What is 27/40 plus 9/13?
27/40 plus 9/13 equals 711/520 (or 1 191/520 as a mixed number) (or 1.367308 in decimal form). Learn the step-by-step solution to add 27/40 and 9/13 using Least Common Denominator and simplification.
Exact Answer
27/40 + 9/13 = 711/520
Simplified Fraction
711/520
Mixed Number
1 191/520
Decimal Value
1.367308
Percentage
136.7308%
Step-by-Step Solution: 27/40 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.
LCD(40, 13) = 520
Step 2
Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 27/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.
27 × 13/40 × 13 = 351/520 and 9 × 40/13 × 40 = 360/520
Step 3
Add the Numerators
Now add the numerators (351 + 360 = 711) and keep the common denominator 520 unchanged.
351 + 360/520 = 711/520
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 711 and 520 is 1, confirming that 711/520 cannot be reduced further—it is already in its simplest irreducible form.
711/520
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (711) is greater than the denominator (520), divide 711 by 520: it goes in 1 whole time(s) with a remainder of 191, giving the mixed number 1 191/520.
711/520 = 1191/520
Step 6
Decimal & Percentage Representation
Dividing the numerator 711 by denominator 520 produces a repeating decimal (approximately 1.367308, or 136.7308%).
711 ÷ 520 = 1.367308 (136.7308%)
Visual Representation
The diagram below illustrates 27/40 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 711/520 |
| Mixed Number Form | 1 191/520 |
| Decimal Form | 1.367308 |
| Percentage | 136.7308% |
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Frequently Asked Questions
What is 27/40 plus 9/13 as a fraction?
27/40 + 9/13 in simplest fraction form is 711/520 (or 1 191/520 as a mixed number).
What is 27/40 plus 9/13 as a decimal?
27/40 + 9/13 converted to a decimal is 1.367308.
What is 27/40 plus 9/13 as a percentage?
27/40 + 9/13 expressed as a percentage is 136.7308%.
How do you write 27/40 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 711/520 can be written as the mixed number 1 191/520.
Does 27/40 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.367308...) because the denominator contains prime factors other than 2 and 5.