What is 2/15 plus 5/9? (Answer: 31/45)

Exact Answer

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Problem: What is 2/15 plus 5/9?
Formula / Expression: 2/15 + 5/9
Final Answer: 31/45
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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 5/9 by 5 so both fractions share the common base 45.
Working: 2 × 3/15 × 3 = 6/45 and 5 × 5/9 × 5 = 25/45

Step 3: Add the Numerators
Now add the numerators (6 + 25 = 31) and keep the common denominator 45 unchanged.
Working: 6 + 25/45 = 31/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 45 is 1, confirming that 31/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 45 produces a repeating decimal (approximately 0.688889, or 68.8889%).
Working: 31 ÷ 45 = 0.688889 (68.8889%)

Key Values:
- Simplified Fraction: 31/45
- Mixed Number Form: 31/45
- Decimal Value: 0.688889
- Percentage: 68.8889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-15-plus-5-9/
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2/15 + 5/9 = 31/45

Simplified Fraction

31/45

Mixed Number

Proper (31/45)

Decimal Value

0.688889

Percentage

68.8889%

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Step-by-Step Solution: 2/15 + 5/9

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 5/9 by 5 so both fractions share the common base 45.

2 × 3/15 × 3 = 6/45 and 5 × 5/9 × 5 = 25/45

Step 3

Add the Numerators

Now add the numerators (6 + 25 = 31) and keep the common denominator 45 unchanged.

6 + 25/45 = 31/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 45 is 1, confirming that 31/45 cannot be reduced further—it is already in its simplest irreducible form.

31/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 45 produces a repeating decimal (approximately 0.688889, or 68.8889%).

31 ÷ 45 = 0.688889 (68.8889%)

Visual Representation

The diagram below illustrates 2/15 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/45`
Mixed Number Form	`31/45`
Decimal Form	`0.688889`
Percentage	`68.8889%`

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Frequently Asked Questions

What is 2/15 plus 5/9 as a fraction?

2/15 + 5/9 in simplest fraction form is 31/45.

What is 2/15 plus 5/9 as a decimal?

2/15 + 5/9 converted to a decimal is 0.688889.

What is 2/15 plus 5/9 as a percentage?

2/15 + 5/9 expressed as a percentage is 68.8889%.

Does 2/15 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.688889...) because the denominator contains prime factors other than 2 and 5.