What is 10/19 plus 10/13? (Answer: 320/247)

Exact Answer

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Problem: What is 10/19 plus 10/13?
Formula / Expression: 10/19 + 10/13
Final Answer: 1 73/247 (320/247)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 13 = 247.
Working: LCD(19, 13) = 247

Step 2: Convert to Equivalent Fractions with Common Denominator 247
Multiply the numerator and denominator of 10/19 by 13, and multiply the numerator and denominator of 10/13 by 19 so both fractions share the common base 247.
Working: 10 × 13/19 × 13 = 130/247 and 10 × 19/13 × 19 = 190/247

Step 3: Add the Numerators
Now add the numerators (130 + 190 = 320) and keep the common denominator 247 unchanged.
Working: 130 + 190/247 = 320/247

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 320 and 247 is 1, confirming that 320/247 cannot be reduced further—it is already in its simplest irreducible form.
Working: 320/247

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (320) is greater than the denominator (247), divide 320 by 247: it goes in 1 whole time(s) with a remainder of 73, giving the mixed number 1 73/247.
Working: 320/247 = 1 73/247

Step 6: Decimal & Percentage Representation
Dividing the numerator 320 by denominator 247 produces a repeating decimal (approximately 1.295547, or 129.5547%).
Working: 320 ÷ 247 = 1.295547 (129.5547%)

Key Values:
- Simplified Fraction: 320/247
- Mixed Number Form: 1 73/247
- Decimal Value: 1.295547
- Percentage: 129.5547%

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Solved with FractionsCalc:
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10/19 + 10/13 = 320/247

Simplified Fraction

320/247

Mixed Number

1 73/247

Decimal Value

1.295547

Percentage

129.5547%

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Step-by-Step Solution: 10/19 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 13 = 247.

LCD(19, 13) = 247

Step 2

Convert to Equivalent Fractions with Common Denominator 247

Multiply the numerator and denominator of 10/19 by 13, and multiply the numerator and denominator of 10/13 by 19 so both fractions share the common base 247.

10 × 13/19 × 13 = 130/247 and 10 × 19/13 × 19 = 190/247

Step 3

Add the Numerators

Now add the numerators (130 + 190 = 320) and keep the common denominator 247 unchanged.

130 + 190/247 = 320/247

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 320 and 247 is 1, confirming that 320/247 cannot be reduced further—it is already in its simplest irreducible form.

320/247

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (320) is greater than the denominator (247), divide 320 by 247: it goes in 1 whole time(s) with a remainder of 73, giving the mixed number 1 73/247.

320/247 = 173/247

Step 6

Decimal & Percentage Representation

Dividing the numerator 320 by denominator 247 produces a repeating decimal (approximately 1.295547, or 129.5547%).

320 ÷ 247 = 1.295547 (129.5547%)

Visual Representation

The diagram below illustrates 10/19 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`320/247`
Mixed Number Form	`1 73/247`
Decimal Form	`1.295547`
Percentage	`129.5547%`

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Frequently Asked Questions

What is 10/19 plus 10/13 as a fraction?

10/19 + 10/13 in simplest fraction form is 320/247 (or 1 73/247 as a mixed number).

What is 10/19 plus 10/13 as a decimal?

10/19 + 10/13 converted to a decimal is 1.295547.

What is 10/19 plus 10/13 as a percentage?

10/19 + 10/13 expressed as a percentage is 129.5547%.

How do you write 10/19 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 320/247 can be written as the mixed number 1 73/247.

Does 10/19 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.295547...) because the denominator contains prime factors other than 2 and 5.