What is 9/23 plus 5/8?
9/23 plus 5/8 equals 187/184 (or 1 3/184 as a mixed number) (or 1.016304 in decimal form). Learn the step-by-step solution to add 9/23 and 5/8 using Least Common Denominator and simplification.
Exact Answer
9/23 + 5/8 = 187/184
Simplified Fraction
187/184
Mixed Number
1 3/184
Decimal Value
1.016304
Percentage
101.6304%
Step-by-Step Solution: 9/23 + 5/8
Step 1
Find the Least Common Denominator (LCD)
The denominators 23 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 8 = 184.
LCD(23, 8) = 184
Step 2
Convert to Equivalent Fractions with Common Denominator 184
Multiply the numerator and denominator of 9/23 by 8, and multiply the numerator and denominator of 5/8 by 23 so both fractions share the common base 184.
9 × 8/23 × 8 = 72/184 and 5 × 23/8 × 23 = 115/184
Step 3
Add the Numerators
Now add the numerators (72 + 115 = 187) and keep the common denominator 184 unchanged.
72 + 115/184 = 187/184
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 187 and 184 is 1, confirming that 187/184 cannot be reduced further—it is already in its simplest irreducible form.
187/184
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (187) is greater than the denominator (184), divide 187 by 184: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/184.
187/184 = 13/184
Step 6
Decimal & Percentage Representation
Dividing the numerator 187 by denominator 184 produces a repeating decimal (approximately 1.016304, or 101.6304%).
187 ÷ 184 = 1.016304 (101.6304%)
Visual Representation
The diagram below illustrates 9/23 plus 5/8 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 187/184 |
| Mixed Number Form | 1 3/184 |
| Decimal Form | 1.016304 |
| Percentage | 101.6304% |
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Frequently Asked Questions
What is 9/23 plus 5/8 as a fraction?
9/23 + 5/8 in simplest fraction form is 187/184 (or 1 3/184 as a mixed number).
What is 9/23 plus 5/8 as a decimal?
9/23 + 5/8 converted to a decimal is 1.016304.
What is 9/23 plus 5/8 as a percentage?
9/23 + 5/8 expressed as a percentage is 101.6304%.
How do you write 9/23 plus 5/8 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 187/184 can be written as the mixed number 1 3/184.
Does 9/23 plus 5/8 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.016304...) because the denominator contains prime factors other than 2 and 5.