What is 2/5 plus 4/9?
2/5 plus 4/9 equals 38/45 (or 0.844444 in decimal form). Learn the step-by-step solution to add 2/5 and 4/9 using Least Common Denominator and simplification.
Exact Answer
2/5 + 4/9 = 38/45
Simplified Fraction
38/45
Mixed Number
Proper (38/45)
Decimal Value
0.844444
Percentage
84.4444%
Step-by-Step Solution: 2/5 + 4/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 5 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 9 = 45.
LCD(5, 9) = 45
Step 2
Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 2/5 by 9, and multiply the numerator and denominator of 4/9 by 5 so both fractions share the common base 45.
2 × 9/5 × 9 = 18/45 and 4 × 5/9 × 5 = 20/45
Step 3
Add the Numerators
Now add the numerators (18 + 20 = 38) and keep the common denominator 45 unchanged.
18 + 20/45 = 38/45
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 38 and 45 is 1, confirming that 38/45 cannot be reduced further—it is already in its simplest irreducible form.
38/45
Step 5
Decimal & Percentage Representation
Dividing the numerator 38 by denominator 45 produces a repeating decimal (approximately 0.844444, or 84.4444%).
38 ÷ 45 = 0.844444 (84.4444%)
Visual Representation
The diagram below illustrates 2/5 plus 4/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 38/45 |
| Mixed Number Form | 38/45 |
| Decimal Form | 0.844444 |
| Percentage | 84.4444% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 2/5 plus 4/9 as a fraction?
2/5 + 4/9 in simplest fraction form is 38/45.
What is 2/5 plus 4/9 as a decimal?
2/5 + 4/9 converted to a decimal is 0.844444.
What is 2/5 plus 4/9 as a percentage?
2/5 + 4/9 expressed as a percentage is 84.4444%.
Does 2/5 plus 4/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.844444...) because the denominator contains prime factors other than 2 and 5.