What is 12/25 plus 11/21? (Answer: 527/525)

Exact Answer

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Problem: What is 12/25 plus 11/21?
Formula / Expression: 12/25 + 11/21
Final Answer: 1 2/525 (527/525)
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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 12/25 by 21, and multiply the numerator and denominator of 11/21 by 25 so both fractions share the common base 525.
Working: 12 × 21/25 × 21 = 252/525 and 11 × 25/21 × 25 = 275/525

Step 3: Add the Numerators
Now add the numerators (252 + 275 = 527) and keep the common denominator 525 unchanged.
Working: 252 + 275/525 = 527/525

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 527 and 525 is 1, confirming that 527/525 cannot be reduced further—it is already in its simplest irreducible form.
Working: 527/525

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (527) is greater than the denominator (525), divide 527 by 525: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/525.
Working: 527/525 = 1 2/525

Step 6: Decimal & Percentage Representation
Dividing the numerator 527 by denominator 525 produces a repeating decimal (approximately 1.00381, or 100.381%).
Working: 527 ÷ 525 = 1.00381 (100.381%)

Key Values:
- Simplified Fraction: 527/525
- Mixed Number Form: 1 2/525
- Decimal Value: 1.00381
- Percentage: 100.381%

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Solved with FractionsCalc:
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12/25 + 11/21 = 527/525

Simplified Fraction

527/525

Mixed Number

1 2/525

Decimal Value

1.00381

Percentage

100.381%

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Step-by-Step Solution: 12/25 + 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 12/25 by 21, and multiply the numerator and denominator of 11/21 by 25 so both fractions share the common base 525.

12 × 21/25 × 21 = 252/525 and 11 × 25/21 × 25 = 275/525

Step 3

Add the Numerators

Now add the numerators (252 + 275 = 527) and keep the common denominator 525 unchanged.

252 + 275/525 = 527/525

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 527 and 525 is 1, confirming that 527/525 cannot be reduced further—it is already in its simplest irreducible form.

527/525

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (527) is greater than the denominator (525), divide 527 by 525: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/525.

527/525 = 12/525

Step 6

Decimal & Percentage Representation

Dividing the numerator 527 by denominator 525 produces a repeating decimal (approximately 1.00381, or 100.381%).

527 ÷ 525 = 1.00381 (100.381%)

Visual Representation

The diagram below illustrates 12/25 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`527/525`
Mixed Number Form	`1 2/525`
Decimal Form	`1.00381`
Percentage	`100.381%`

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Frequently Asked Questions

What is 12/25 plus 11/21 as a fraction?

12/25 + 11/21 in simplest fraction form is 527/525 (or 1 2/525 as a mixed number).

What is 12/25 plus 11/21 as a decimal?

12/25 + 11/21 converted to a decimal is 1.00381.

What is 12/25 plus 11/21 as a percentage?

12/25 + 11/21 expressed as a percentage is 100.381%.

How do you write 12/25 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 527/525 can be written as the mixed number 1 2/525.

Does 12/25 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.00381...) because the denominator contains prime factors other than 2 and 5.