What is 3/10 plus 2/3? (Answer: 29/30)

Exact Answer

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Problem: What is 3/10 plus 2/3?
Formula / Expression: 3/10 + 2/3
Final Answer: 29/30
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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 3/10 by 3, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.
Working: 3 × 3/10 × 3 = 9/30 and 2 × 10/3 × 10 = 20/30

Step 3: Add the Numerators
Now add the numerators (9 + 20 = 29) and keep the common denominator 30 unchanged.
Working: 9 + 20/30 = 29/30

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 30 is 1, confirming that 29/30 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 30 produces a repeating decimal (approximately 0.966667, or 96.6667%).
Working: 29 ÷ 30 = 0.966667 (96.6667%)

Key Values:
- Simplified Fraction: 29/30
- Mixed Number Form: 29/30
- Decimal Value: 0.966667
- Percentage: 96.6667%

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Solved with FractionsCalc:
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3/10 + 2/3 = 29/30

Simplified Fraction

29/30

Mixed Number

Proper (29/30)

Decimal Value

0.966667

Percentage

96.6667%

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Step-by-Step Solution: 3/10 + 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 3/10 by 3, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.

3 × 3/10 × 3 = 9/30 and 2 × 10/3 × 10 = 20/30

Step 3

Add the Numerators

Now add the numerators (9 + 20 = 29) and keep the common denominator 30 unchanged.

9 + 20/30 = 29/30

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 30 is 1, confirming that 29/30 cannot be reduced further—it is already in its simplest irreducible form.

29/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 30 produces a repeating decimal (approximately 0.966667, or 96.6667%).

29 ÷ 30 = 0.966667 (96.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/30`
Mixed Number Form	`29/30`
Decimal Form	`0.966667`
Percentage	`96.6667%`

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Frequently Asked Questions

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

3/10 + 2/3 in simplest fraction form is 29/30.

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

3/10 + 2/3 converted to a decimal is 0.966667.

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

3/10 + 2/3 expressed as a percentage is 96.6667%.

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

It results in a repeating decimal (approximately 0.966667...) because the denominator contains prime factors other than 2 and 5.