What is 2/10 plus 1/3? (Answer: 8/15)

Exact Answer

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Problem: What is 2/10 plus 1/3?
Formula / Expression: 2/10 + 1/3
Final Answer: 8/15
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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 1/3 by 10 so both fractions share the common base 30.
Working: 2 × 3/10 × 3 = 6/30 and 1 × 10/3 × 10 = 10/30

Step 3: Add the Numerators
Now add the numerators (6 + 10 = 16) and keep the common denominator 30 unchanged.
Working: 6 + 10/30 = 16/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 16 and 30, which is 2. Divide both the numerator and denominator by 2.
Working: 16 ÷ 2/30 ÷ 2 = 8/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 15 produces a repeating decimal (approximately 0.533333, or 53.3333%).
Working: 8 ÷ 15 = 0.533333 (53.3333%)

Key Values:
- Simplified Fraction: 8/15
- Mixed Number Form: 8/15
- Decimal Value: 0.533333
- Percentage: 53.3333%

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Solved with FractionsCalc:
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2/10 + 1/3 = 8/15

Simplified Fraction

8/15

Mixed Number

Proper (8/15)

Decimal Value

0.533333

Percentage

53.3333%

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Step-by-Step Solution: 2/10 + 1/3

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 1/3 by 10 so both fractions share the common base 30.

2 × 3/10 × 3 = 6/30 and 1 × 10/3 × 10 = 10/30

Step 3

Add the Numerators

Now add the numerators (6 + 10 = 16) and keep the common denominator 30 unchanged.

6 + 10/30 = 16/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 16 and 30, which is 2. Divide both the numerator and denominator by 2.

16 ÷ 2/30 ÷ 2 = 8/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 15 produces a repeating decimal (approximately 0.533333, or 53.3333%).

8 ÷ 15 = 0.533333 (53.3333%)

Visual Representation

The diagram below illustrates 2/10 plus 1/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/15`
Mixed Number Form	`8/15`
Decimal Form	`0.533333`
Percentage	`53.3333%`

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Frequently Asked Questions

What is 2/10 plus 1/3 as a fraction?

2/10 + 1/3 in simplest fraction form is 8/15.

What is 2/10 plus 1/3 as a decimal?

2/10 + 1/3 converted to a decimal is 0.533333.

What is 2/10 plus 1/3 as a percentage?

2/10 + 1/3 expressed as a percentage is 53.3333%.

Does 2/10 plus 1/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.533333...) because the denominator contains prime factors other than 2 and 5.