What is 2/15 plus 3/8? (Answer: 61/120)

Exact Answer

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Problem: What is 2/15 plus 3/8?
Formula / Expression: 2/15 + 3/8
Final Answer: 61/120
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 8 = 120.
Working: LCD(15, 8) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 2/15 by 8, and multiply the numerator and denominator of 3/8 by 15 so both fractions share the common base 120.
Working: 2 × 8/15 × 8 = 16/120 and 3 × 15/8 × 15 = 45/120

Step 3: Add the Numerators
Now add the numerators (16 + 45 = 61) and keep the common denominator 120 unchanged.
Working: 16 + 45/120 = 61/120

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 120 is 1, confirming that 61/120 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/120

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 120 produces a repeating decimal (approximately 0.508333, or 50.8333%).
Working: 61 ÷ 120 = 0.508333 (50.8333%)

Key Values:
- Simplified Fraction: 61/120
- Mixed Number Form: 61/120
- Decimal Value: 0.508333
- Percentage: 50.8333%

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2/15 + 3/8 = 61/120

Simplified Fraction

61/120

Mixed Number

Proper (61/120)

Decimal Value

0.508333

Percentage

50.8333%

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Step-by-Step Solution: 2/15 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 8 = 120.

LCD(15, 8) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 2/15 by 8, and multiply the numerator and denominator of 3/8 by 15 so both fractions share the common base 120.

2 × 8/15 × 8 = 16/120 and 3 × 15/8 × 15 = 45/120

Step 3

Add the Numerators

Now add the numerators (16 + 45 = 61) and keep the common denominator 120 unchanged.

16 + 45/120 = 61/120

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 120 is 1, confirming that 61/120 cannot be reduced further—it is already in its simplest irreducible form.

61/120

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 120 produces a repeating decimal (approximately 0.508333, or 50.8333%).

61 ÷ 120 = 0.508333 (50.8333%)

Visual Representation

The diagram below illustrates 2/15 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/120`
Mixed Number Form	`61/120`
Decimal Form	`0.508333`
Percentage	`50.8333%`

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Frequently Asked Questions

What is 2/15 plus 3/8 as a fraction?

2/15 + 3/8 in simplest fraction form is 61/120.

What is 2/15 plus 3/8 as a decimal?

2/15 + 3/8 converted to a decimal is 0.508333.

What is 2/15 plus 3/8 as a percentage?

2/15 + 3/8 expressed as a percentage is 50.8333%.

Does 2/15 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.508333...) because the denominator contains prime factors other than 2 and 5.