What is 13/25 plus 11/21? (Answer: 548/525)

Exact Answer

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Problem: What is 13/25 plus 11/21?
Formula / Expression: 13/25 + 11/21
Final Answer: 1 23/525 (548/525)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 21 = 525.
Working: LCD(25, 21) = 525

Step 2: Convert to Equivalent Fractions with Common Denominator 525
Multiply the numerator and denominator of 13/25 by 21, and multiply the numerator and denominator of 11/21 by 25 so both fractions share the common base 525.
Working: 13 × 21/25 × 21 = 273/525 and 11 × 25/21 × 25 = 275/525

Step 3: Add the Numerators
Now add the numerators (273 + 275 = 548) and keep the common denominator 525 unchanged.
Working: 273 + 275/525 = 548/525

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 548 and 525 is 1, confirming that 548/525 cannot be reduced further—it is already in its simplest irreducible form.
Working: 548/525

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (548) is greater than the denominator (525), divide 548 by 525: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/525.
Working: 548/525 = 1 23/525

Step 6: Decimal & Percentage Representation
Dividing the numerator 548 by denominator 525 produces a repeating decimal (approximately 1.04381, or 104.381%).
Working: 548 ÷ 525 = 1.04381 (104.381%)

Key Values:
- Simplified Fraction: 548/525
- Mixed Number Form: 1 23/525
- Decimal Value: 1.04381
- Percentage: 104.381%

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Solved with FractionsCalc:
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13/25 + 11/21 = 548/525

Simplified Fraction

548/525

Mixed Number

1 23/525

Decimal Value

1.04381

Percentage

104.381%

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Step-by-Step Solution: 13/25 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 21 = 525.

LCD(25, 21) = 525

Step 2

Convert to Equivalent Fractions with Common Denominator 525

Multiply the numerator and denominator of 13/25 by 21, and multiply the numerator and denominator of 11/21 by 25 so both fractions share the common base 525.

13 × 21/25 × 21 = 273/525 and 11 × 25/21 × 25 = 275/525

Step 3

Add the Numerators

Now add the numerators (273 + 275 = 548) and keep the common denominator 525 unchanged.

273 + 275/525 = 548/525

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 548 and 525 is 1, confirming that 548/525 cannot be reduced further—it is already in its simplest irreducible form.

548/525

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (548) is greater than the denominator (525), divide 548 by 525: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/525.

548/525 = 123/525

Step 6

Decimal & Percentage Representation

Dividing the numerator 548 by denominator 525 produces a repeating decimal (approximately 1.04381, or 104.381%).

548 ÷ 525 = 1.04381 (104.381%)

Visual Representation

The diagram below illustrates 13/25 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`548/525`
Mixed Number Form	`1 23/525`
Decimal Form	`1.04381`
Percentage	`104.381%`

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Frequently Asked Questions

What is 13/25 plus 11/21 as a fraction?

13/25 + 11/21 in simplest fraction form is 548/525 (or 1 23/525 as a mixed number).

What is 13/25 plus 11/21 as a decimal?

13/25 + 11/21 converted to a decimal is 1.04381.

What is 13/25 plus 11/21 as a percentage?

13/25 + 11/21 expressed as a percentage is 104.381%.

How do you write 13/25 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 548/525 can be written as the mixed number 1 23/525.

Does 13/25 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.04381...) because the denominator contains prime factors other than 2 and 5.