What is 25/46 plus 9/13? (Answer: 739/598)

Exact Answer

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Problem: What is 25/46 plus 9/13?
Formula / Expression: 25/46 + 9/13
Final Answer: 1 141/598 (739/598)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 46 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 13 = 598.
Working: LCD(46, 13) = 598

Step 2: Convert to Equivalent Fractions with Common Denominator 598
Multiply the numerator and denominator of 25/46 by 13, and multiply the numerator and denominator of 9/13 by 46 so both fractions share the common base 598.
Working: 25 × 13/46 × 13 = 325/598 and 9 × 46/13 × 46 = 414/598

Step 3: Add the Numerators
Now add the numerators (325 + 414 = 739) and keep the common denominator 598 unchanged.
Working: 325 + 414/598 = 739/598

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 739 and 598 is 1, confirming that 739/598 cannot be reduced further—it is already in its simplest irreducible form.
Working: 739/598

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (739) is greater than the denominator (598), divide 739 by 598: it goes in 1 whole time(s) with a remainder of 141, giving the mixed number 1 141/598.
Working: 739/598 = 1 141/598

Step 6: Decimal & Percentage Representation
Dividing the numerator 739 by denominator 598 produces a repeating decimal (approximately 1.235786, or 123.5786%).
Working: 739 ÷ 598 = 1.235786 (123.5786%)

Key Values:
- Simplified Fraction: 739/598
- Mixed Number Form: 1 141/598
- Decimal Value: 1.235786
- Percentage: 123.5786%

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Solved with FractionsCalc:
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25/46 + 9/13 = 739/598

Simplified Fraction

739/598

Mixed Number

1 141/598

Decimal Value

1.235786

Percentage

123.5786%

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Step-by-Step Solution: 25/46 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 46 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 13 = 598.

LCD(46, 13) = 598

Step 2

Convert to Equivalent Fractions with Common Denominator 598

Multiply the numerator and denominator of 25/46 by 13, and multiply the numerator and denominator of 9/13 by 46 so both fractions share the common base 598.

25 × 13/46 × 13 = 325/598 and 9 × 46/13 × 46 = 414/598

Step 3

Add the Numerators

Now add the numerators (325 + 414 = 739) and keep the common denominator 598 unchanged.

325 + 414/598 = 739/598

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 739 and 598 is 1, confirming that 739/598 cannot be reduced further—it is already in its simplest irreducible form.

739/598

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (739) is greater than the denominator (598), divide 739 by 598: it goes in 1 whole time(s) with a remainder of 141, giving the mixed number 1 141/598.

739/598 = 1141/598

Step 6

Decimal & Percentage Representation

Dividing the numerator 739 by denominator 598 produces a repeating decimal (approximately 1.235786, or 123.5786%).

739 ÷ 598 = 1.235786 (123.5786%)

Visual Representation

The diagram below illustrates 25/46 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`739/598`
Mixed Number Form	`1 141/598`
Decimal Form	`1.235786`
Percentage	`123.5786%`

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Frequently Asked Questions

What is 25/46 plus 9/13 as a fraction?

25/46 + 9/13 in simplest fraction form is 739/598 (or 1 141/598 as a mixed number).

What is 25/46 plus 9/13 as a decimal?

25/46 + 9/13 converted to a decimal is 1.235786.

What is 25/46 plus 9/13 as a percentage?

25/46 + 9/13 expressed as a percentage is 123.5786%.

How do you write 25/46 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 739/598 can be written as the mixed number 1 141/598.

Does 25/46 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.235786...) because the denominator contains prime factors other than 2 and 5.