What is 8/25 plus 10/21? (Answer: 418/525)

Exact Answer

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Problem: What is 8/25 plus 10/21?
Formula / Expression: 8/25 + 10/21
Final Answer: 418/525
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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 8/25 by 21, and multiply the numerator and denominator of 10/21 by 25 so both fractions share the common base 525.
Working: 8 × 21/25 × 21 = 168/525 and 10 × 25/21 × 25 = 250/525

Step 3: Add the Numerators
Now add the numerators (168 + 250 = 418) and keep the common denominator 525 unchanged.
Working: 168 + 250/525 = 418/525

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 418 and 525 is 1, confirming that 418/525 cannot be reduced further—it is already in its simplest irreducible form.
Working: 418/525

Step 5: Decimal & Percentage Representation
Dividing the numerator 418 by denominator 525 produces a repeating decimal (approximately 0.79619, or 79.619%).
Working: 418 ÷ 525 = 0.79619 (79.619%)

Key Values:
- Simplified Fraction: 418/525
- Mixed Number Form: 418/525
- Decimal Value: 0.79619
- Percentage: 79.619%

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Solved with FractionsCalc:
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8/25 + 10/21 = 418/525

Simplified Fraction

418/525

Mixed Number

Proper (418/525)

Decimal Value

0.79619

Percentage

79.619%

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Step-by-Step Solution: 8/25 + 10/21

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 8/25 by 21, and multiply the numerator and denominator of 10/21 by 25 so both fractions share the common base 525.

8 × 21/25 × 21 = 168/525 and 10 × 25/21 × 25 = 250/525

Step 3

Add the Numerators

Now add the numerators (168 + 250 = 418) and keep the common denominator 525 unchanged.

168 + 250/525 = 418/525

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 418 and 525 is 1, confirming that 418/525 cannot be reduced further—it is already in its simplest irreducible form.

418/525

Step 5

Decimal & Percentage Representation

Dividing the numerator 418 by denominator 525 produces a repeating decimal (approximately 0.79619, or 79.619%).

418 ÷ 525 = 0.79619 (79.619%)

Visual Representation

The diagram below illustrates 8/25 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`418/525`
Mixed Number Form	`418/525`
Decimal Form	`0.79619`
Percentage	`79.619%`

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Frequently Asked Questions

What is 8/25 plus 10/21 as a fraction?

8/25 + 10/21 in simplest fraction form is 418/525.

What is 8/25 plus 10/21 as a decimal?

8/25 + 10/21 converted to a decimal is 0.79619.

What is 8/25 plus 10/21 as a percentage?

8/25 + 10/21 expressed as a percentage is 79.619%.

Does 8/25 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.79619...) because the denominator contains prime factors other than 2 and 5.