What is 1/2 plus 2/3? (Answer: 7/6)

Exact Answer

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Problem: What is 1/2 plus 2/3?
Formula / Expression: 1/2 + 2/3
Final Answer: 1 1/6 (7/6)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 6
Multiply the numerator and denominator of 1/2 by 3, and multiply the numerator and denominator of 2/3 by 2 so both fractions share the common base 6.
Working: 1 × 3/2 × 3 = 3/6 and 2 × 2/3 × 2 = 4/6

Step 3: Add the Numerators
Now add the numerators (3 + 4 = 7) and keep the common denominator 6 unchanged.
Working: 3 + 4/6 = 7/6

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 6 is 1, confirming that 7/6 cannot be reduced further—it is already in its simplest irreducible form.
Working: 7/6

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (7) is greater than the denominator (6), divide 7 by 6: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/6.
Working: 7/6 = 1 1/6

Step 6: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 6 produces a repeating decimal (approximately 1.166667, or 116.6667%).
Working: 7 ÷ 6 = 1.166667 (116.6667%)

Key Values:
- Simplified Fraction: 7/6
- Mixed Number Form: 1 1/6
- Decimal Value: 1.166667
- Percentage: 116.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-2-3/
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1/2 + 2/3 = 7/6

Simplified Fraction

7/6

Mixed Number

1 1/6

Decimal Value

1.166667

Percentage

116.6667%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(2, 3) = 6

Step 2

Convert to Equivalent Fractions with Common Denominator 6

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

1 × 3/2 × 3 = 3/6 and 2 × 2/3 × 2 = 4/6

Step 3

Add the Numerators

Now add the numerators (3 + 4 = 7) and keep the common denominator 6 unchanged.

3 + 4/6 = 7/6

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 7 and 6 is 1, confirming that 7/6 cannot be reduced further—it is already in its simplest irreducible form.

7/6

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (7) is greater than the denominator (6), divide 7 by 6: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/6.

7/6 = 11/6

Step 6

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 6 produces a repeating decimal (approximately 1.166667, or 116.6667%).

7 ÷ 6 = 1.166667 (116.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/6`
Mixed Number Form	`1 1/6`
Decimal Form	`1.166667`
Percentage	`116.6667%`

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Frequently Asked Questions

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

1/2 + 2/3 in simplest fraction form is 7/6 (or 1 1/6 as a mixed number).

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

1/2 + 2/3 converted to a decimal is 1.166667.

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

1/2 + 2/3 expressed as a percentage is 116.6667%.

How do you write 1/2 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 7/6 can be written as the mixed number 1 1/6.

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

It results in a repeating decimal (approximately 1.166667...) because the denominator contains prime factors other than 2 and 5.