What is 2/4 plus 13/23?
2/4 plus 13/23 equals 49/46 (or 1 3/46 as a mixed number) (or 1.065217 in decimal form). Learn the step-by-step solution to add 2/4 and 13/23 using Least Common Denominator and simplification.
Exact Answer
2/4 + 13/23 = 49/46
Simplified Fraction
49/46
Mixed Number
1 3/46
Decimal Value
1.065217
Percentage
106.5217%
Step-by-Step Solution: 2/4 + 13/23
Step 1
Find the Least Common Denominator (LCD)
The denominators 4 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 23 = 92.
LCD(4, 23) = 92
Step 2
Convert to Equivalent Fractions with Common Denominator 92
Multiply the numerator and denominator of 2/4 by 23, and multiply the numerator and denominator of 13/23 by 4 so both fractions share the common base 92.
2 × 23/4 × 23 = 46/92 and 13 × 4/23 × 4 = 52/92
Step 3
Add the Numerators
Now add the numerators (46 + 52 = 98) and keep the common denominator 92 unchanged.
46 + 52/92 = 98/92
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 98 and 92, which is 2. Divide both the numerator and denominator by 2.
98 ÷ 2/92 ÷ 2 = 49/46
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (49) is greater than the denominator (46), divide 49 by 46: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/46.
49/46 = 13/46
Step 6
Decimal & Percentage Representation
Dividing the numerator 49 by denominator 46 produces a repeating decimal (approximately 1.065217, or 106.5217%).
49 ÷ 46 = 1.065217 (106.5217%)
Visual Representation
The diagram below illustrates 2/4 plus 13/23 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 49/46 |
| Mixed Number Form | 1 3/46 |
| Decimal Form | 1.065217 |
| Percentage | 106.5217% |
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Frequently Asked Questions
What is 2/4 plus 13/23 as a fraction?
2/4 + 13/23 in simplest fraction form is 49/46 (or 1 3/46 as a mixed number).
What is 2/4 plus 13/23 as a decimal?
2/4 + 13/23 converted to a decimal is 1.065217.
What is 2/4 plus 13/23 as a percentage?
2/4 + 13/23 expressed as a percentage is 106.5217%.
How do you write 2/4 plus 13/23 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 49/46 can be written as the mixed number 1 3/46.
Does 2/4 plus 13/23 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.065217...) because the denominator contains prime factors other than 2 and 5.