What is 24/47 plus 9/13? (Answer: 735/611)

Exact Answer

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Problem: What is 24/47 plus 9/13?
Formula / Expression: 24/47 + 9/13
Final Answer: 1 124/611 (735/611)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 47 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 47 × 13 = 611.
Working: LCD(47, 13) = 611

Step 2: Convert to Equivalent Fractions with Common Denominator 611
Multiply the numerator and denominator of 24/47 by 13, and multiply the numerator and denominator of 9/13 by 47 so both fractions share the common base 611.
Working: 24 × 13/47 × 13 = 312/611 and 9 × 47/13 × 47 = 423/611

Step 3: Add the Numerators
Now add the numerators (312 + 423 = 735) and keep the common denominator 611 unchanged.
Working: 312 + 423/611 = 735/611

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 735 and 611 is 1, confirming that 735/611 cannot be reduced further—it is already in its simplest irreducible form.
Working: 735/611

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (735) is greater than the denominator (611), divide 735 by 611: it goes in 1 whole time(s) with a remainder of 124, giving the mixed number 1 124/611.
Working: 735/611 = 1 124/611

Step 6: Decimal & Percentage Representation
Dividing the numerator 735 by denominator 611 produces a repeating decimal (approximately 1.202946, or 120.2946%).
Working: 735 ÷ 611 = 1.202946 (120.2946%)

Key Values:
- Simplified Fraction: 735/611
- Mixed Number Form: 1 124/611
- Decimal Value: 1.202946
- Percentage: 120.2946%

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Solved with FractionsCalc:
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24/47 + 9/13 = 735/611

Simplified Fraction

735/611

Mixed Number

1 124/611

Decimal Value

1.202946

Percentage

120.2946%

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Step-by-Step Solution: 24/47 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 47 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 47 × 13 = 611.

LCD(47, 13) = 611

Step 2

Convert to Equivalent Fractions with Common Denominator 611

Multiply the numerator and denominator of 24/47 by 13, and multiply the numerator and denominator of 9/13 by 47 so both fractions share the common base 611.

24 × 13/47 × 13 = 312/611 and 9 × 47/13 × 47 = 423/611

Step 3

Add the Numerators

Now add the numerators (312 + 423 = 735) and keep the common denominator 611 unchanged.

312 + 423/611 = 735/611

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 735 and 611 is 1, confirming that 735/611 cannot be reduced further—it is already in its simplest irreducible form.

735/611

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (735) is greater than the denominator (611), divide 735 by 611: it goes in 1 whole time(s) with a remainder of 124, giving the mixed number 1 124/611.

735/611 = 1124/611

Step 6

Decimal & Percentage Representation

Dividing the numerator 735 by denominator 611 produces a repeating decimal (approximately 1.202946, or 120.2946%).

735 ÷ 611 = 1.202946 (120.2946%)

Visual Representation

The diagram below illustrates 24/47 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`735/611`
Mixed Number Form	`1 124/611`
Decimal Form	`1.202946`
Percentage	`120.2946%`

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Frequently Asked Questions

What is 24/47 plus 9/13 as a fraction?

24/47 + 9/13 in simplest fraction form is 735/611 (or 1 124/611 as a mixed number).

What is 24/47 plus 9/13 as a decimal?

24/47 + 9/13 converted to a decimal is 1.202946.

What is 24/47 plus 9/13 as a percentage?

24/47 + 9/13 expressed as a percentage is 120.2946%.

How do you write 24/47 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 735/611 can be written as the mixed number 1 124/611.

Does 24/47 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.202946...) because the denominator contains prime factors other than 2 and 5.