What is 23/45 plus 9/13? (Answer: 704/585)

Exact Answer

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Problem: What is 23/45 plus 9/13?
Formula / Expression: 23/45 + 9/13
Final Answer: 1 119/585 (704/585)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 45 × 13 = 585.
Working: LCD(45, 13) = 585

Step 2: Convert to Equivalent Fractions with Common Denominator 585
Multiply the numerator and denominator of 23/45 by 13, and multiply the numerator and denominator of 9/13 by 45 so both fractions share the common base 585.
Working: 23 × 13/45 × 13 = 299/585 and 9 × 45/13 × 45 = 405/585

Step 3: Add the Numerators
Now add the numerators (299 + 405 = 704) and keep the common denominator 585 unchanged.
Working: 299 + 405/585 = 704/585

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 704 and 585 is 1, confirming that 704/585 cannot be reduced further—it is already in its simplest irreducible form.
Working: 704/585

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (704) is greater than the denominator (585), divide 704 by 585: it goes in 1 whole time(s) with a remainder of 119, giving the mixed number 1 119/585.
Working: 704/585 = 1 119/585

Step 6: Decimal & Percentage Representation
Dividing the numerator 704 by denominator 585 produces a repeating decimal (approximately 1.203419, or 120.3419%).
Working: 704 ÷ 585 = 1.203419 (120.3419%)

Key Values:
- Simplified Fraction: 704/585
- Mixed Number Form: 1 119/585
- Decimal Value: 1.203419
- Percentage: 120.3419%

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Solved with FractionsCalc:
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23/45 + 9/13 = 704/585

Simplified Fraction

704/585

Mixed Number

1 119/585

Decimal Value

1.203419

Percentage

120.3419%

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Step-by-Step Solution: 23/45 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 45 × 13 = 585.

LCD(45, 13) = 585

Step 2

Convert to Equivalent Fractions with Common Denominator 585

Multiply the numerator and denominator of 23/45 by 13, and multiply the numerator and denominator of 9/13 by 45 so both fractions share the common base 585.

23 × 13/45 × 13 = 299/585 and 9 × 45/13 × 45 = 405/585

Step 3

Add the Numerators

Now add the numerators (299 + 405 = 704) and keep the common denominator 585 unchanged.

299 + 405/585 = 704/585

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 704 and 585 is 1, confirming that 704/585 cannot be reduced further—it is already in its simplest irreducible form.

704/585

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (704) is greater than the denominator (585), divide 704 by 585: it goes in 1 whole time(s) with a remainder of 119, giving the mixed number 1 119/585.

704/585 = 1119/585

Step 6

Decimal & Percentage Representation

Dividing the numerator 704 by denominator 585 produces a repeating decimal (approximately 1.203419, or 120.3419%).

704 ÷ 585 = 1.203419 (120.3419%)

Visual Representation

The diagram below illustrates 23/45 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`704/585`
Mixed Number Form	`1 119/585`
Decimal Form	`1.203419`
Percentage	`120.3419%`

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Frequently Asked Questions

What is 23/45 plus 9/13 as a fraction?

23/45 + 9/13 in simplest fraction form is 704/585 (or 1 119/585 as a mixed number).

What is 23/45 plus 9/13 as a decimal?

23/45 + 9/13 converted to a decimal is 1.203419.

What is 23/45 plus 9/13 as a percentage?

23/45 + 9/13 expressed as a percentage is 120.3419%.

How do you write 23/45 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 704/585 can be written as the mixed number 1 119/585.

Does 23/45 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.203419...) because the denominator contains prime factors other than 2 and 5.