What is 9/20 plus 8/13?
9/20 plus 8/13 equals 277/260 (or 1 17/260 as a mixed number) (or 1.065385 in decimal form). Learn the step-by-step solution to add 9/20 and 8/13 using Least Common Denominator and simplification.
Exact Answer
9/20 + 8/13 = 277/260
Simplified Fraction
277/260
Mixed Number
1 17/260
Decimal Value
1.065385
Percentage
106.5385%
Step-by-Step Solution: 9/20 + 8/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 20 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 13 = 260.
LCD(20, 13) = 260
Step 2
Convert to Equivalent Fractions with Common Denominator 260
Multiply the numerator and denominator of 9/20 by 13, and multiply the numerator and denominator of 8/13 by 20 so both fractions share the common base 260.
9 × 13/20 × 13 = 117/260 and 8 × 20/13 × 20 = 160/260
Step 3
Add the Numerators
Now add the numerators (117 + 160 = 277) and keep the common denominator 260 unchanged.
117 + 160/260 = 277/260
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 277 and 260 is 1, confirming that 277/260 cannot be reduced further—it is already in its simplest irreducible form.
277/260
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (277) is greater than the denominator (260), divide 277 by 260: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/260.
277/260 = 117/260
Step 6
Decimal & Percentage Representation
Dividing the numerator 277 by denominator 260 produces a repeating decimal (approximately 1.065385, or 106.5385%).
277 ÷ 260 = 1.065385 (106.5385%)
Visual Representation
The diagram below illustrates 9/20 plus 8/13 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 277/260 |
| Mixed Number Form | 1 17/260 |
| Decimal Form | 1.065385 |
| Percentage | 106.5385% |
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Frequently Asked Questions
What is 9/20 plus 8/13 as a fraction?
9/20 + 8/13 in simplest fraction form is 277/260 (or 1 17/260 as a mixed number).
What is 9/20 plus 8/13 as a decimal?
9/20 + 8/13 converted to a decimal is 1.065385.
What is 9/20 plus 8/13 as a percentage?
9/20 + 8/13 expressed as a percentage is 106.5385%.
How do you write 9/20 plus 8/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 277/260 can be written as the mixed number 1 17/260.
Does 9/20 plus 8/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.065385...) because the denominator contains prime factors other than 2 and 5.