What is 10/17 plus 9/13?
10/17 plus 9/13 equals 283/221 (or 1 62/221 as a mixed number) (or 1.280543 in decimal form). Learn the step-by-step solution to add 10/17 and 9/13 using Least Common Denominator and simplification.
Exact Answer
10/17 + 9/13 = 283/221
Simplified Fraction
283/221
Mixed Number
1 62/221
Decimal Value
1.280543
Percentage
128.0543%
Step-by-Step Solution: 10/17 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 17 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 13 = 221.
LCD(17, 13) = 221
Step 2
Convert to Equivalent Fractions with Common Denominator 221
Multiply the numerator and denominator of 10/17 by 13, and multiply the numerator and denominator of 9/13 by 17 so both fractions share the common base 221.
10 × 13/17 × 13 = 130/221 and 9 × 17/13 × 17 = 153/221
Step 3
Add the Numerators
Now add the numerators (130 + 153 = 283) and keep the common denominator 221 unchanged.
130 + 153/221 = 283/221
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 283 and 221 is 1, confirming that 283/221 cannot be reduced further—it is already in its simplest irreducible form.
283/221
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (283) is greater than the denominator (221), divide 283 by 221: it goes in 1 whole time(s) with a remainder of 62, giving the mixed number 1 62/221.
283/221 = 162/221
Step 6
Decimal & Percentage Representation
Dividing the numerator 283 by denominator 221 produces a repeating decimal (approximately 1.280543, or 128.0543%).
283 ÷ 221 = 1.280543 (128.0543%)
Visual Representation
The diagram below illustrates 10/17 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 283/221 |
| Mixed Number Form | 1 62/221 |
| Decimal Form | 1.280543 |
| Percentage | 128.0543% |
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Frequently Asked Questions
What is 10/17 plus 9/13 as a fraction?
10/17 + 9/13 in simplest fraction form is 283/221 (or 1 62/221 as a mixed number).
What is 10/17 plus 9/13 as a decimal?
10/17 + 9/13 converted to a decimal is 1.280543.
What is 10/17 plus 9/13 as a percentage?
10/17 + 9/13 expressed as a percentage is 128.0543%.
How do you write 10/17 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 283/221 can be written as the mixed number 1 62/221.
Does 10/17 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.280543...) because the denominator contains prime factors other than 2 and 5.