What is 2/6 plus 3/4? (Answer: 13/12)

Exact Answer

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Problem: What is 2/6 plus 3/4?
Formula / Expression: 2/6 + 3/4
Final Answer: 1 1/12 (13/12)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 12 (which is smaller than their product 6 × 4 = 24, keeping the calculation simpler).
Working: LCD(6, 4) = 12

Step 2: Convert to Equivalent Fractions with Common Denominator 12
Multiply the numerator and denominator of 2/6 by 2, and multiply the numerator and denominator of 3/4 by 3 so both fractions share the common base 12.
Working: 2 × 2/6 × 2 = 4/12 and 3 × 3/4 × 3 = 9/12

Step 3: Add the Numerators
Now add the numerators (4 + 9 = 13) and keep the common denominator 12 unchanged.
Working: 4 + 9/12 = 13/12

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 12 is 1, confirming that 13/12 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/12

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (13) is greater than the denominator (12), divide 13 by 12: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/12.
Working: 13/12 = 1 1/12

Step 6: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 12 produces a repeating decimal (approximately 1.083333, or 108.3333%).
Working: 13 ÷ 12 = 1.083333 (108.3333%)

Key Values:
- Simplified Fraction: 13/12
- Mixed Number Form: 1 1/12
- Decimal Value: 1.083333
- Percentage: 108.3333%

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Solved with FractionsCalc:
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2/6 + 3/4 = 13/12

Simplified Fraction

13/12

Mixed Number

1 1/12

Decimal Value

1.083333

Percentage

108.3333%

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Step-by-Step Solution: 2/6 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 12 (which is smaller than their product 6 × 4 = 24, keeping the calculation simpler).

LCD(6, 4) = 12

Step 2

Convert to Equivalent Fractions with Common Denominator 12

Multiply the numerator and denominator of 2/6 by 2, and multiply the numerator and denominator of 3/4 by 3 so both fractions share the common base 12.

2 × 2/6 × 2 = 4/12 and 3 × 3/4 × 3 = 9/12

Step 3

Add the Numerators

Now add the numerators (4 + 9 = 13) and keep the common denominator 12 unchanged.

4 + 9/12 = 13/12

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 12 is 1, confirming that 13/12 cannot be reduced further—it is already in its simplest irreducible form.

13/12

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (13) is greater than the denominator (12), divide 13 by 12: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/12.

13/12 = 11/12

Step 6

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 12 produces a repeating decimal (approximately 1.083333, or 108.3333%).

13 ÷ 12 = 1.083333 (108.3333%)

Visual Representation

The diagram below illustrates 2/6 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/12`
Mixed Number Form	`1 1/12`
Decimal Form	`1.083333`
Percentage	`108.3333%`

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Frequently Asked Questions

What is 2/6 plus 3/4 as a fraction?

2/6 + 3/4 in simplest fraction form is 13/12 (or 1 1/12 as a mixed number).

What is 2/6 plus 3/4 as a decimal?

2/6 + 3/4 converted to a decimal is 1.083333.

What is 2/6 plus 3/4 as a percentage?

2/6 + 3/4 expressed as a percentage is 108.3333%.

How do you write 2/6 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 13/12 can be written as the mixed number 1 1/12.

Does 2/6 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.083333...) because the denominator contains prime factors other than 2 and 5.