What is 25/48 plus 9/13? (Answer: 757/624)

Exact Answer

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Problem: What is 25/48 plus 9/13?
Formula / Expression: 25/48 + 9/13
Final Answer: 1 133/624 (757/624)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 48 × 13 = 624.
Working: LCD(48, 13) = 624

Step 2: Convert to Equivalent Fractions with Common Denominator 624
Multiply the numerator and denominator of 25/48 by 13, and multiply the numerator and denominator of 9/13 by 48 so both fractions share the common base 624.
Working: 25 × 13/48 × 13 = 325/624 and 9 × 48/13 × 48 = 432/624

Step 3: Add the Numerators
Now add the numerators (325 + 432 = 757) and keep the common denominator 624 unchanged.
Working: 325 + 432/624 = 757/624

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 757 and 624 is 1, confirming that 757/624 cannot be reduced further—it is already in its simplest irreducible form.
Working: 757/624

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (757) is greater than the denominator (624), divide 757 by 624: it goes in 1 whole time(s) with a remainder of 133, giving the mixed number 1 133/624.
Working: 757/624 = 1 133/624

Step 6: Decimal & Percentage Representation
Dividing the numerator 757 by denominator 624 produces a repeating decimal (approximately 1.213141, or 121.3141%).
Working: 757 ÷ 624 = 1.213141 (121.3141%)

Key Values:
- Simplified Fraction: 757/624
- Mixed Number Form: 1 133/624
- Decimal Value: 1.213141
- Percentage: 121.3141%

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Solved with FractionsCalc:
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25/48 + 9/13 = 757/624

Simplified Fraction

757/624

Mixed Number

1 133/624

Decimal Value

1.213141

Percentage

121.3141%

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Step-by-Step Solution: 25/48 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 48 × 13 = 624.

LCD(48, 13) = 624

Step 2

Convert to Equivalent Fractions with Common Denominator 624

Multiply the numerator and denominator of 25/48 by 13, and multiply the numerator and denominator of 9/13 by 48 so both fractions share the common base 624.

25 × 13/48 × 13 = 325/624 and 9 × 48/13 × 48 = 432/624

Step 3

Add the Numerators

Now add the numerators (325 + 432 = 757) and keep the common denominator 624 unchanged.

325 + 432/624 = 757/624

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 757 and 624 is 1, confirming that 757/624 cannot be reduced further—it is already in its simplest irreducible form.

757/624

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (757) is greater than the denominator (624), divide 757 by 624: it goes in 1 whole time(s) with a remainder of 133, giving the mixed number 1 133/624.

757/624 = 1133/624

Step 6

Decimal & Percentage Representation

Dividing the numerator 757 by denominator 624 produces a repeating decimal (approximately 1.213141, or 121.3141%).

757 ÷ 624 = 1.213141 (121.3141%)

Visual Representation

The diagram below illustrates 25/48 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`757/624`
Mixed Number Form	`1 133/624`
Decimal Form	`1.213141`
Percentage	`121.3141%`

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Frequently Asked Questions

What is 25/48 plus 9/13 as a fraction?

25/48 + 9/13 in simplest fraction form is 757/624 (or 1 133/624 as a mixed number).

What is 25/48 plus 9/13 as a decimal?

25/48 + 9/13 converted to a decimal is 1.213141.

What is 25/48 plus 9/13 as a percentage?

25/48 + 9/13 expressed as a percentage is 121.3141%.

How do you write 25/48 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 757/624 can be written as the mixed number 1 133/624.

Does 25/48 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.213141...) because the denominator contains prime factors other than 2 and 5.