What is 25/49 plus 9/13? (Answer: 766/637)

Exact Answer

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Problem: What is 25/49 plus 9/13?
Formula / Expression: 25/49 + 9/13
Final Answer: 1 129/637 (766/637)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 13 = 637.
Working: LCD(49, 13) = 637

Step 2: Convert to Equivalent Fractions with Common Denominator 637
Multiply the numerator and denominator of 25/49 by 13, and multiply the numerator and denominator of 9/13 by 49 so both fractions share the common base 637.
Working: 25 × 13/49 × 13 = 325/637 and 9 × 49/13 × 49 = 441/637

Step 3: Add the Numerators
Now add the numerators (325 + 441 = 766) and keep the common denominator 637 unchanged.
Working: 325 + 441/637 = 766/637

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 766 and 637 is 1, confirming that 766/637 cannot be reduced further—it is already in its simplest irreducible form.
Working: 766/637

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (766) is greater than the denominator (637), divide 766 by 637: it goes in 1 whole time(s) with a remainder of 129, giving the mixed number 1 129/637.
Working: 766/637 = 1 129/637

Step 6: Decimal & Percentage Representation
Dividing the numerator 766 by denominator 637 produces a repeating decimal (approximately 1.202512, or 120.2512%).
Working: 766 ÷ 637 = 1.202512 (120.2512%)

Key Values:
- Simplified Fraction: 766/637
- Mixed Number Form: 1 129/637
- Decimal Value: 1.202512
- Percentage: 120.2512%

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25/49 + 9/13 = 766/637

Simplified Fraction

766/637

Mixed Number

1 129/637

Decimal Value

1.202512

Percentage

120.2512%

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Step-by-Step Solution: 25/49 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 13 = 637.

LCD(49, 13) = 637

Step 2

Convert to Equivalent Fractions with Common Denominator 637

Multiply the numerator and denominator of 25/49 by 13, and multiply the numerator and denominator of 9/13 by 49 so both fractions share the common base 637.

25 × 13/49 × 13 = 325/637 and 9 × 49/13 × 49 = 441/637

Step 3

Add the Numerators

Now add the numerators (325 + 441 = 766) and keep the common denominator 637 unchanged.

325 + 441/637 = 766/637

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 766 and 637 is 1, confirming that 766/637 cannot be reduced further—it is already in its simplest irreducible form.

766/637

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (766) is greater than the denominator (637), divide 766 by 637: it goes in 1 whole time(s) with a remainder of 129, giving the mixed number 1 129/637.

766/637 = 1129/637

Step 6

Decimal & Percentage Representation

Dividing the numerator 766 by denominator 637 produces a repeating decimal (approximately 1.202512, or 120.2512%).

766 ÷ 637 = 1.202512 (120.2512%)

Visual Representation

The diagram below illustrates 25/49 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`766/637`
Mixed Number Form	`1 129/637`
Decimal Form	`1.202512`
Percentage	`120.2512%`

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Frequently Asked Questions

What is 25/49 plus 9/13 as a fraction?

25/49 + 9/13 in simplest fraction form is 766/637 (or 1 129/637 as a mixed number).

What is 25/49 plus 9/13 as a decimal?

25/49 + 9/13 converted to a decimal is 1.202512.

What is 25/49 plus 9/13 as a percentage?

25/49 + 9/13 expressed as a percentage is 120.2512%.

How do you write 25/49 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 766/637 can be written as the mixed number 1 129/637.

Does 25/49 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.202512...) because the denominator contains prime factors other than 2 and 5.