What is 4/9 plus 4/5?
4/9 plus 4/5 equals 56/45 (or 1 11/45 as a mixed number) (or 1.244444 in decimal form). Learn the step-by-step solution to add 4/9 and 4/5 using Least Common Denominator and simplification.
Exact Answer
4/9 + 4/5 = 56/45
Simplified Fraction
56/45
Mixed Number
1 11/45
Decimal Value
1.244444
Percentage
124.4444%
Step-by-Step Solution: 4/9 + 4/5
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 5 = 45.
LCD(9, 5) = 45
Step 2
Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 4/9 by 5, and multiply the numerator and denominator of 4/5 by 9 so both fractions share the common base 45.
4 × 5/9 × 5 = 20/45 and 4 × 9/5 × 9 = 36/45
Step 3
Add the Numerators
Now add the numerators (20 + 36 = 56) and keep the common denominator 45 unchanged.
20 + 36/45 = 56/45
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 56 and 45 is 1, confirming that 56/45 cannot be reduced further—it is already in its simplest irreducible form.
56/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (56) is greater than the denominator (45), divide 56 by 45: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/45.
56/45 = 111/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 56 by denominator 45 produces a repeating decimal (approximately 1.244444, or 124.4444%).
56 ÷ 45 = 1.244444 (124.4444%)
Visual Representation
The diagram below illustrates 4/9 plus 4/5 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 56/45 |
| Mixed Number Form | 1 11/45 |
| Decimal Form | 1.244444 |
| Percentage | 124.4444% |
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Frequently Asked Questions
What is 4/9 plus 4/5 as a fraction?
4/9 + 4/5 in simplest fraction form is 56/45 (or 1 11/45 as a mixed number).
What is 4/9 plus 4/5 as a decimal?
4/9 + 4/5 converted to a decimal is 1.244444.
What is 4/9 plus 4/5 as a percentage?
4/9 + 4/5 expressed as a percentage is 124.4444%.
How do you write 4/9 plus 4/5 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 56/45 can be written as the mixed number 1 11/45.
Does 4/9 plus 4/5 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.244444...) because the denominator contains prime factors other than 2 and 5.