What is 2/15 plus 1/3? (Answer: 7/15)

Exact Answer

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Problem: What is 2/15 plus 1/3?
Formula / Expression: 2/15 + 1/3
Final Answer: 7/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 15 is an exact multiple of 3 (3 × 5 = 15). The Least Common Denominator (LCD) is simply 15, meaning we only need to scale one fraction.
Working: LCD(15, 3) = 15

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 2/15 by 1, and multiply the numerator and denominator of 1/3 by 5 so both fractions share the common base 15.
Working: 2 × 1/15 × 1 = 2/15 and 1 × 5/3 × 5 = 5/15

Step 3: Add the Numerators
Now add the numerators (2 + 5 = 7) and keep the common denominator 15 unchanged.
Working: 2 + 5/15 = 7/15

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 15 is 1, confirming that 7/15 cannot be reduced further—it is already in its simplest irreducible form.
Working: 7/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).
Working: 7 ÷ 15 = 0.466667 (46.6667%)

Key Values:
- Simplified Fraction: 7/15
- Mixed Number Form: 7/15
- Decimal Value: 0.466667
- Percentage: 46.6667%

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Solved with FractionsCalc:
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2/15 + 1/3 = 7/15

Simplified Fraction

7/15

Mixed Number

Proper (7/15)

Decimal Value

0.466667

Percentage

46.6667%

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Step-by-Step Solution: 2/15 + 1/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 15 is an exact multiple of 3 (3 × 5 = 15). The Least Common Denominator (LCD) is simply 15, meaning we only need to scale one fraction.

LCD(15, 3) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

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

2 × 1/15 × 1 = 2/15 and 1 × 5/3 × 5 = 5/15

Step 3

Add the Numerators

Now add the numerators (2 + 5 = 7) and keep the common denominator 15 unchanged.

2 + 5/15 = 7/15

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 7 and 15 is 1, confirming that 7/15 cannot be reduced further—it is already in its simplest irreducible form.

7/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).

7 ÷ 15 = 0.466667 (46.6667%)

Visual Representation

The diagram below illustrates 2/15 plus 1/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/15`
Mixed Number Form	`7/15`
Decimal Form	`0.466667`
Percentage	`46.6667%`

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Frequently Asked Questions

What is 2/15 plus 1/3 as a fraction?

2/15 + 1/3 in simplest fraction form is 7/15.

What is 2/15 plus 1/3 as a decimal?

2/15 + 1/3 converted to a decimal is 0.466667.

What is 2/15 plus 1/3 as a percentage?

2/15 + 1/3 expressed as a percentage is 46.6667%.

Does 2/15 plus 1/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.466667...) because the denominator contains prime factors other than 2 and 5.