What is 1/4 plus 2/3? (Answer: 11/12)

Exact Answer

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Problem: What is 1/4 plus 2/3?
Formula / Expression: 1/4 + 2/3
Final Answer: 11/12
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 3 = 12.
Working: LCD(4, 3) = 12

Step 2: Convert to Equivalent Fractions with Common Denominator 12
Multiply the numerator and denominator of 1/4 by 3, and multiply the numerator and denominator of 2/3 by 4 so both fractions share the common base 12.
Working: 1 × 3/4 × 3 = 3/12 and 2 × 4/3 × 4 = 8/12

Step 3: Add the Numerators
Now add the numerators (3 + 8 = 11) and keep the common denominator 12 unchanged.
Working: 3 + 8/12 = 11/12

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 12 is 1, confirming that 11/12 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 12 produces a repeating decimal (approximately 0.916667, or 91.6667%).
Working: 11 ÷ 12 = 0.916667 (91.6667%)

Key Values:
- Simplified Fraction: 11/12
- Mixed Number Form: 11/12
- Decimal Value: 0.916667
- Percentage: 91.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-2-3/
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1/4 + 2/3 = 11/12

Simplified Fraction

11/12

Mixed Number

Proper (11/12)

Decimal Value

0.916667

Percentage

91.6667%

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Step-by-Step Solution: 1/4 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 3 = 12.

LCD(4, 3) = 12

Step 2

Convert to Equivalent Fractions with Common Denominator 12

Multiply the numerator and denominator of 1/4 by 3, and multiply the numerator and denominator of 2/3 by 4 so both fractions share the common base 12.

1 × 3/4 × 3 = 3/12 and 2 × 4/3 × 4 = 8/12

Step 3

Add the Numerators

Now add the numerators (3 + 8 = 11) and keep the common denominator 12 unchanged.

3 + 8/12 = 11/12

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 12 is 1, confirming that 11/12 cannot be reduced further—it is already in its simplest irreducible form.

11/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 12 produces a repeating decimal (approximately 0.916667, or 91.6667%).

11 ÷ 12 = 0.916667 (91.6667%)

Visual Representation

The diagram below illustrates 1/4 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/12`
Mixed Number Form	`11/12`
Decimal Form	`0.916667`
Percentage	`91.6667%`

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Frequently Asked Questions

What is 1/4 plus 2/3 as a fraction?

1/4 + 2/3 in simplest fraction form is 11/12.

What is 1/4 plus 2/3 as a decimal?

1/4 + 2/3 converted to a decimal is 0.916667.

What is 1/4 plus 2/3 as a percentage?

1/4 + 2/3 expressed as a percentage is 91.6667%.

Does 1/4 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.916667...) because the denominator contains prime factors other than 2 and 5.