What is 7/13 plus 3/5?
7/13 plus 3/5 equals 74/65 (or 1 9/65 as a mixed number) (or 1.138462 in decimal form). Learn the step-by-step solution to add 7/13 and 3/5 using Least Common Denominator and simplification.
Exact Answer
7/13 + 3/5 = 74/65
Simplified Fraction
74/65
Mixed Number
1 9/65
Decimal Value
1.138462
Percentage
113.8462%
Step-by-Step Solution: 7/13 + 3/5
Step 1
Find the Least Common Denominator (LCD)
The denominators 13 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 5 = 65.
LCD(13, 5) = 65
Step 2
Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 7/13 by 5, and multiply the numerator and denominator of 3/5 by 13 so both fractions share the common base 65.
7 × 5/13 × 5 = 35/65 and 3 × 13/5 × 13 = 39/65
Step 3
Add the Numerators
Now add the numerators (35 + 39 = 74) and keep the common denominator 65 unchanged.
35 + 39/65 = 74/65
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 74 and 65 is 1, confirming that 74/65 cannot be reduced further—it is already in its simplest irreducible form.
74/65
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (74) is greater than the denominator (65), divide 74 by 65: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/65.
74/65 = 19/65
Step 6
Decimal & Percentage Representation
Dividing the numerator 74 by denominator 65 produces a repeating decimal (approximately 1.138462, or 113.8462%).
74 ÷ 65 = 1.138462 (113.8462%)
Visual Representation
The diagram below illustrates 7/13 plus 3/5 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 74/65 |
| Mixed Number Form | 1 9/65 |
| Decimal Form | 1.138462 |
| Percentage | 113.8462% |
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Frequently Asked Questions
What is 7/13 plus 3/5 as a fraction?
7/13 + 3/5 in simplest fraction form is 74/65 (or 1 9/65 as a mixed number).
What is 7/13 plus 3/5 as a decimal?
7/13 + 3/5 converted to a decimal is 1.138462.
What is 7/13 plus 3/5 as a percentage?
7/13 + 3/5 expressed as a percentage is 113.8462%.
How do you write 7/13 plus 3/5 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 74/65 can be written as the mixed number 1 9/65.
Does 7/13 plus 3/5 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.138462...) because the denominator contains prime factors other than 2 and 5.