What is 5/12 plus 10/13? (Answer: 185/156)

Exact Answer

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Problem: What is 5/12 plus 10/13?
Formula / Expression: 5/12 + 10/13
Final Answer: 1 29/156 (185/156)
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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 5/12 by 13, and multiply the numerator and denominator of 10/13 by 12 so both fractions share the common base 156.
Working: 5 × 13/12 × 13 = 65/156 and 10 × 12/13 × 12 = 120/156

Step 3: Add the Numerators
Now add the numerators (65 + 120 = 185) and keep the common denominator 156 unchanged.
Working: 65 + 120/156 = 185/156

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 185 and 156 is 1, confirming that 185/156 cannot be reduced further—it is already in its simplest irreducible form.
Working: 185/156

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (185) is greater than the denominator (156), divide 185 by 156: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/156.
Working: 185/156 = 1 29/156

Step 6: Decimal & Percentage Representation
Dividing the numerator 185 by denominator 156 produces a repeating decimal (approximately 1.185897, or 118.5897%).
Working: 185 ÷ 156 = 1.185897 (118.5897%)

Key Values:
- Simplified Fraction: 185/156
- Mixed Number Form: 1 29/156
- Decimal Value: 1.185897
- Percentage: 118.5897%

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Solved with FractionsCalc:
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5/12 + 10/13 = 185/156

Simplified Fraction

185/156

Mixed Number

1 29/156

Decimal Value

1.185897

Percentage

118.5897%

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Step-by-Step Solution: 5/12 + 10/13

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 5/12 by 13, and multiply the numerator and denominator of 10/13 by 12 so both fractions share the common base 156.

5 × 13/12 × 13 = 65/156 and 10 × 12/13 × 12 = 120/156

Step 3

Add the Numerators

Now add the numerators (65 + 120 = 185) and keep the common denominator 156 unchanged.

65 + 120/156 = 185/156

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 185 and 156 is 1, confirming that 185/156 cannot be reduced further—it is already in its simplest irreducible form.

185/156

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (185) is greater than the denominator (156), divide 185 by 156: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/156.

185/156 = 129/156

Step 6

Decimal & Percentage Representation

Dividing the numerator 185 by denominator 156 produces a repeating decimal (approximately 1.185897, or 118.5897%).

185 ÷ 156 = 1.185897 (118.5897%)

Visual Representation

The diagram below illustrates 5/12 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`185/156`
Mixed Number Form	`1 29/156`
Decimal Form	`1.185897`
Percentage	`118.5897%`

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Frequently Asked Questions

What is 5/12 plus 10/13 as a fraction?

5/12 + 10/13 in simplest fraction form is 185/156 (or 1 29/156 as a mixed number).

What is 5/12 plus 10/13 as a decimal?

5/12 + 10/13 converted to a decimal is 1.185897.

What is 5/12 plus 10/13 as a percentage?

5/12 + 10/13 expressed as a percentage is 118.5897%.

How do you write 5/12 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 185/156 can be written as the mixed number 1 29/156.

Does 5/12 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.185897...) because the denominator contains prime factors other than 2 and 5.