What is 5/14 plus 10/13? (Answer: 205/182)

Exact Answer

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Problem: What is 5/14 plus 10/13?
Formula / Expression: 5/14 + 10/13
Final Answer: 1 23/182 (205/182)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 13 = 182.
Working: LCD(14, 13) = 182

Step 2: Convert to Equivalent Fractions with Common Denominator 182
Multiply the numerator and denominator of 5/14 by 13, and multiply the numerator and denominator of 10/13 by 14 so both fractions share the common base 182.
Working: 5 × 13/14 × 13 = 65/182 and 10 × 14/13 × 14 = 140/182

Step 3: Add the Numerators
Now add the numerators (65 + 140 = 205) and keep the common denominator 182 unchanged.
Working: 65 + 140/182 = 205/182

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 205 and 182 is 1, confirming that 205/182 cannot be reduced further—it is already in its simplest irreducible form.
Working: 205/182

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (205) is greater than the denominator (182), divide 205 by 182: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/182.
Working: 205/182 = 1 23/182

Step 6: Decimal & Percentage Representation
Dividing the numerator 205 by denominator 182 produces a repeating decimal (approximately 1.126374, or 112.6374%).
Working: 205 ÷ 182 = 1.126374 (112.6374%)

Key Values:
- Simplified Fraction: 205/182
- Mixed Number Form: 1 23/182
- Decimal Value: 1.126374
- Percentage: 112.6374%

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Solved with FractionsCalc:
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5/14 + 10/13 = 205/182

Simplified Fraction

205/182

Mixed Number

1 23/182

Decimal Value

1.126374

Percentage

112.6374%

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Step-by-Step Solution: 5/14 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 13 = 182.

LCD(14, 13) = 182

Step 2

Convert to Equivalent Fractions with Common Denominator 182

Multiply the numerator and denominator of 5/14 by 13, and multiply the numerator and denominator of 10/13 by 14 so both fractions share the common base 182.

5 × 13/14 × 13 = 65/182 and 10 × 14/13 × 14 = 140/182

Step 3

Add the Numerators

Now add the numerators (65 + 140 = 205) and keep the common denominator 182 unchanged.

65 + 140/182 = 205/182

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 205 and 182 is 1, confirming that 205/182 cannot be reduced further—it is already in its simplest irreducible form.

205/182

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (205) is greater than the denominator (182), divide 205 by 182: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/182.

205/182 = 123/182

Step 6

Decimal & Percentage Representation

Dividing the numerator 205 by denominator 182 produces a repeating decimal (approximately 1.126374, or 112.6374%).

205 ÷ 182 = 1.126374 (112.6374%)

Visual Representation

The diagram below illustrates 5/14 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`205/182`
Mixed Number Form	`1 23/182`
Decimal Form	`1.126374`
Percentage	`112.6374%`

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Frequently Asked Questions

What is 5/14 plus 10/13 as a fraction?

5/14 + 10/13 in simplest fraction form is 205/182 (or 1 23/182 as a mixed number).

What is 5/14 plus 10/13 as a decimal?

5/14 + 10/13 converted to a decimal is 1.126374.

What is 5/14 plus 10/13 as a percentage?

5/14 + 10/13 expressed as a percentage is 112.6374%.

How do you write 5/14 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 205/182 can be written as the mixed number 1 23/182.

Does 5/14 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.126374...) because the denominator contains prime factors other than 2 and 5.