What is 4/23 plus 4/9?
4/23 plus 4/9 equals 128/207 (or 0.618357 in decimal form). Learn the step-by-step solution to add 4/23 and 4/9 using Least Common Denominator and simplification.
Exact Answer
4/23 + 4/9 = 128/207
Simplified Fraction
128/207
Mixed Number
Proper (128/207)
Decimal Value
0.618357
Percentage
61.8357%
Step-by-Step Solution: 4/23 + 4/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 23 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 9 = 207.
LCD(23, 9) = 207
Step 2
Convert to Equivalent Fractions with Common Denominator 207
Multiply the numerator and denominator of 4/23 by 9, and multiply the numerator and denominator of 4/9 by 23 so both fractions share the common base 207.
4 × 9/23 × 9 = 36/207 and 4 × 23/9 × 23 = 92/207
Step 3
Add the Numerators
Now add the numerators (36 + 92 = 128) and keep the common denominator 207 unchanged.
36 + 92/207 = 128/207
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 128 and 207 is 1, confirming that 128/207 cannot be reduced further—it is already in its simplest irreducible form.
128/207
Step 5
Decimal & Percentage Representation
Dividing the numerator 128 by denominator 207 produces a repeating decimal (approximately 0.618357, or 61.8357%).
128 ÷ 207 = 0.618357 (61.8357%)
Visual Representation
The diagram below illustrates 4/23 plus 4/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 128/207 |
| Mixed Number Form | 128/207 |
| Decimal Form | 0.618357 |
| Percentage | 61.8357% |
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Frequently Asked Questions
What is 4/23 plus 4/9 as a fraction?
4/23 + 4/9 in simplest fraction form is 128/207.
What is 4/23 plus 4/9 as a decimal?
4/23 + 4/9 converted to a decimal is 0.618357.
What is 4/23 plus 4/9 as a percentage?
4/23 + 4/9 expressed as a percentage is 61.8357%.
Does 4/23 plus 4/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.618357...) because the denominator contains prime factors other than 2 and 5.