What is 3/11 plus 3/4? (Answer: 45/44)

Exact Answer

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Problem: What is 3/11 plus 3/4?
Formula / Expression: 3/11 + 3/4
Final Answer: 1 1/44 (45/44)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 4 = 44.
Working: LCD(11, 4) = 44

Step 2: Convert to Equivalent Fractions with Common Denominator 44
Multiply the numerator and denominator of 3/11 by 4, and multiply the numerator and denominator of 3/4 by 11 so both fractions share the common base 44.
Working: 3 × 4/11 × 4 = 12/44 and 3 × 11/4 × 11 = 33/44

Step 3: Add the Numerators
Now add the numerators (12 + 33 = 45) and keep the common denominator 44 unchanged.
Working: 12 + 33/44 = 45/44

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 45 and 44 is 1, confirming that 45/44 cannot be reduced further—it is already in its simplest irreducible form.
Working: 45/44

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (45) is greater than the denominator (44), divide 45 by 44: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/44.
Working: 45/44 = 1 1/44

Step 6: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 44 produces a repeating decimal (approximately 1.022727, or 102.2727%).
Working: 45 ÷ 44 = 1.022727 (102.2727%)

Key Values:
- Simplified Fraction: 45/44
- Mixed Number Form: 1 1/44
- Decimal Value: 1.022727
- Percentage: 102.2727%

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Solved with FractionsCalc:
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3/11 + 3/4 = 45/44

Simplified Fraction

45/44

Mixed Number

1 1/44

Decimal Value

1.022727

Percentage

102.2727%

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Step-by-Step Solution: 3/11 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 4 = 44.

LCD(11, 4) = 44

Step 2

Convert to Equivalent Fractions with Common Denominator 44

Multiply the numerator and denominator of 3/11 by 4, and multiply the numerator and denominator of 3/4 by 11 so both fractions share the common base 44.

3 × 4/11 × 4 = 12/44 and 3 × 11/4 × 11 = 33/44

Step 3

Add the Numerators

Now add the numerators (12 + 33 = 45) and keep the common denominator 44 unchanged.

12 + 33/44 = 45/44

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 45 and 44 is 1, confirming that 45/44 cannot be reduced further—it is already in its simplest irreducible form.

45/44

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (45) is greater than the denominator (44), divide 45 by 44: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/44.

45/44 = 11/44

Step 6

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 44 produces a repeating decimal (approximately 1.022727, or 102.2727%).

45 ÷ 44 = 1.022727 (102.2727%)

Visual Representation

The diagram below illustrates 3/11 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/44`
Mixed Number Form	`1 1/44`
Decimal Form	`1.022727`
Percentage	`102.2727%`

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Frequently Asked Questions

What is 3/11 plus 3/4 as a fraction?

3/11 + 3/4 in simplest fraction form is 45/44 (or 1 1/44 as a mixed number).

What is 3/11 plus 3/4 as a decimal?

3/11 + 3/4 converted to a decimal is 1.022727.

What is 3/11 plus 3/4 as a percentage?

3/11 + 3/4 expressed as a percentage is 102.2727%.

How do you write 3/11 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 45/44 can be written as the mixed number 1 1/44.

Does 3/11 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.022727...) because the denominator contains prime factors other than 2 and 5.