What is 10/21 plus 12/25? (Answer: 502/525)

Exact Answer

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Problem: What is 10/21 plus 12/25?
Formula / Expression: 10/21 + 12/25
Final Answer: 502/525
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 525
Multiply the numerator and denominator of 10/21 by 25, and multiply the numerator and denominator of 12/25 by 21 so both fractions share the common base 525.
Working: 10 × 25/21 × 25 = 250/525 and 12 × 21/25 × 21 = 252/525

Step 3: Add the Numerators
Now add the numerators (250 + 252 = 502) and keep the common denominator 525 unchanged.
Working: 250 + 252/525 = 502/525

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 502 and 525 is 1, confirming that 502/525 cannot be reduced further—it is already in its simplest irreducible form.
Working: 502/525

Step 5: Decimal & Percentage Representation
Dividing the numerator 502 by denominator 525 produces a repeating decimal (approximately 0.95619, or 95.619%).
Working: 502 ÷ 525 = 0.95619 (95.619%)

Key Values:
- Simplified Fraction: 502/525
- Mixed Number Form: 502/525
- Decimal Value: 0.95619
- Percentage: 95.619%

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Solved with FractionsCalc:
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10/21 + 12/25 = 502/525

Simplified Fraction

502/525

Mixed Number

Proper (502/525)

Decimal Value

0.95619

Percentage

95.619%

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Step-by-Step Solution: 10/21 + 12/25

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 25) = 525

Step 2

Convert to Equivalent Fractions with Common Denominator 525

Multiply the numerator and denominator of 10/21 by 25, and multiply the numerator and denominator of 12/25 by 21 so both fractions share the common base 525.

10 × 25/21 × 25 = 250/525 and 12 × 21/25 × 21 = 252/525

Step 3

Add the Numerators

Now add the numerators (250 + 252 = 502) and keep the common denominator 525 unchanged.

250 + 252/525 = 502/525

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 502 and 525 is 1, confirming that 502/525 cannot be reduced further—it is already in its simplest irreducible form.

502/525

Step 5

Decimal & Percentage Representation

Dividing the numerator 502 by denominator 525 produces a repeating decimal (approximately 0.95619, or 95.619%).

502 ÷ 525 = 0.95619 (95.619%)

Visual Representation

The diagram below illustrates 10/21 plus 12/25 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`502/525`
Mixed Number Form	`502/525`
Decimal Form	`0.95619`
Percentage	`95.619%`

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Frequently Asked Questions

What is 10/21 plus 12/25 as a fraction?

10/21 + 12/25 in simplest fraction form is 502/525.

What is 10/21 plus 12/25 as a decimal?

10/21 + 12/25 converted to a decimal is 0.95619.

What is 10/21 plus 12/25 as a percentage?

10/21 + 12/25 expressed as a percentage is 95.619%.

Does 10/21 plus 12/25 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.95619...) because the denominator contains prime factors other than 2 and 5.