What is 5/13 plus 3/4?
5/13 plus 3/4 equals 59/52 (or 1 7/52 as a mixed number) (or 1.134615 in decimal form). Learn the step-by-step solution to add 5/13 and 3/4 using Least Common Denominator and simplification.
Exact Answer
5/13 + 3/4 = 59/52
Simplified Fraction
59/52
Mixed Number
1 7/52
Decimal Value
1.134615
Percentage
113.4615%
Step-by-Step Solution: 5/13 + 3/4
Step 1
Find the Least Common Denominator (LCD)
The denominators 13 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 4 = 52.
LCD(13, 4) = 52
Step 2
Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 5/13 by 4, and multiply the numerator and denominator of 3/4 by 13 so both fractions share the common base 52.
5 × 4/13 × 4 = 20/52 and 3 × 13/4 × 13 = 39/52
Step 3
Add the Numerators
Now add the numerators (20 + 39 = 59) and keep the common denominator 52 unchanged.
20 + 39/52 = 59/52
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 52 is 1, confirming that 59/52 cannot be reduced further—it is already in its simplest irreducible form.
59/52
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (52), divide 59 by 52: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/52.
59/52 = 17/52
Step 6
Decimal & Percentage Representation
Dividing the numerator 59 by denominator 52 produces a repeating decimal (approximately 1.134615, or 113.4615%).
59 ÷ 52 = 1.134615 (113.4615%)
Visual Representation
The diagram below illustrates 5/13 plus 3/4 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 59/52 |
| Mixed Number Form | 1 7/52 |
| Decimal Form | 1.134615 |
| Percentage | 113.4615% |
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Frequently Asked Questions
What is 5/13 plus 3/4 as a fraction?
5/13 + 3/4 in simplest fraction form is 59/52 (or 1 7/52 as a mixed number).
What is 5/13 plus 3/4 as a decimal?
5/13 + 3/4 converted to a decimal is 1.134615.
What is 5/13 plus 3/4 as a percentage?
5/13 + 3/4 expressed as a percentage is 113.4615%.
How do you write 5/13 plus 3/4 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 59/52 can be written as the mixed number 1 7/52.
Does 5/13 plus 3/4 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.134615...) because the denominator contains prime factors other than 2 and 5.