What is 10/19 plus 7/13?
10/19 plus 7/13 equals 263/247 (or 1 16/247 as a mixed number) (or 1.064777 in decimal form). Learn the step-by-step solution to add 10/19 and 7/13 using Least Common Denominator and simplification.
Exact Answer
10/19 + 7/13 = 263/247
Simplified Fraction
263/247
Mixed Number
1 16/247
Decimal Value
1.064777
Percentage
106.4777%
Step-by-Step Solution: 10/19 + 7/13
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 7/13 by 19 so both fractions share the common base 247.
10 × 13/19 × 13 = 130/247 and 7 × 19/13 × 19 = 133/247
Step 3
Add the Numerators
Now add the numerators (130 + 133 = 263) and keep the common denominator 247 unchanged.
130 + 133/247 = 263/247
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 263 and 247 is 1, confirming that 263/247 cannot be reduced further—it is already in its simplest irreducible form.
263/247
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (263) is greater than the denominator (247), divide 263 by 247: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/247.
263/247 = 116/247
Step 6
Decimal & Percentage Representation
Dividing the numerator 263 by denominator 247 produces a repeating decimal (approximately 1.064777, or 106.4777%).
263 ÷ 247 = 1.064777 (106.4777%)
Visual Representation
The diagram below illustrates 10/19 plus 7/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 263/247 |
| Mixed Number Form | 1 16/247 |
| Decimal Form | 1.064777 |
| Percentage | 106.4777% |
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Frequently Asked Questions
What is 10/19 plus 7/13 as a fraction?
10/19 + 7/13 in simplest fraction form is 263/247 (or 1 16/247 as a mixed number).
What is 10/19 plus 7/13 as a decimal?
10/19 + 7/13 converted to a decimal is 1.064777.
What is 10/19 plus 7/13 as a percentage?
10/19 + 7/13 expressed as a percentage is 106.4777%.
How do you write 10/19 plus 7/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 263/247 can be written as the mixed number 1 16/247.
Does 10/19 plus 7/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.064777...) because the denominator contains prime factors other than 2 and 5.