What is 1/5 plus 2/3? (Answer: 13/15)

Exact Answer

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Problem: What is 1/5 plus 2/3?
Formula / Expression: 1/5 + 2/3
Final Answer: 13/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 3 = 15.
Working: LCD(5, 3) = 15

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 1/5 by 3, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.
Working: 1 × 3/5 × 3 = 3/15 and 2 × 5/3 × 5 = 10/15

Step 3: Add the Numerators
Now add the numerators (3 + 10 = 13) and keep the common denominator 15 unchanged.
Working: 3 + 10/15 = 13/15

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 15 is 1, confirming that 13/15 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 15 produces a repeating decimal (approximately 0.866667, or 86.6667%).
Working: 13 ÷ 15 = 0.866667 (86.6667%)

Key Values:
- Simplified Fraction: 13/15
- Mixed Number Form: 13/15
- Decimal Value: 0.866667
- Percentage: 86.6667%

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1/5 + 2/3 = 13/15

Simplified Fraction

13/15

Mixed Number

Proper (13/15)

Decimal Value

0.866667

Percentage

86.6667%

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Step-by-Step Solution: 1/5 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 3 = 15.

LCD(5, 3) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

Multiply the numerator and denominator of 1/5 by 3, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.

1 × 3/5 × 3 = 3/15 and 2 × 5/3 × 5 = 10/15

Step 3

Add the Numerators

Now add the numerators (3 + 10 = 13) and keep the common denominator 15 unchanged.

3 + 10/15 = 13/15

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 15 is 1, confirming that 13/15 cannot be reduced further—it is already in its simplest irreducible form.

13/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 15 produces a repeating decimal (approximately 0.866667, or 86.6667%).

13 ÷ 15 = 0.866667 (86.6667%)

Visual Representation

The diagram below illustrates 1/5 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/15`
Mixed Number Form	`13/15`
Decimal Form	`0.866667`
Percentage	`86.6667%`

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Frequently Asked Questions

What is 1/5 plus 2/3 as a fraction?

1/5 + 2/3 in simplest fraction form is 13/15.

What is 1/5 plus 2/3 as a decimal?

1/5 + 2/3 converted to a decimal is 0.866667.

What is 1/5 plus 2/3 as a percentage?

1/5 + 2/3 expressed as a percentage is 86.6667%.

Does 1/5 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.866667...) because the denominator contains prime factors other than 2 and 5.