What is 13/40 plus 9/13? (Answer: 529/520)

Exact Answer

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Problem: What is 13/40 plus 9/13?
Formula / Expression: 13/40 + 9/13
Final Answer: 1 9/520 (529/520)
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Step-by-Step Solution:

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.
Working: LCD(40, 13) = 520

Step 2: Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 13/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.
Working: 13 × 13/40 × 13 = 169/520 and 9 × 40/13 × 40 = 360/520

Step 3: Add the Numerators
Now add the numerators (169 + 360 = 529) and keep the common denominator 520 unchanged.
Working: 169 + 360/520 = 529/520

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 529 and 520 is 1, confirming that 529/520 cannot be reduced further—it is already in its simplest irreducible form.
Working: 529/520

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (529) is greater than the denominator (520), divide 529 by 520: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/520.
Working: 529/520 = 1 9/520

Step 6: Decimal & Percentage Representation
Dividing the numerator 529 by denominator 520 produces a repeating decimal (approximately 1.017308, or 101.7308%).
Working: 529 ÷ 520 = 1.017308 (101.7308%)

Key Values:
- Simplified Fraction: 529/520
- Mixed Number Form: 1 9/520
- Decimal Value: 1.017308
- Percentage: 101.7308%

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Solved with FractionsCalc:
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13/40 + 9/13 = 529/520

Simplified Fraction

529/520

Mixed Number

1 9/520

Decimal Value

1.017308

Percentage

101.7308%

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Step-by-Step Solution: 13/40 + 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 13/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.

13 × 13/40 × 13 = 169/520 and 9 × 40/13 × 40 = 360/520

Step 3

Add the Numerators

Now add the numerators (169 + 360 = 529) and keep the common denominator 520 unchanged.

169 + 360/520 = 529/520

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 529 and 520 is 1, confirming that 529/520 cannot be reduced further—it is already in its simplest irreducible form.

529/520

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (529) is greater than the denominator (520), divide 529 by 520: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/520.

529/520 = 19/520

Step 6

Decimal & Percentage Representation

Dividing the numerator 529 by denominator 520 produces a repeating decimal (approximately 1.017308, or 101.7308%).

529 ÷ 520 = 1.017308 (101.7308%)

Visual Representation

The diagram below illustrates 13/40 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`529/520`
Mixed Number Form	`1 9/520`
Decimal Form	`1.017308`
Percentage	`101.7308%`

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Frequently Asked Questions

What is 13/40 plus 9/13 as a fraction?

13/40 + 9/13 in simplest fraction form is 529/520 (or 1 9/520 as a mixed number).

What is 13/40 plus 9/13 as a decimal?

13/40 + 9/13 converted to a decimal is 1.017308.

What is 13/40 plus 9/13 as a percentage?

13/40 + 9/13 expressed as a percentage is 101.7308%.

How do you write 13/40 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 529/520 can be written as the mixed number 1 9/520.

Does 13/40 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.017308...) because the denominator contains prime factors other than 2 and 5.