What is 2/7 plus 8/15? (Answer: 86/105)

Exact Answer

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Problem: What is 2/7 plus 8/15?
Formula / Expression: 2/7 + 8/15
Final Answer: 86/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 15 = 105.
Working: LCD(7, 15) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/7 by 15, and multiply the numerator and denominator of 8/15 by 7 so both fractions share the common base 105.
Working: 2 × 15/7 × 15 = 30/105 and 8 × 7/15 × 7 = 56/105

Step 3: Add the Numerators
Now add the numerators (30 + 56 = 86) and keep the common denominator 105 unchanged.
Working: 30 + 56/105 = 86/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 86 and 105 is 1, confirming that 86/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 86/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 105 produces a repeating decimal (approximately 0.819048, or 81.9048%).
Working: 86 ÷ 105 = 0.819048 (81.9048%)

Key Values:
- Simplified Fraction: 86/105
- Mixed Number Form: 86/105
- Decimal Value: 0.819048
- Percentage: 81.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-8-15/
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2/7 + 8/15 = 86/105

Simplified Fraction

86/105

Mixed Number

Proper (86/105)

Decimal Value

0.819048

Percentage

81.9048%

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Step-by-Step Solution: 2/7 + 8/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 15 = 105.

LCD(7, 15) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/7 by 15, and multiply the numerator and denominator of 8/15 by 7 so both fractions share the common base 105.

2 × 15/7 × 15 = 30/105 and 8 × 7/15 × 7 = 56/105

Step 3

Add the Numerators

Now add the numerators (30 + 56 = 86) and keep the common denominator 105 unchanged.

30 + 56/105 = 86/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 86 and 105 is 1, confirming that 86/105 cannot be reduced further—it is already in its simplest irreducible form.

86/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 105 produces a repeating decimal (approximately 0.819048, or 81.9048%).

86 ÷ 105 = 0.819048 (81.9048%)

Visual Representation

The diagram below illustrates 2/7 plus 8/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/105`
Mixed Number Form	`86/105`
Decimal Form	`0.819048`
Percentage	`81.9048%`

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Frequently Asked Questions

What is 2/7 plus 8/15 as a fraction?

2/7 + 8/15 in simplest fraction form is 86/105.

What is 2/7 plus 8/15 as a decimal?

2/7 + 8/15 converted to a decimal is 0.819048.

What is 2/7 plus 8/15 as a percentage?

2/7 + 8/15 expressed as a percentage is 81.9048%.

Does 2/7 plus 8/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.819048...) because the denominator contains prime factors other than 2 and 5.