What is 3/25 plus 10/13? (Answer: 289/325)

Exact Answer

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Problem: What is 3/25 plus 10/13?
Formula / Expression: 3/25 + 10/13
Final Answer: 289/325
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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 3/25 by 13, and multiply the numerator and denominator of 10/13 by 25 so both fractions share the common base 325.
Working: 3 × 13/25 × 13 = 39/325 and 10 × 25/13 × 25 = 250/325

Step 3: Add the Numerators
Now add the numerators (39 + 250 = 289) and keep the common denominator 325 unchanged.
Working: 39 + 250/325 = 289/325

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 289 and 325 is 1, confirming that 289/325 cannot be reduced further—it is already in its simplest irreducible form.
Working: 289/325

Step 5: Decimal & Percentage Representation
Dividing the numerator 289 by denominator 325 produces a repeating decimal (approximately 0.889231, or 88.9231%).
Working: 289 ÷ 325 = 0.889231 (88.9231%)

Key Values:
- Simplified Fraction: 289/325
- Mixed Number Form: 289/325
- Decimal Value: 0.889231
- Percentage: 88.9231%

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3/25 + 10/13 = 289/325

Simplified Fraction

289/325

Mixed Number

Proper (289/325)

Decimal Value

0.889231

Percentage

88.9231%

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Step-by-Step Solution: 3/25 + 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 3/25 by 13, and multiply the numerator and denominator of 10/13 by 25 so both fractions share the common base 325.

3 × 13/25 × 13 = 39/325 and 10 × 25/13 × 25 = 250/325

Step 3

Add the Numerators

Now add the numerators (39 + 250 = 289) and keep the common denominator 325 unchanged.

39 + 250/325 = 289/325

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 289 and 325 is 1, confirming that 289/325 cannot be reduced further—it is already in its simplest irreducible form.

289/325

Step 5

Decimal & Percentage Representation

Dividing the numerator 289 by denominator 325 produces a repeating decimal (approximately 0.889231, or 88.9231%).

289 ÷ 325 = 0.889231 (88.9231%)

Visual Representation

The diagram below illustrates 3/25 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`289/325`
Mixed Number Form	`289/325`
Decimal Form	`0.889231`
Percentage	`88.9231%`

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Frequently Asked Questions

What is 3/25 plus 10/13 as a fraction?

3/25 + 10/13 in simplest fraction form is 289/325.

What is 3/25 plus 10/13 as a decimal?

3/25 + 10/13 converted to a decimal is 0.889231.

What is 3/25 plus 10/13 as a percentage?

3/25 + 10/13 expressed as a percentage is 88.9231%.

Does 3/25 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.889231...) because the denominator contains prime factors other than 2 and 5.