What is 9/13 plus 4/5?
9/13 plus 4/5 equals 97/65 (or 1 32/65 as a mixed number) (or 1.492308 in decimal form). Learn the step-by-step solution to add 9/13 and 4/5 using Least Common Denominator and simplification.
Exact Answer
9/13 + 4/5 = 97/65
Simplified Fraction
97/65
Mixed Number
1 32/65
Decimal Value
1.492308
Percentage
149.2308%
Step-by-Step Solution: 9/13 + 4/5
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 9/13 by 5, and multiply the numerator and denominator of 4/5 by 13 so both fractions share the common base 65.
9 × 5/13 × 5 = 45/65 and 4 × 13/5 × 13 = 52/65
Step 3
Add the Numerators
Now add the numerators (45 + 52 = 97) and keep the common denominator 65 unchanged.
45 + 52/65 = 97/65
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 65 is 1, confirming that 97/65 cannot be reduced further—it is already in its simplest irreducible form.
97/65
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (97) is greater than the denominator (65), divide 97 by 65: it goes in 1 whole time(s) with a remainder of 32, giving the mixed number 1 32/65.
97/65 = 132/65
Step 6
Decimal & Percentage Representation
Dividing the numerator 97 by denominator 65 produces a repeating decimal (approximately 1.492308, or 149.2308%).
97 ÷ 65 = 1.492308 (149.2308%)
Visual Representation
The diagram below illustrates 9/13 plus 4/5 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 97/65 |
| Mixed Number Form | 1 32/65 |
| Decimal Form | 1.492308 |
| Percentage | 149.2308% |
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Frequently Asked Questions
What is 9/13 plus 4/5 as a fraction?
9/13 + 4/5 in simplest fraction form is 97/65 (or 1 32/65 as a mixed number).
What is 9/13 plus 4/5 as a decimal?
9/13 + 4/5 converted to a decimal is 1.492308.
What is 9/13 plus 4/5 as a percentage?
9/13 + 4/5 expressed as a percentage is 149.2308%.
How do you write 9/13 plus 4/5 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 97/65 can be written as the mixed number 1 32/65.
Does 9/13 plus 4/5 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.492308...) because the denominator contains prime factors other than 2 and 5.