What is 3/10 plus 2/6? (Answer: 19/30)

Exact Answer

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Problem: What is 3/10 plus 2/6?
Formula / Expression: 3/10 + 2/6
Final Answer: 19/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 30 (which is smaller than their product 10 × 6 = 60, keeping the calculation simpler).
Working: LCD(10, 6) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 3/10 by 3, and multiply the numerator and denominator of 2/6 by 5 so both fractions share the common base 30.
Working: 3 × 3/10 × 3 = 9/30 and 2 × 5/6 × 5 = 10/30

Step 3: Add the Numerators
Now add the numerators (9 + 10 = 19) and keep the common denominator 30 unchanged.
Working: 9 + 10/30 = 19/30

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 30 is 1, confirming that 19/30 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 30 produces a repeating decimal (approximately 0.633333, or 63.3333%).
Working: 19 ÷ 30 = 0.633333 (63.3333%)

Key Values:
- Simplified Fraction: 19/30
- Mixed Number Form: 19/30
- Decimal Value: 0.633333
- Percentage: 63.3333%

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Solved with FractionsCalc:
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3/10 + 2/6 = 19/30

Simplified Fraction

19/30

Mixed Number

Proper (19/30)

Decimal Value

0.633333

Percentage

63.3333%

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Step-by-Step Solution: 3/10 + 2/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 30 (which is smaller than their product 10 × 6 = 60, keeping the calculation simpler).

LCD(10, 6) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 3/10 by 3, and multiply the numerator and denominator of 2/6 by 5 so both fractions share the common base 30.

3 × 3/10 × 3 = 9/30 and 2 × 5/6 × 5 = 10/30

Step 3

Add the Numerators

Now add the numerators (9 + 10 = 19) and keep the common denominator 30 unchanged.

9 + 10/30 = 19/30

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 30 is 1, confirming that 19/30 cannot be reduced further—it is already in its simplest irreducible form.

19/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 30 produces a repeating decimal (approximately 0.633333, or 63.3333%).

19 ÷ 30 = 0.633333 (63.3333%)

Visual Representation

The diagram below illustrates 3/10 plus 2/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/30`
Mixed Number Form	`19/30`
Decimal Form	`0.633333`
Percentage	`63.3333%`

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Frequently Asked Questions

What is 3/10 plus 2/6 as a fraction?

3/10 + 2/6 in simplest fraction form is 19/30.

What is 3/10 plus 2/6 as a decimal?

3/10 + 2/6 converted to a decimal is 0.633333.

What is 3/10 plus 2/6 as a percentage?

3/10 + 2/6 expressed as a percentage is 63.3333%.

Does 3/10 plus 2/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.633333...) because the denominator contains prime factors other than 2 and 5.