What is 1/4 plus 1/3? (Answer: 7/12)

Exact Answer

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Problem: What is 1/4 plus 1/3?
Formula / Expression: 1/4 + 1/3
Final Answer: 7/12
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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 1/3 by 4 so both fractions share the common base 12.
Working: 1 × 3/4 × 3 = 3/12 and 1 × 4/3 × 4 = 4/12

Step 3: Add the Numerators
Now add the numerators (3 + 4 = 7) and keep the common denominator 12 unchanged.
Working: 3 + 4/12 = 7/12

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 12 is 1, confirming that 7/12 cannot be reduced further—it is already in its simplest irreducible form.
Working: 7/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 12 produces a repeating decimal (approximately 0.583333, or 58.3333%).
Working: 7 ÷ 12 = 0.583333 (58.3333%)

Key Values:
- Simplified Fraction: 7/12
- Mixed Number Form: 7/12
- Decimal Value: 0.583333
- Percentage: 58.3333%

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Solved with FractionsCalc:
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1/4 + 1/3 = 7/12

Simplified Fraction

7/12

Mixed Number

Proper (7/12)

Decimal Value

0.583333

Percentage

58.3333%

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

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 1/3 by 4 so both fractions share the common base 12.

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

Step 3

Add the Numerators

Now add the numerators (3 + 4 = 7) and keep the common denominator 12 unchanged.

3 + 4/12 = 7/12

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 7 and 12 is 1, confirming that 7/12 cannot be reduced further—it is already in its simplest irreducible form.

7/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 12 produces a repeating decimal (approximately 0.583333, or 58.3333%).

7 ÷ 12 = 0.583333 (58.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/12`
Mixed Number Form	`7/12`
Decimal Form	`0.583333`
Percentage	`58.3333%`

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Frequently Asked Questions

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

1/4 + 1/3 in simplest fraction form is 7/12.

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

1/4 + 1/3 converted to a decimal is 0.583333.

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

1/4 + 1/3 expressed as a percentage is 58.3333%.

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

It results in a repeating decimal (approximately 0.583333...) because the denominator contains prime factors other than 2 and 5.