What is 9/22 plus 6/13?
9/22 plus 6/13 equals 249/286 (or 0.870629 in decimal form). Learn the step-by-step solution to add 9/22 and 6/13 using Least Common Denominator and simplification.
Exact Answer
9/22 + 6/13 = 249/286
Simplified Fraction
249/286
Mixed Number
Proper (249/286)
Decimal Value
0.870629
Percentage
87.0629%
Step-by-Step Solution: 9/22 + 6/13
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 6/13 by 22 so both fractions share the common base 286.
9 × 13/22 × 13 = 117/286 and 6 × 22/13 × 22 = 132/286
Step 3
Add the Numerators
Now add the numerators (117 + 132 = 249) and keep the common denominator 286 unchanged.
117 + 132/286 = 249/286
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 249 and 286 is 1, confirming that 249/286 cannot be reduced further—it is already in its simplest irreducible form.
249/286
Step 5
Decimal & Percentage Representation
Dividing the numerator 249 by denominator 286 produces a repeating decimal (approximately 0.870629, or 87.0629%).
249 ÷ 286 = 0.870629 (87.0629%)
Visual Representation
The diagram below illustrates 9/22 plus 6/13 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 249/286 |
| Mixed Number Form | 249/286 |
| Decimal Form | 0.870629 |
| Percentage | 87.0629% |
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Frequently Asked Questions
What is 9/22 plus 6/13 as a fraction?
9/22 + 6/13 in simplest fraction form is 249/286.
What is 9/22 plus 6/13 as a decimal?
9/22 + 6/13 converted to a decimal is 0.870629.
What is 9/22 plus 6/13 as a percentage?
9/22 + 6/13 expressed as a percentage is 87.0629%.
Does 9/22 plus 6/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.870629...) because the denominator contains prime factors other than 2 and 5.