What is 25/47 plus 9/13? (Answer: 748/611)

Exact Answer

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Problem: What is 25/47 plus 9/13?
Formula / Expression: 25/47 + 9/13
Final Answer: 1 137/611 (748/611)
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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 25/47 by 13, and multiply the numerator and denominator of 9/13 by 47 so both fractions share the common base 611.
Working: 25 × 13/47 × 13 = 325/611 and 9 × 47/13 × 47 = 423/611

Step 3: Add the Numerators
Now add the numerators (325 + 423 = 748) and keep the common denominator 611 unchanged.
Working: 325 + 423/611 = 748/611

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 748 and 611 is 1, confirming that 748/611 cannot be reduced further—it is already in its simplest irreducible form.
Working: 748/611

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (748) is greater than the denominator (611), divide 748 by 611: it goes in 1 whole time(s) with a remainder of 137, giving the mixed number 1 137/611.
Working: 748/611 = 1 137/611

Step 6: Decimal & Percentage Representation
Dividing the numerator 748 by denominator 611 produces a repeating decimal (approximately 1.224223, or 122.4223%).
Working: 748 ÷ 611 = 1.224223 (122.4223%)

Key Values:
- Simplified Fraction: 748/611
- Mixed Number Form: 1 137/611
- Decimal Value: 1.224223
- Percentage: 122.4223%

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Solved with FractionsCalc:
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25/47 + 9/13 = 748/611

Simplified Fraction

748/611

Mixed Number

1 137/611

Decimal Value

1.224223

Percentage

122.4223%

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Step-by-Step Solution: 25/47 + 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 25/47 by 13, and multiply the numerator and denominator of 9/13 by 47 so both fractions share the common base 611.

25 × 13/47 × 13 = 325/611 and 9 × 47/13 × 47 = 423/611

Step 3

Add the Numerators

Now add the numerators (325 + 423 = 748) and keep the common denominator 611 unchanged.

325 + 423/611 = 748/611

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 748 and 611 is 1, confirming that 748/611 cannot be reduced further—it is already in its simplest irreducible form.

748/611

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (748) is greater than the denominator (611), divide 748 by 611: it goes in 1 whole time(s) with a remainder of 137, giving the mixed number 1 137/611.

748/611 = 1137/611

Step 6

Decimal & Percentage Representation

Dividing the numerator 748 by denominator 611 produces a repeating decimal (approximately 1.224223, or 122.4223%).

748 ÷ 611 = 1.224223 (122.4223%)

Visual Representation

The diagram below illustrates 25/47 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`748/611`
Mixed Number Form	`1 137/611`
Decimal Form	`1.224223`
Percentage	`122.4223%`

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Frequently Asked Questions

What is 25/47 plus 9/13 as a fraction?

25/47 + 9/13 in simplest fraction form is 748/611 (or 1 137/611 as a mixed number).

What is 25/47 plus 9/13 as a decimal?

25/47 + 9/13 converted to a decimal is 1.224223.

What is 25/47 plus 9/13 as a percentage?

25/47 + 9/13 expressed as a percentage is 122.4223%.

How do you write 25/47 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 748/611 can be written as the mixed number 1 137/611.

Does 25/47 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.224223...) because the denominator contains prime factors other than 2 and 5.