What is 9/22 plus 10/13?
9/22 plus 10/13 equals 337/286 (or 1 51/286 as a mixed number) (or 1.178322 in decimal form). Learn the step-by-step solution to add 9/22 and 10/13 using Least Common Denominator and simplification.
Exact Answer
9/22 + 10/13 = 337/286
Simplified Fraction
337/286
Mixed Number
1 51/286
Decimal Value
1.178322
Percentage
117.8322%
Step-by-Step Solution: 9/22 + 10/13
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 9/22 by 13, and multiply the numerator and denominator of 10/13 by 22 so both fractions share the common base 286.
9 × 13/22 × 13 = 117/286 and 10 × 22/13 × 22 = 220/286
Step 3
Add the Numerators
Now add the numerators (117 + 220 = 337) and keep the common denominator 286 unchanged.
117 + 220/286 = 337/286
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 337 and 286 is 1, confirming that 337/286 cannot be reduced further—it is already in its simplest irreducible form.
337/286
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (337) is greater than the denominator (286), divide 337 by 286: it goes in 1 whole time(s) with a remainder of 51, giving the mixed number 1 51/286.
337/286 = 151/286
Step 6
Decimal & Percentage Representation
Dividing the numerator 337 by denominator 286 produces a repeating decimal (approximately 1.178322, or 117.8322%).
337 ÷ 286 = 1.178322 (117.8322%)
Visual Representation
The diagram below illustrates 9/22 plus 10/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 337/286 |
| Mixed Number Form | 1 51/286 |
| Decimal Form | 1.178322 |
| Percentage | 117.8322% |
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Frequently Asked Questions
What is 9/22 plus 10/13 as a fraction?
9/22 + 10/13 in simplest fraction form is 337/286 (or 1 51/286 as a mixed number).
What is 9/22 plus 10/13 as a decimal?
9/22 + 10/13 converted to a decimal is 1.178322.
What is 9/22 plus 10/13 as a percentage?
9/22 + 10/13 expressed as a percentage is 117.8322%.
How do you write 9/22 plus 10/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 337/286 can be written as the mixed number 1 51/286.
Does 9/22 plus 10/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.178322...) because the denominator contains prime factors other than 2 and 5.