What is 2/5 plus 9/22?
2/5 plus 9/22 equals 89/110 (or 0.809091 in decimal form). Learn the step-by-step solution to add 2/5 and 9/22 using Least Common Denominator and simplification.
Exact Answer
2/5 + 9/22 = 89/110
Simplified Fraction
89/110
Mixed Number
Proper (89/110)
Decimal Value
0.809091
Percentage
80.9091%
Step-by-Step Solution: 2/5 + 9/22
Step 1
Find the Least Common Denominator (LCD)
The denominators 5 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 22 = 110.
LCD(5, 22) = 110
Step 2
Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 2/5 by 22, and multiply the numerator and denominator of 9/22 by 5 so both fractions share the common base 110.
2 × 22/5 × 22 = 44/110 and 9 × 5/22 × 5 = 45/110
Step 3
Add the Numerators
Now add the numerators (44 + 45 = 89) and keep the common denominator 110 unchanged.
44 + 45/110 = 89/110
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 110 is 1, confirming that 89/110 cannot be reduced further—it is already in its simplest irreducible form.
89/110
Step 5
Decimal & Percentage Representation
Dividing the numerator 89 by denominator 110 produces a repeating decimal (approximately 0.809091, or 80.9091%).
89 ÷ 110 = 0.809091 (80.9091%)
Visual Representation
The diagram below illustrates 2/5 plus 9/22 visually:
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=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 89/110 |
| Mixed Number Form | 89/110 |
| Decimal Form | 0.809091 |
| Percentage | 80.9091% |
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Frequently Asked Questions
What is 2/5 plus 9/22 as a fraction?
2/5 + 9/22 in simplest fraction form is 89/110.
What is 2/5 plus 9/22 as a decimal?
2/5 + 9/22 converted to a decimal is 0.809091.
What is 2/5 plus 9/22 as a percentage?
2/5 + 9/22 expressed as a percentage is 80.9091%.
Does 2/5 plus 9/22 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.809091...) because the denominator contains prime factors other than 2 and 5.