What is 23/44 plus 9/13?
23/44 plus 9/13 equals 695/572 (or 1 123/572 as a mixed number) (or 1.215035 in decimal form). Learn the step-by-step solution to add 23/44 and 9/13 using Least Common Denominator and simplification.
Exact Answer
23/44 + 9/13 = 695/572
Simplified Fraction
695/572
Mixed Number
1 123/572
Decimal Value
1.215035
Percentage
121.5035%
Step-by-Step Solution: 23/44 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 44 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 44 × 13 = 572.
LCD(44, 13) = 572
Step 2
Convert to Equivalent Fractions with Common Denominator 572
Multiply the numerator and denominator of 23/44 by 13, and multiply the numerator and denominator of 9/13 by 44 so both fractions share the common base 572.
23 × 13/44 × 13 = 299/572 and 9 × 44/13 × 44 = 396/572
Step 3
Add the Numerators
Now add the numerators (299 + 396 = 695) and keep the common denominator 572 unchanged.
299 + 396/572 = 695/572
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 695 and 572 is 1, confirming that 695/572 cannot be reduced further—it is already in its simplest irreducible form.
695/572
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (695) is greater than the denominator (572), divide 695 by 572: it goes in 1 whole time(s) with a remainder of 123, giving the mixed number 1 123/572.
695/572 = 1123/572
Step 6
Decimal & Percentage Representation
Dividing the numerator 695 by denominator 572 produces a repeating decimal (approximately 1.215035, or 121.5035%).
695 ÷ 572 = 1.215035 (121.5035%)
Visual Representation
The diagram below illustrates 23/44 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 695/572 |
| Mixed Number Form | 1 123/572 |
| Decimal Form | 1.215035 |
| Percentage | 121.5035% |
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Frequently Asked Questions
What is 23/44 plus 9/13 as a fraction?
23/44 + 9/13 in simplest fraction form is 695/572 (or 1 123/572 as a mixed number).
What is 23/44 plus 9/13 as a decimal?
23/44 + 9/13 converted to a decimal is 1.215035.
What is 23/44 plus 9/13 as a percentage?
23/44 + 9/13 expressed as a percentage is 121.5035%.
How do you write 23/44 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 695/572 can be written as the mixed number 1 123/572.
Does 23/44 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.215035...) because the denominator contains prime factors other than 2 and 5.