What is 2/4 plus 7/13?
2/4 plus 7/13 equals 27/26 (or 1 1/26 as a mixed number) (or 1.038462 in decimal form). Learn the step-by-step solution to add 2/4 and 7/13 using Least Common Denominator and simplification.
Exact Answer
2/4 + 7/13 = 27/26
Simplified Fraction
27/26
Mixed Number
1 1/26
Decimal Value
1.038462
Percentage
103.8462%
Step-by-Step Solution: 2/4 + 7/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 4 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 13 = 52.
LCD(4, 13) = 52
Step 2
Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 2/4 by 13, and multiply the numerator and denominator of 7/13 by 4 so both fractions share the common base 52.
2 × 13/4 × 13 = 26/52 and 7 × 4/13 × 4 = 28/52
Step 3
Add the Numerators
Now add the numerators (26 + 28 = 54) and keep the common denominator 52 unchanged.
26 + 28/52 = 54/52
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 54 and 52, which is 2. Divide both the numerator and denominator by 2.
54 ÷ 2/52 ÷ 2 = 27/26
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (27) is greater than the denominator (26), divide 27 by 26: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/26.
27/26 = 11/26
Step 6
Decimal & Percentage Representation
Dividing the numerator 27 by denominator 26 produces a repeating decimal (approximately 1.038462, or 103.8462%).
27 ÷ 26 = 1.038462 (103.8462%)
Visual Representation
The diagram below illustrates 2/4 plus 7/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 27/26 |
| Mixed Number Form | 1 1/26 |
| Decimal Form | 1.038462 |
| Percentage | 103.8462% |
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Frequently Asked Questions
What is 2/4 plus 7/13 as a fraction?
2/4 + 7/13 in simplest fraction form is 27/26 (or 1 1/26 as a mixed number).
What is 2/4 plus 7/13 as a decimal?
2/4 + 7/13 converted to a decimal is 1.038462.
What is 2/4 plus 7/13 as a percentage?
2/4 + 7/13 expressed as a percentage is 103.8462%.
How do you write 2/4 plus 7/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 27/26 can be written as the mixed number 1 1/26.
Does 2/4 plus 7/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.038462...) because the denominator contains prime factors other than 2 and 5.