What is 9/23 plus 3/4?
9/23 plus 3/4 equals 105/92 (or 1 13/92 as a mixed number) (or 1.141304 in decimal form). Learn the step-by-step solution to add 9/23 and 3/4 using Least Common Denominator and simplification.
Exact Answer
9/23 + 3/4 = 105/92
Simplified Fraction
105/92
Mixed Number
1 13/92
Decimal Value
1.141304
Percentage
114.1304%
Step-by-Step Solution: 9/23 + 3/4
Step 1
Find the Least Common Denominator (LCD)
The denominators 23 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 4 = 92.
LCD(23, 4) = 92
Step 2
Convert to Equivalent Fractions with Common Denominator 92
Multiply the numerator and denominator of 9/23 by 4, and multiply the numerator and denominator of 3/4 by 23 so both fractions share the common base 92.
9 × 4/23 × 4 = 36/92 and 3 × 23/4 × 23 = 69/92
Step 3
Add the Numerators
Now add the numerators (36 + 69 = 105) and keep the common denominator 92 unchanged.
36 + 69/92 = 105/92
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 105 and 92 is 1, confirming that 105/92 cannot be reduced further—it is already in its simplest irreducible form.
105/92
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (105) is greater than the denominator (92), divide 105 by 92: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/92.
105/92 = 113/92
Step 6
Decimal & Percentage Representation
Dividing the numerator 105 by denominator 92 produces a repeating decimal (approximately 1.141304, or 114.1304%).
105 ÷ 92 = 1.141304 (114.1304%)
Visual Representation
The diagram below illustrates 9/23 plus 3/4 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 105/92 |
| Mixed Number Form | 1 13/92 |
| Decimal Form | 1.141304 |
| Percentage | 114.1304% |
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Frequently Asked Questions
What is 9/23 plus 3/4 as a fraction?
9/23 + 3/4 in simplest fraction form is 105/92 (or 1 13/92 as a mixed number).
What is 9/23 plus 3/4 as a decimal?
9/23 + 3/4 converted to a decimal is 1.141304.
What is 9/23 plus 3/4 as a percentage?
9/23 + 3/4 expressed as a percentage is 114.1304%.
How do you write 9/23 plus 3/4 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 105/92 can be written as the mixed number 1 13/92.
Does 9/23 plus 3/4 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.141304...) because the denominator contains prime factors other than 2 and 5.