What is 1/3 plus 1/2? (Answer: 5/6)

Exact Answer

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Problem: What is 1/3 plus 1/2?
Formula / Expression: 1/3 + 1/2
Final Answer: 5/6
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 2 = 6.
Working: LCD(3, 2) = 6

Step 2: Convert to Equivalent Fractions with Common Denominator 6
Multiply the numerator and denominator of 1/3 by 2, and multiply the numerator and denominator of 1/2 by 3 so both fractions share the common base 6.
Working: 1 × 2/3 × 2 = 2/6 and 1 × 3/2 × 3 = 3/6

Step 3: Add the Numerators
Now add the numerators (2 + 3 = 5) and keep the common denominator 6 unchanged.
Working: 2 + 3/6 = 5/6

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 6 is 1, confirming that 5/6 cannot be reduced further—it is already in its simplest irreducible form.
Working: 5/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).
Working: 5 ÷ 6 = 0.833333 (83.3333%)

Key Values:
- Simplified Fraction: 5/6
- Mixed Number Form: 5/6
- Decimal Value: 0.833333
- Percentage: 83.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-3-plus-1-2/
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1/3 + 1/2 = 5/6

Simplified Fraction

5/6

Mixed Number

Proper (5/6)

Decimal Value

0.833333

Percentage

83.3333%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 2 = 6.

LCD(3, 2) = 6

Step 2

Convert to Equivalent Fractions with Common Denominator 6

Multiply the numerator and denominator of 1/3 by 2, and multiply the numerator and denominator of 1/2 by 3 so both fractions share the common base 6.

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

Step 3

Add the Numerators

Now add the numerators (2 + 3 = 5) and keep the common denominator 6 unchanged.

2 + 3/6 = 5/6

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 6 is 1, confirming that 5/6 cannot be reduced further—it is already in its simplest irreducible form.

5/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).

5 ÷ 6 = 0.833333 (83.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/6`
Mixed Number Form	`5/6`
Decimal Form	`0.833333`
Percentage	`83.3333%`

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Frequently Asked Questions

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

1/3 + 1/2 in simplest fraction form is 5/6.

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

1/3 + 1/2 converted to a decimal is 0.833333.

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

1/3 + 1/2 expressed as a percentage is 83.3333%.

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

It results in a repeating decimal (approximately 0.833333...) because the denominator contains prime factors other than 2 and 5.