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

Exact Answer

==================================================
Problem: What is 1/6 plus 2/3?
Formula / Expression: 1/6 + 2/3
Final Answer: 5/6
==================================================

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(6, 3) = 6

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

Step 3: Add the Numerators
Now add the numerators (1 + 4 = 5) and keep the common denominator 6 unchanged.
Working: 1 + 4/6 = 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%

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

1/6 + 2/3 = 5/6

Simplified Fraction

5/6

Mixed Number

Proper (5/6)

Decimal Value

0.833333

Percentage

83.3333%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 1/6 + 2/3

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(6, 3) = 6

Step 2

Convert to Equivalent Fractions with Common Denominator 6

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

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

Step 3

Add the Numerators

Now add the numerators (1 + 4 = 5) and keep the common denominator 6 unchanged.

1 + 4/6 = 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 1/6 plus 2/3 visually:

Summary & Alternative Representations

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

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/6 plus 2/3 as a fraction?

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

What is 1/6 plus 2/3 as a decimal?

1/6 + 2/3 converted to a decimal is 0.833333.

What is 1/6 plus 2/3 as a percentage?

1/6 + 2/3 expressed as a percentage is 83.3333%.

Does 1/6 plus 2/3 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.