What is 19/40 plus 7/13?
19/40 plus 7/13 equals 527/520 (or 1 7/520 as a mixed number) (or 1.013462 in decimal form). Learn the step-by-step solution to add 19/40 and 7/13 using Least Common Denominator and simplification.
Exact Answer
19/40 + 7/13 = 527/520
Simplified Fraction
527/520
Mixed Number
1 7/520
Decimal Value
1.013462
Percentage
101.3462%
Step-by-Step Solution: 19/40 + 7/13
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 19/40 by 13, and multiply the numerator and denominator of 7/13 by 40 so both fractions share the common base 520.
19 × 13/40 × 13 = 247/520 and 7 × 40/13 × 40 = 280/520
Step 3
Add the Numerators
Now add the numerators (247 + 280 = 527) and keep the common denominator 520 unchanged.
247 + 280/520 = 527/520
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 527 and 520 is 1, confirming that 527/520 cannot be reduced further—it is already in its simplest irreducible form.
527/520
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (527) is greater than the denominator (520), divide 527 by 520: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/520.
527/520 = 17/520
Step 6
Decimal & Percentage Representation
Dividing the numerator 527 by denominator 520 produces a repeating decimal (approximately 1.013462, or 101.3462%).
527 ÷ 520 = 1.013462 (101.3462%)
Visual Representation
The diagram below illustrates 19/40 plus 7/13 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 527/520 |
| Mixed Number Form | 1 7/520 |
| Decimal Form | 1.013462 |
| Percentage | 101.3462% |
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Frequently Asked Questions
What is 19/40 plus 7/13 as a fraction?
19/40 + 7/13 in simplest fraction form is 527/520 (or 1 7/520 as a mixed number).
What is 19/40 plus 7/13 as a decimal?
19/40 + 7/13 converted to a decimal is 1.013462.
What is 19/40 plus 7/13 as a percentage?
19/40 + 7/13 expressed as a percentage is 101.3462%.
How do you write 19/40 plus 7/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 527/520 can be written as the mixed number 1 7/520.
Does 19/40 plus 7/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.013462...) because the denominator contains prime factors other than 2 and 5.