What is 2/8 plus 9/15? (Answer: 17/20)

Exact Answer

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Problem: What is 2/8 plus 9/15?
Formula / Expression: 2/8 + 9/15
Final Answer: 17/20
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 2/8 by 15, and multiply the numerator and denominator of 9/15 by 8 so both fractions share the common base 120.
Working: 2 × 15/8 × 15 = 30/120 and 9 × 8/15 × 8 = 72/120

Step 3: Add the Numerators
Now add the numerators (30 + 72 = 102) and keep the common denominator 120 unchanged.
Working: 30 + 72/120 = 102/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 120, which is 6. Divide both the numerator and denominator by 6.
Working: 102 ÷ 6/120 ÷ 6 = 17/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 20 yields an exact terminating decimal of 0.85 (or 85%).
Working: 17 ÷ 20 = 0.85 (85%)

Key Values:
- Simplified Fraction: 17/20
- Mixed Number Form: 17/20
- Decimal Value: 0.85
- Percentage: 85%

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Solved with FractionsCalc:
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2/8 + 9/15 = 17/20

Simplified Fraction

17/20

Mixed Number

Proper (17/20)

Decimal Value

0.85

Percentage

85%

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Step-by-Step Solution: 2/8 + 9/15

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 15) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 2/8 by 15, and multiply the numerator and denominator of 9/15 by 8 so both fractions share the common base 120.

2 × 15/8 × 15 = 30/120 and 9 × 8/15 × 8 = 72/120

Step 3

Add the Numerators

Now add the numerators (30 + 72 = 102) and keep the common denominator 120 unchanged.

30 + 72/120 = 102/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 120, which is 6. Divide both the numerator and denominator by 6.

102 ÷ 6/120 ÷ 6 = 17/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 20 yields an exact terminating decimal of 0.85 (or 85%).

17 ÷ 20 = 0.85 (85%)

Visual Representation

The diagram below illustrates 2/8 plus 9/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/20`
Mixed Number Form	`17/20`
Decimal Form	`0.85`
Percentage	`85%`

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Frequently Asked Questions

What is 2/8 plus 9/15 as a fraction?

2/8 + 9/15 in simplest fraction form is 17/20.

What is 2/8 plus 9/15 as a decimal?

2/8 + 9/15 converted to a decimal is 0.85.

What is 2/8 plus 9/15 as a percentage?

2/8 + 9/15 expressed as a percentage is 85%.

Does 2/8 plus 9/15 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.85) because the denominator in simplest terms contains only prime factors 2 and/or 5.