What is 9/25 plus 10/13? (Answer: 367/325)

Exact Answer

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Problem: What is 9/25 plus 10/13?
Formula / Expression: 9/25 + 10/13
Final Answer: 1 42/325 (367/325)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 13 = 325.
Working: LCD(25, 13) = 325

Step 2: Convert to Equivalent Fractions with Common Denominator 325
Multiply the numerator and denominator of 9/25 by 13, and multiply the numerator and denominator of 10/13 by 25 so both fractions share the common base 325.
Working: 9 × 13/25 × 13 = 117/325 and 10 × 25/13 × 25 = 250/325

Step 3: Add the Numerators
Now add the numerators (117 + 250 = 367) and keep the common denominator 325 unchanged.
Working: 117 + 250/325 = 367/325

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 367 and 325 is 1, confirming that 367/325 cannot be reduced further—it is already in its simplest irreducible form.
Working: 367/325

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (367) is greater than the denominator (325), divide 367 by 325: it goes in 1 whole time(s) with a remainder of 42, giving the mixed number 1 42/325.
Working: 367/325 = 1 42/325

Step 6: Decimal & Percentage Representation
Dividing the numerator 367 by denominator 325 produces a repeating decimal (approximately 1.129231, or 112.9231%).
Working: 367 ÷ 325 = 1.129231 (112.9231%)

Key Values:
- Simplified Fraction: 367/325
- Mixed Number Form: 1 42/325
- Decimal Value: 1.129231
- Percentage: 112.9231%

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9/25 + 10/13 = 367/325

Simplified Fraction

367/325

Mixed Number

1 42/325

Decimal Value

1.129231

Percentage

112.9231%

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Step-by-Step Solution: 9/25 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 13 = 325.

LCD(25, 13) = 325

Step 2

Convert to Equivalent Fractions with Common Denominator 325

Multiply the numerator and denominator of 9/25 by 13, and multiply the numerator and denominator of 10/13 by 25 so both fractions share the common base 325.

9 × 13/25 × 13 = 117/325 and 10 × 25/13 × 25 = 250/325

Step 3

Add the Numerators

Now add the numerators (117 + 250 = 367) and keep the common denominator 325 unchanged.

117 + 250/325 = 367/325

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 367 and 325 is 1, confirming that 367/325 cannot be reduced further—it is already in its simplest irreducible form.

367/325

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (367) is greater than the denominator (325), divide 367 by 325: it goes in 1 whole time(s) with a remainder of 42, giving the mixed number 1 42/325.

367/325 = 142/325

Step 6

Decimal & Percentage Representation

Dividing the numerator 367 by denominator 325 produces a repeating decimal (approximately 1.129231, or 112.9231%).

367 ÷ 325 = 1.129231 (112.9231%)

Visual Representation

The diagram below illustrates 9/25 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`367/325`
Mixed Number Form	`1 42/325`
Decimal Form	`1.129231`
Percentage	`112.9231%`

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Frequently Asked Questions

What is 9/25 plus 10/13 as a fraction?

9/25 + 10/13 in simplest fraction form is 367/325 (or 1 42/325 as a mixed number).

What is 9/25 plus 10/13 as a decimal?

9/25 + 10/13 converted to a decimal is 1.129231.

What is 9/25 plus 10/13 as a percentage?

9/25 + 10/13 expressed as a percentage is 112.9231%.

How do you write 9/25 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 367/325 can be written as the mixed number 1 42/325.

Does 9/25 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.129231...) because the denominator contains prime factors other than 2 and 5.