What is 2/10 plus 2/3? (Answer: 13/15)

Exact Answer

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Problem: What is 2/10 plus 2/3?
Formula / Expression: 2/10 + 2/3
Final Answer: 13/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 3 = 30.
Working: LCD(10, 3) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 2/10 by 3, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.
Working: 2 × 3/10 × 3 = 6/30 and 2 × 10/3 × 10 = 20/30

Step 3: Add the Numerators
Now add the numerators (6 + 20 = 26) and keep the common denominator 30 unchanged.
Working: 6 + 20/30 = 26/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 30, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/30 ÷ 2 = 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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Solved with FractionsCalc:
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2/10 + 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: 2/10 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 3 = 30.

LCD(10, 3) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 2/10 by 3, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.

2 × 3/10 × 3 = 6/30 and 2 × 10/3 × 10 = 20/30

Step 3

Add the Numerators

Now add the numerators (6 + 20 = 26) and keep the common denominator 30 unchanged.

6 + 20/30 = 26/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 30, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/30 ÷ 2 = 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 2/10 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 2/10 plus 2/3 as a fraction?

2/10 + 2/3 in simplest fraction form is 13/15.

What is 2/10 plus 2/3 as a decimal?

2/10 + 2/3 converted to a decimal is 0.866667.

What is 2/10 plus 2/3 as a percentage?

2/10 + 2/3 expressed as a percentage is 86.6667%.

Does 2/10 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.