What is 15/22 plus 9/13?
15/22 plus 9/13 equals 393/286 (or 1 107/286 as a mixed number) (or 1.374126 in decimal form). Learn the step-by-step solution to add 15/22 and 9/13 using Least Common Denominator and simplification.
Exact Answer
15/22 + 9/13 = 393/286
Simplified Fraction
393/286
Mixed Number
1 107/286
Decimal Value
1.374126
Percentage
137.4126%
Step-by-Step Solution: 15/22 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.
LCD(22, 13) = 286
Step 2
Convert to Equivalent Fractions with Common Denominator 286
Multiply the numerator and denominator of 15/22 by 13, and multiply the numerator and denominator of 9/13 by 22 so both fractions share the common base 286.
15 × 13/22 × 13 = 195/286 and 9 × 22/13 × 22 = 198/286
Step 3
Add the Numerators
Now add the numerators (195 + 198 = 393) and keep the common denominator 286 unchanged.
195 + 198/286 = 393/286
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 393 and 286 is 1, confirming that 393/286 cannot be reduced further—it is already in its simplest irreducible form.
393/286
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (393) is greater than the denominator (286), divide 393 by 286: it goes in 1 whole time(s) with a remainder of 107, giving the mixed number 1 107/286.
393/286 = 1107/286
Step 6
Decimal & Percentage Representation
Dividing the numerator 393 by denominator 286 produces a repeating decimal (approximately 1.374126, or 137.4126%).
393 ÷ 286 = 1.374126 (137.4126%)
Visual Representation
The diagram below illustrates 15/22 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 393/286 |
| Mixed Number Form | 1 107/286 |
| Decimal Form | 1.374126 |
| Percentage | 137.4126% |
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Frequently Asked Questions
What is 15/22 plus 9/13 as a fraction?
15/22 + 9/13 in simplest fraction form is 393/286 (or 1 107/286 as a mixed number).
What is 15/22 plus 9/13 as a decimal?
15/22 + 9/13 converted to a decimal is 1.374126.
What is 15/22 plus 9/13 as a percentage?
15/22 + 9/13 expressed as a percentage is 137.4126%.
How do you write 15/22 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 393/286 can be written as the mixed number 1 107/286.
Does 15/22 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.374126...) because the denominator contains prime factors other than 2 and 5.