What is 2/15 plus 5/8? (Answer: 91/120)

Exact Answer

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Problem: What is 2/15 plus 5/8?
Formula / Expression: 2/15 + 5/8
Final Answer: 91/120
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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 5/8 by 15 so both fractions share the common base 120.
Working: 2 × 8/15 × 8 = 16/120 and 5 × 15/8 × 15 = 75/120

Step 3: Add the Numerators
Now add the numerators (16 + 75 = 91) and keep the common denominator 120 unchanged.
Working: 16 + 75/120 = 91/120

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 91 and 120 is 1, confirming that 91/120 cannot be reduced further—it is already in its simplest irreducible form.
Working: 91/120

Step 5: Decimal & Percentage Representation
Dividing the numerator 91 by denominator 120 produces a repeating decimal (approximately 0.758333, or 75.8333%).
Working: 91 ÷ 120 = 0.758333 (75.8333%)

Key Values:
- Simplified Fraction: 91/120
- Mixed Number Form: 91/120
- Decimal Value: 0.758333
- Percentage: 75.8333%

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Solved with FractionsCalc:
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2/15 + 5/8 = 91/120

Simplified Fraction

91/120

Mixed Number

Proper (91/120)

Decimal Value

0.758333

Percentage

75.8333%

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Step-by-Step Solution: 2/15 + 5/8

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 5/8 by 15 so both fractions share the common base 120.

2 × 8/15 × 8 = 16/120 and 5 × 15/8 × 15 = 75/120

Step 3

Add the Numerators

Now add the numerators (16 + 75 = 91) and keep the common denominator 120 unchanged.

16 + 75/120 = 91/120

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 91 and 120 is 1, confirming that 91/120 cannot be reduced further—it is already in its simplest irreducible form.

91/120

Step 5

Decimal & Percentage Representation

Dividing the numerator 91 by denominator 120 produces a repeating decimal (approximately 0.758333, or 75.8333%).

91 ÷ 120 = 0.758333 (75.8333%)

Visual Representation

The diagram below illustrates 2/15 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`91/120`
Mixed Number Form	`91/120`
Decimal Form	`0.758333`
Percentage	`75.8333%`

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Frequently Asked Questions

What is 2/15 plus 5/8 as a fraction?

2/15 + 5/8 in simplest fraction form is 91/120.

What is 2/15 plus 5/8 as a decimal?

2/15 + 5/8 converted to a decimal is 0.758333.

What is 2/15 plus 5/8 as a percentage?

2/15 + 5/8 expressed as a percentage is 75.8333%.

Does 2/15 plus 5/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.758333...) because the denominator contains prime factors other than 2 and 5.