What is 1/9 plus 4/5?
1/9 plus 4/5 equals 41/45 (or 0.911111 in decimal form). Learn the step-by-step solution to add 1/9 and 4/5 using Least Common Denominator and simplification.
Exact Answer
1/9 + 4/5 = 41/45
Simplified Fraction
41/45
Mixed Number
Proper (41/45)
Decimal Value
0.911111
Percentage
91.1111%
Step-by-Step Solution: 1/9 + 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 1/9 by 5, and multiply the numerator and denominator of 4/5 by 9 so both fractions share the common base 45.
1 × 5/9 × 5 = 5/45 and 4 × 9/5 × 9 = 36/45
Step 3
Add the Numerators
Now add the numerators (5 + 36 = 41) and keep the common denominator 45 unchanged.
5 + 36/45 = 41/45
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 45 is 1, confirming that 41/45 cannot be reduced further—it is already in its simplest irreducible form.
41/45
Step 5
Decimal & Percentage Representation
Dividing the numerator 41 by denominator 45 produces a repeating decimal (approximately 0.911111, or 91.1111%).
41 ÷ 45 = 0.911111 (91.1111%)
Visual Representation
The diagram below illustrates 1/9 plus 4/5 visually:
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=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 41/45 |
| Mixed Number Form | 41/45 |
| Decimal Form | 0.911111 |
| Percentage | 91.1111% |
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Frequently Asked Questions
What is 1/9 plus 4/5 as a fraction?
1/9 + 4/5 in simplest fraction form is 41/45.
What is 1/9 plus 4/5 as a decimal?
1/9 + 4/5 converted to a decimal is 0.911111.
What is 1/9 plus 4/5 as a percentage?
1/9 + 4/5 expressed as a percentage is 91.1111%.
Does 1/9 plus 4/5 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.911111...) because the denominator contains prime factors other than 2 and 5.