What is 3/12 plus 11/13? (Answer: 57/52)

Exact Answer

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Problem: What is 3/12 plus 11/13?
Formula / Expression: 3/12 + 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 12 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 12 × 13 = 156.
Working: LCD(12, 13) = 156

Step 2: Convert to Equivalent Fractions with Common Denominator 156
Multiply the numerator and denominator of 3/12 by 13, and multiply the numerator and denominator of 11/13 by 12 so both fractions share the common base 156.
Working: 3 × 13/12 × 13 = 39/156 and 11 × 12/13 × 12 = 132/156

Step 3: Add the Numerators
Now add the numerators (39 + 132 = 171) and keep the common denominator 156 unchanged.
Working: 39 + 132/156 = 171/156

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 171 and 156, which is 3. Divide both the numerator and denominator by 3.
Working: 171 ÷ 3/156 ÷ 3 = 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:
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3/12 + 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: 3/12 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 12 × 13 = 156.

LCD(12, 13) = 156

Step 2

Convert to Equivalent Fractions with Common Denominator 156

Multiply the numerator and denominator of 3/12 by 13, and multiply the numerator and denominator of 11/13 by 12 so both fractions share the common base 156.

3 × 13/12 × 13 = 39/156 and 11 × 12/13 × 12 = 132/156

Step 3

Add the Numerators

Now add the numerators (39 + 132 = 171) and keep the common denominator 156 unchanged.

39 + 132/156 = 171/156

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 171 and 156, which is 3. Divide both the numerator and denominator by 3.

171 ÷ 3/156 ÷ 3 = 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 3/12 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 3/12 plus 11/13 as a fraction?

3/12 + 11/13 in simplest fraction form is 57/52 (or 1 5/52 as a mixed number).

What is 3/12 plus 11/13 as a decimal?

3/12 + 11/13 converted to a decimal is 1.096154.

What is 3/12 plus 11/13 as a percentage?

3/12 + 11/13 expressed as a percentage is 109.6154%.

How do you write 3/12 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 3/12 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.