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

Exact Answer

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

Step 1: Convert Mixed Numbers to Improper Fractions
First, convert both mixed numbers into improper fractions using the formula (Whole × Denominator + Numerator) / Denominator:
• 1 1/4 = (1 × 4 + 1)/4 = 5/4
• 1 1/2 = (1 × 2 + 1)/2 = 3/2
Working: 1 1/4 = 5/4 and 1 1/2 = 3/2

Step 2: 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 3: Convert to Equivalent Fractions with Common Denominator 4
Multiply the numerator and denominator of 5/4 by 1, and multiply the numerator and denominator of 3/2 by 2 so both fractions share the common base 4.
Working: 5 × 1/4 × 1 = 5/4 and 3 × 2/2 × 2 = 6/4

Step 4: Add the Numerators
Now add the numerators (5 + 6 = 11) and keep the common denominator 4 unchanged.
Working: 5 + 6/4 = 11/4

Step 5: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 4 is 1, confirming that 11/4 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/4

Step 6: Convert Improper Fraction to a Mixed Number
Since the numerator (11) is greater than the denominator (4), divide 11 by 4: it goes in 2 whole time(s) with a remainder of 3, giving the mixed number 2 3/4.
Working: 11/4 = 2 3/4

Step 7: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 4 yields an exact terminating decimal of 2.75 (or 275%).
Working: 11 ÷ 4 = 2.75 (275%)

Key Values:
- Simplified Fraction: 11/4
- Mixed Number Form: 2 3/4
- Decimal Value: 2.75
- Percentage: 275%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-1-4-plus-1-1-2/
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11/4 + 11/2 = 23/4

Simplified Fraction

11/4

Mixed Number

2 3/4

Decimal Value

2.75

Percentage

275%

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

Step 1

Convert Mixed Numbers to Improper Fractions

First, convert both mixed numbers into improper fractions using the formula (Whole × Denominator + Numerator) / Denominator:
• 1 1/4 = (1 × 4 + 1)/4 = 5/4
• 1 1/2 = (1 × 2 + 1)/2 = 3/2

11/4 = 5/4 and 11/2 = 3/2

Step 2

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 3

Convert to Equivalent Fractions with Common Denominator 4

Multiply the numerator and denominator of 5/4 by 1, and multiply the numerator and denominator of 3/2 by 2 so both fractions share the common base 4.

5 × 1/4 × 1 = 5/4 and 3 × 2/2 × 2 = 6/4

Step 4

Add the Numerators

Now add the numerators (5 + 6 = 11) and keep the common denominator 4 unchanged.

5 + 6/4 = 11/4

Step 5

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 4 is 1, confirming that 11/4 cannot be reduced further—it is already in its simplest irreducible form.

11/4

Step 6

Convert Improper Fraction to a Mixed Number

Since the numerator (11) is greater than the denominator (4), divide 11 by 4: it goes in 2 whole time(s) with a remainder of 3, giving the mixed number 2 3/4.

11/4 = 23/4

Step 7

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 4 yields an exact terminating decimal of 2.75 (or 275%).

11 ÷ 4 = 2.75 (275%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/4`
Mixed Number Form	`2 3/4`
Decimal Form	`2.75`
Percentage	`275%`

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Frequently Asked Questions

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

1 1/4 + 1 1/2 in simplest fraction form is 11/4 (or 2 3/4 as a mixed number).

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

1 1/4 + 1 1/2 converted to a decimal is 2.75.

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

1 1/4 + 1 1/2 expressed as a percentage is 275%.

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

Because the numerator is greater than the denominator, the improper fraction 11/4 can be written as the mixed number 2 3/4.

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

It results in an exact terminating decimal (2.75) because the denominator in simplest terms contains only prime factors 2 and/or 5.