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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
Notice that 6 is an exact multiple of 3 (3 × 2 = 6). The Least Common Denominator (LCD) is simply 6, meaning we only need to scale one fraction.
Working: LCD(3, 6) = 6

Step 2: Convert to Equivalent Fractions with Common Denominator 6
Multiply the numerator and denominator of 2/3 by 2, and multiply the numerator and denominator of 5/6 by 1 so both fractions share the common base 6.
Working: 2 × 2/3 × 2 = 4/6 and 5 × 1/6 × 1 = 5/6

Step 3: Add the Numerators
Now add the numerators (4 + 5 = 9) and keep the common denominator 6 unchanged.
Working: 4 + 5/6 = 9/6

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 9 and 6, which is 3. Divide both the numerator and denominator by 3.
Working: 9 ÷ 3/6 ÷ 3 = 3/2

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (3) is greater than the denominator (2), divide 3 by 2: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/2.
Working: 3/2 = 1 1/2

Step 6: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 2 yields an exact terminating decimal of 1.5 (or 150%).
Working: 3 ÷ 2 = 1.5 (150%)

Key Values:
- Simplified Fraction: 3/2
- Mixed Number Form: 1 1/2
- Decimal Value: 1.5
- Percentage: 150%

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2/3 + 5/6 = 3/2

Simplified Fraction

3/2

Mixed Number

1 1/2

Decimal Value

1.5

Percentage

150%

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Step-by-Step Solution: 2/3 + 5/6

Step 1

Find the Least Common Denominator (LCD)

Notice that 6 is an exact multiple of 3 (3 × 2 = 6). The Least Common Denominator (LCD) is simply 6, meaning we only need to scale one fraction.

LCD(3, 6) = 6

Step 2

Convert to Equivalent Fractions with Common Denominator 6

Multiply the numerator and denominator of 2/3 by 2, and multiply the numerator and denominator of 5/6 by 1 so both fractions share the common base 6.

2 × 2/3 × 2 = 4/6 and 5 × 1/6 × 1 = 5/6

Step 3

Add the Numerators

Now add the numerators (4 + 5 = 9) and keep the common denominator 6 unchanged.

4 + 5/6 = 9/6

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 9 and 6, which is 3. Divide both the numerator and denominator by 3.

9 ÷ 3/6 ÷ 3 = 3/2

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (3) is greater than the denominator (2), divide 3 by 2: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/2.

3/2 = 11/2

Step 6

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 2 yields an exact terminating decimal of 1.5 (or 150%).

3 ÷ 2 = 1.5 (150%)

Visual Representation

The diagram below illustrates 2/3 plus 5/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/2`
Mixed Number Form	`1 1/2`
Decimal Form	`1.5`
Percentage	`150%`

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Frequently Asked Questions

What is 2/3 plus 5/6 as a fraction?

2/3 + 5/6 in simplest fraction form is 3/2 (or 1 1/2 as a mixed number).

What is 2/3 plus 5/6 as a decimal?

2/3 + 5/6 converted to a decimal is 1.5.

What is 2/3 plus 5/6 as a percentage?

2/3 + 5/6 expressed as a percentage is 150%.

How do you write 2/3 plus 5/6 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 3/2 can be written as the mixed number 1 1/2.

Does 2/3 plus 5/6 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.