What is 23/40 plus 9/13? (Answer: 659/520)

Exact Answer

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Problem: What is 23/40 plus 9/13?
Formula / Expression: 23/40 + 9/13
Final Answer: 1 139/520 (659/520)
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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 23/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.
Working: 23 × 13/40 × 13 = 299/520 and 9 × 40/13 × 40 = 360/520

Step 3: Add the Numerators
Now add the numerators (299 + 360 = 659) and keep the common denominator 520 unchanged.
Working: 299 + 360/520 = 659/520

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 659 and 520 is 1, confirming that 659/520 cannot be reduced further—it is already in its simplest irreducible form.
Working: 659/520

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (659) is greater than the denominator (520), divide 659 by 520: it goes in 1 whole time(s) with a remainder of 139, giving the mixed number 1 139/520.
Working: 659/520 = 1 139/520

Step 6: Decimal & Percentage Representation
Dividing the numerator 659 by denominator 520 produces a repeating decimal (approximately 1.267308, or 126.7308%).
Working: 659 ÷ 520 = 1.267308 (126.7308%)

Key Values:
- Simplified Fraction: 659/520
- Mixed Number Form: 1 139/520
- Decimal Value: 1.267308
- Percentage: 126.7308%

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Solved with FractionsCalc:
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23/40 + 9/13 = 659/520

Simplified Fraction

659/520

Mixed Number

1 139/520

Decimal Value

1.267308

Percentage

126.7308%

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Step-by-Step Solution: 23/40 + 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 23/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.

23 × 13/40 × 13 = 299/520 and 9 × 40/13 × 40 = 360/520

Step 3

Add the Numerators

Now add the numerators (299 + 360 = 659) and keep the common denominator 520 unchanged.

299 + 360/520 = 659/520

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 659 and 520 is 1, confirming that 659/520 cannot be reduced further—it is already in its simplest irreducible form.

659/520

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (659) is greater than the denominator (520), divide 659 by 520: it goes in 1 whole time(s) with a remainder of 139, giving the mixed number 1 139/520.

659/520 = 1139/520

Step 6

Decimal & Percentage Representation

Dividing the numerator 659 by denominator 520 produces a repeating decimal (approximately 1.267308, or 126.7308%).

659 ÷ 520 = 1.267308 (126.7308%)

Visual Representation

The diagram below illustrates 23/40 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`659/520`
Mixed Number Form	`1 139/520`
Decimal Form	`1.267308`
Percentage	`126.7308%`

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Frequently Asked Questions

What is 23/40 plus 9/13 as a fraction?

23/40 + 9/13 in simplest fraction form is 659/520 (or 1 139/520 as a mixed number).

What is 23/40 plus 9/13 as a decimal?

23/40 + 9/13 converted to a decimal is 1.267308.

What is 23/40 plus 9/13 as a percentage?

23/40 + 9/13 expressed as a percentage is 126.7308%.

How do you write 23/40 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 659/520 can be written as the mixed number 1 139/520.

Does 23/40 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.267308...) because the denominator contains prime factors other than 2 and 5.