What is 1/4 plus 11/13? (Answer: 57/52)

Exact Answer

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Problem: What is 1/4 plus 11/13?
Formula / Expression: 1/4 + 11/13
Final Answer: 1 5/52 (57/52)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 13 = 52.
Working: LCD(4, 13) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 1/4 by 13, and multiply the numerator and denominator of 11/13 by 4 so both fractions share the common base 52.
Working: 1 × 13/4 × 13 = 13/52 and 11 × 4/13 × 4 = 44/52

Step 3: Add the Numerators
Now add the numerators (13 + 44 = 57) and keep the common denominator 52 unchanged.
Working: 13 + 44/52 = 57/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 57 and 52 is 1, confirming that 57/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 57/52

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (57) is greater than the denominator (52), divide 57 by 52: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/52.
Working: 57/52 = 1 5/52

Step 6: Decimal & Percentage Representation
Dividing the numerator 57 by denominator 52 produces a repeating decimal (approximately 1.096154, or 109.6154%).
Working: 57 ÷ 52 = 1.096154 (109.6154%)

Key Values:
- Simplified Fraction: 57/52
- Mixed Number Form: 1 5/52
- Decimal Value: 1.096154
- Percentage: 109.6154%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-11-13/
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1/4 + 11/13 = 57/52

Simplified Fraction

57/52

Mixed Number

1 5/52

Decimal Value

1.096154

Percentage

109.6154%

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Step-by-Step Solution: 1/4 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 13 = 52.

LCD(4, 13) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 1/4 by 13, and multiply the numerator and denominator of 11/13 by 4 so both fractions share the common base 52.

1 × 13/4 × 13 = 13/52 and 11 × 4/13 × 4 = 44/52

Step 3

Add the Numerators

Now add the numerators (13 + 44 = 57) and keep the common denominator 52 unchanged.

13 + 44/52 = 57/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 57 and 52 is 1, confirming that 57/52 cannot be reduced further—it is already in its simplest irreducible form.

57/52

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (57) is greater than the denominator (52), divide 57 by 52: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/52.

57/52 = 15/52

Step 6

Decimal & Percentage Representation

Dividing the numerator 57 by denominator 52 produces a repeating decimal (approximately 1.096154, or 109.6154%).

57 ÷ 52 = 1.096154 (109.6154%)

Visual Representation

The diagram below illustrates 1/4 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`57/52`
Mixed Number Form	`1 5/52`
Decimal Form	`1.096154`
Percentage	`109.6154%`

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Frequently Asked Questions

What is 1/4 plus 11/13 as a fraction?

1/4 + 11/13 in simplest fraction form is 57/52 (or 1 5/52 as a mixed number).

What is 1/4 plus 11/13 as a decimal?

1/4 + 11/13 converted to a decimal is 1.096154.

What is 1/4 plus 11/13 as a percentage?

1/4 + 11/13 expressed as a percentage is 109.6154%.

How do you write 1/4 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 57/52 can be written as the mixed number 1 5/52.

Does 1/4 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.096154...) because the denominator contains prime factors other than 2 and 5.