 plus 2/9? (Answer: 16/45)

Exact Answer

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Problem: What is 2/15 plus 2/9?
Formula / Expression: 2/15 + 2/9
Final Answer: 16/45
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 2/15 by 3, and multiply the numerator and denominator of 2/9 by 5 so both fractions share the common base 45.
Working: 2 × 3/15 × 3 = 6/45 and 2 × 5/9 × 5 = 10/45

Step 3: Add the Numerators
Now add the numerators (6 + 10 = 16) and keep the common denominator 45 unchanged.
Working: 6 + 10/45 = 16/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 16 and 45 is 1, confirming that 16/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 16/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 45 produces a repeating decimal (approximately 0.355556, or 35.5556%).
Working: 16 ÷ 45 = 0.355556 (35.5556%)

Key Values:
- Simplified Fraction: 16/45
- Mixed Number Form: 16/45
- Decimal Value: 0.355556
- Percentage: 35.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-15-plus-2-9/
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2/15 + 2/9 = 16/45

Simplified Fraction

16/45

Mixed Number

Proper (16/45)

Decimal Value

0.355556

Percentage

35.5556%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(15, 9) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

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

2 × 3/15 × 3 = 6/45 and 2 × 5/9 × 5 = 10/45

Step 3

Add the Numerators

Now add the numerators (6 + 10 = 16) and keep the common denominator 45 unchanged.

6 + 10/45 = 16/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 16 and 45 is 1, confirming that 16/45 cannot be reduced further—it is already in its simplest irreducible form.

16/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 45 produces a repeating decimal (approximately 0.355556, or 35.5556%).

16 ÷ 45 = 0.355556 (35.5556%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/45`
Mixed Number Form	`16/45`
Decimal Form	`0.355556`
Percentage	`35.5556%`

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Frequently Asked Questions

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

2/15 + 2/9 in simplest fraction form is 16/45.

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

2/15 + 2/9 converted to a decimal is 0.355556.

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

2/15 + 2/9 expressed as a percentage is 35.5556%.

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

It results in a repeating decimal (approximately 0.355556...) because the denominator contains prime factors other than 2 and 5.