What is 2/6 plus 3/5? (Answer: 14/15)

Exact Answer

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Problem: What is 2/6 plus 3/5?
Formula / Expression: 2/6 + 3/5
Final Answer: 14/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 5 = 30.
Working: LCD(6, 5) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 2/6 by 5, and multiply the numerator and denominator of 3/5 by 6 so both fractions share the common base 30.
Working: 2 × 5/6 × 5 = 10/30 and 3 × 6/5 × 6 = 18/30

Step 3: Add the Numerators
Now add the numerators (10 + 18 = 28) and keep the common denominator 30 unchanged.
Working: 10 + 18/30 = 28/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 30, which is 2. Divide both the numerator and denominator by 2.
Working: 28 ÷ 2/30 ÷ 2 = 14/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 15 produces a repeating decimal (approximately 0.933333, or 93.3333%).
Working: 14 ÷ 15 = 0.933333 (93.3333%)

Key Values:
- Simplified Fraction: 14/15
- Mixed Number Form: 14/15
- Decimal Value: 0.933333
- Percentage: 93.3333%

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2/6 + 3/5 = 14/15

Simplified Fraction

14/15

Mixed Number

Proper (14/15)

Decimal Value

0.933333

Percentage

93.3333%

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Step-by-Step Solution: 2/6 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 5 = 30.

LCD(6, 5) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 2/6 by 5, and multiply the numerator and denominator of 3/5 by 6 so both fractions share the common base 30.

2 × 5/6 × 5 = 10/30 and 3 × 6/5 × 6 = 18/30

Step 3

Add the Numerators

Now add the numerators (10 + 18 = 28) and keep the common denominator 30 unchanged.

10 + 18/30 = 28/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 30, which is 2. Divide both the numerator and denominator by 2.

28 ÷ 2/30 ÷ 2 = 14/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 15 produces a repeating decimal (approximately 0.933333, or 93.3333%).

14 ÷ 15 = 0.933333 (93.3333%)

Visual Representation

The diagram below illustrates 2/6 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/15`
Mixed Number Form	`14/15`
Decimal Form	`0.933333`
Percentage	`93.3333%`

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Frequently Asked Questions

What is 2/6 plus 3/5 as a fraction?

2/6 + 3/5 in simplest fraction form is 14/15.

What is 2/6 plus 3/5 as a decimal?

2/6 + 3/5 converted to a decimal is 0.933333.

What is 2/6 plus 3/5 as a percentage?

2/6 + 3/5 expressed as a percentage is 93.3333%.

Does 2/6 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.933333...) because the denominator contains prime factors other than 2 and 5.