What is 2/5 plus 7/9?
2/5 plus 7/9 equals 53/45 (or 1 8/45 as a mixed number) (or 1.177778 in decimal form). Learn the step-by-step solution to add 2/5 and 7/9 using Least Common Denominator and simplification.
Exact Answer
2/5 + 7/9 = 53/45
Simplified Fraction
53/45
Mixed Number
1 8/45
Decimal Value
1.177778
Percentage
117.7778%
Step-by-Step Solution: 2/5 + 7/9
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 7/9 by 5 so both fractions share the common base 45.
2 × 9/5 × 9 = 18/45 and 7 × 5/9 × 5 = 35/45
Step 3
Add the Numerators
Now add the numerators (18 + 35 = 53) and keep the common denominator 45 unchanged.
18 + 35/45 = 53/45
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 45 is 1, confirming that 53/45 cannot be reduced further—it is already in its simplest irreducible form.
53/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (53) is greater than the denominator (45), divide 53 by 45: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/45.
53/45 = 18/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 53 by denominator 45 produces a repeating decimal (approximately 1.177778, or 117.7778%).
53 ÷ 45 = 1.177778 (117.7778%)
Visual Representation
The diagram below illustrates 2/5 plus 7/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 53/45 |
| Mixed Number Form | 1 8/45 |
| Decimal Form | 1.177778 |
| Percentage | 117.7778% |
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Frequently Asked Questions
What is 2/5 plus 7/9 as a fraction?
2/5 + 7/9 in simplest fraction form is 53/45 (or 1 8/45 as a mixed number).
What is 2/5 plus 7/9 as a decimal?
2/5 + 7/9 converted to a decimal is 1.177778.
What is 2/5 plus 7/9 as a percentage?
2/5 + 7/9 expressed as a percentage is 117.7778%.
How do you write 2/5 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 53/45 can be written as the mixed number 1 8/45.
Does 2/5 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.177778...) because the denominator contains prime factors other than 2 and 5.