What is 1/2 plus 3/4? (Answer: 5/4)

Exact Answer

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Problem: What is 1/2 plus 3/4?
Formula / Expression: 1/2 + 3/4
Final Answer: 1 1/4 (5/4)
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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(2, 4) = 4

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

Step 3: Add the Numerators
Now add the numerators (2 + 3 = 5) and keep the common denominator 4 unchanged.
Working: 2 + 3/4 = 5/4

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 4 is 1, confirming that 5/4 cannot be reduced further—it is already in its simplest irreducible form.
Working: 5/4

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (5) is greater than the denominator (4), divide 5 by 4: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/4.
Working: 5/4 = 1 1/4

Step 6: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 4 yields an exact terminating decimal of 1.25 (or 125%).
Working: 5 ÷ 4 = 1.25 (125%)

Key Values:
- Simplified Fraction: 5/4
- Mixed Number Form: 1 1/4
- Decimal Value: 1.25
- Percentage: 125%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-3-4/
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1/2 + 3/4 = 5/4

Simplified Fraction

5/4

Mixed Number

1 1/4

Decimal Value

1.25

Percentage

125%

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

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(2, 4) = 4

Step 2

Convert to Equivalent Fractions with Common Denominator 4

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

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

Step 3

Add the Numerators

Now add the numerators (2 + 3 = 5) and keep the common denominator 4 unchanged.

2 + 3/4 = 5/4

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 4 is 1, confirming that 5/4 cannot be reduced further—it is already in its simplest irreducible form.

5/4

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (5) is greater than the denominator (4), divide 5 by 4: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/4.

5/4 = 11/4

Step 6

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 4 yields an exact terminating decimal of 1.25 (or 125%).

5 ÷ 4 = 1.25 (125%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/4`
Mixed Number Form	`1 1/4`
Decimal Form	`1.25`
Percentage	`125%`

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Frequently Asked Questions

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

1/2 + 3/4 in simplest fraction form is 5/4 (or 1 1/4 as a mixed number).

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

1/2 + 3/4 converted to a decimal is 1.25.

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

1/2 + 3/4 expressed as a percentage is 125%.

How do you write 1/2 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 5/4 can be written as the mixed number 1 1/4.

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

It results in an exact terminating decimal (1.25) because the denominator in simplest terms contains only prime factors 2 and/or 5.