What is 24/45 plus 9/13? (Answer: 239/195)

Exact Answer

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Problem: What is 24/45 plus 9/13?
Formula / Expression: 24/45 + 9/13
Final Answer: 1 44/195 (239/195)
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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 24/45 by 13, and multiply the numerator and denominator of 9/13 by 45 so both fractions share the common base 585.
Working: 24 × 13/45 × 13 = 312/585 and 9 × 45/13 × 45 = 405/585

Step 3: Add the Numerators
Now add the numerators (312 + 405 = 717) and keep the common denominator 585 unchanged.
Working: 312 + 405/585 = 717/585

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 717 and 585, which is 3. Divide both the numerator and denominator by 3.
Working: 717 ÷ 3/585 ÷ 3 = 239/195

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (239) is greater than the denominator (195), divide 239 by 195: it goes in 1 whole time(s) with a remainder of 44, giving the mixed number 1 44/195.
Working: 239/195 = 1 44/195

Step 6: Decimal & Percentage Representation
Dividing the numerator 239 by denominator 195 produces a repeating decimal (approximately 1.225641, or 122.5641%).
Working: 239 ÷ 195 = 1.225641 (122.5641%)

Key Values:
- Simplified Fraction: 239/195
- Mixed Number Form: 1 44/195
- Decimal Value: 1.225641
- Percentage: 122.5641%

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Solved with FractionsCalc:
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24/45 + 9/13 = 239/195

Simplified Fraction

239/195

Mixed Number

1 44/195

Decimal Value

1.225641

Percentage

122.5641%

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Step-by-Step Solution: 24/45 + 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 24/45 by 13, and multiply the numerator and denominator of 9/13 by 45 so both fractions share the common base 585.

24 × 13/45 × 13 = 312/585 and 9 × 45/13 × 45 = 405/585

Step 3

Add the Numerators

Now add the numerators (312 + 405 = 717) and keep the common denominator 585 unchanged.

312 + 405/585 = 717/585

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 717 and 585, which is 3. Divide both the numerator and denominator by 3.

717 ÷ 3/585 ÷ 3 = 239/195

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (239) is greater than the denominator (195), divide 239 by 195: it goes in 1 whole time(s) with a remainder of 44, giving the mixed number 1 44/195.

239/195 = 144/195

Step 6

Decimal & Percentage Representation

Dividing the numerator 239 by denominator 195 produces a repeating decimal (approximately 1.225641, or 122.5641%).

239 ÷ 195 = 1.225641 (122.5641%)

Visual Representation

The diagram below illustrates 24/45 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`239/195`
Mixed Number Form	`1 44/195`
Decimal Form	`1.225641`
Percentage	`122.5641%`

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Frequently Asked Questions

What is 24/45 plus 9/13 as a fraction?

24/45 + 9/13 in simplest fraction form is 239/195 (or 1 44/195 as a mixed number).

What is 24/45 plus 9/13 as a decimal?

24/45 + 9/13 converted to a decimal is 1.225641.

What is 24/45 plus 9/13 as a percentage?

24/45 + 9/13 expressed as a percentage is 122.5641%.

How do you write 24/45 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 239/195 can be written as the mixed number 1 44/195.

Does 24/45 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.225641...) because the denominator contains prime factors other than 2 and 5.