What is 3/25 plus 7/13? (Answer: 214/325)

Exact Answer

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Problem: What is 3/25 plus 7/13?
Formula / Expression: 3/25 + 7/13
Final Answer: 214/325
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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 7/13 by 25 so both fractions share the common base 325.
Working: 3 × 13/25 × 13 = 39/325 and 7 × 25/13 × 25 = 175/325

Step 3: Add the Numerators
Now add the numerators (39 + 175 = 214) and keep the common denominator 325 unchanged.
Working: 39 + 175/325 = 214/325

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 214 and 325 is 1, confirming that 214/325 cannot be reduced further—it is already in its simplest irreducible form.
Working: 214/325

Step 5: Decimal & Percentage Representation
Dividing the numerator 214 by denominator 325 produces a repeating decimal (approximately 0.658462, or 65.8462%).
Working: 214 ÷ 325 = 0.658462 (65.8462%)

Key Values:
- Simplified Fraction: 214/325
- Mixed Number Form: 214/325
- Decimal Value: 0.658462
- Percentage: 65.8462%

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Solved with FractionsCalc:
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3/25 + 7/13 = 214/325

Simplified Fraction

214/325

Mixed Number

Proper (214/325)

Decimal Value

0.658462

Percentage

65.8462%

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Step-by-Step Solution: 3/25 + 7/13

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 7/13 by 25 so both fractions share the common base 325.

3 × 13/25 × 13 = 39/325 and 7 × 25/13 × 25 = 175/325

Step 3

Add the Numerators

Now add the numerators (39 + 175 = 214) and keep the common denominator 325 unchanged.

39 + 175/325 = 214/325

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 214 and 325 is 1, confirming that 214/325 cannot be reduced further—it is already in its simplest irreducible form.

214/325

Step 5

Decimal & Percentage Representation

Dividing the numerator 214 by denominator 325 produces a repeating decimal (approximately 0.658462, or 65.8462%).

214 ÷ 325 = 0.658462 (65.8462%)

Visual Representation

The diagram below illustrates 3/25 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`214/325`
Mixed Number Form	`214/325`
Decimal Form	`0.658462`
Percentage	`65.8462%`

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Frequently Asked Questions

What is 3/25 plus 7/13 as a fraction?

3/25 + 7/13 in simplest fraction form is 214/325.

What is 3/25 plus 7/13 as a decimal?

3/25 + 7/13 converted to a decimal is 0.658462.

What is 3/25 plus 7/13 as a percentage?

3/25 + 7/13 expressed as a percentage is 65.8462%.

Does 3/25 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.658462...) because the denominator contains prime factors other than 2 and 5.