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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
Notice that 4 is an exact multiple of 2 (2 × 2 = 4). The Least Common Denominator (LCD) is simply 4, meaning we only need to scale one fraction.
Working: LCD(4, 2) = 4

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

Step 3: Add the Numerators
Now add the numerators (1 + 2 = 3) and keep the common denominator 4 unchanged.
Working: 1 + 2/4 = 3/4

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 3 and 4 is 1, confirming that 3/4 cannot be reduced further—it is already in its simplest irreducible form.
Working: 3/4

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).
Working: 3 ÷ 4 = 0.75 (75%)

Key Values:
- Simplified Fraction: 3/4
- Mixed Number Form: 3/4
- Decimal Value: 0.75
- Percentage: 75%

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

Simplified Fraction

3/4

Mixed Number

Proper (3/4)

Decimal Value

0.75

Percentage

75%

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

Step 1

Find the Least Common Denominator (LCD)

Notice that 4 is an exact multiple of 2 (2 × 2 = 4). The Least Common Denominator (LCD) is simply 4, meaning we only need to scale one fraction.

LCD(4, 2) = 4

Step 2

Convert to Equivalent Fractions with Common Denominator 4

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

1 × 1/4 × 1 = 1/4 and 1 × 2/2 × 2 = 2/4

Step 3

Add the Numerators

Now add the numerators (1 + 2 = 3) and keep the common denominator 4 unchanged.

1 + 2/4 = 3/4

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 3 and 4 is 1, confirming that 3/4 cannot be reduced further—it is already in its simplest irreducible form.

3/4

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).

3 ÷ 4 = 0.75 (75%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/4`
Mixed Number Form	`3/4`
Decimal Form	`0.75`
Percentage	`75%`

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Frequently Asked Questions

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

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

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

1/4 + 1/2 converted to a decimal is 0.75.

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

1/4 + 1/2 expressed as a percentage is 75%.

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

It results in an exact terminating decimal (0.75) because the denominator in simplest terms contains only prime factors 2 and/or 5.