What is 10/59 plus 5/21? (Answer: 505/1239)

Exact Answer

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Problem: What is 10/59 plus 5/21?
Formula / Expression: 10/59 + 5/21
Final Answer: 505/1239
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 59 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 59 × 21 = 1239.
Working: LCD(59, 21) = 1239

Step 2: Convert to Equivalent Fractions with Common Denominator 1239
Multiply the numerator and denominator of 10/59 by 21, and multiply the numerator and denominator of 5/21 by 59 so both fractions share the common base 1239.
Working: 10 × 21/59 × 21 = 210/1239 and 5 × 59/21 × 59 = 295/1239

Step 3: Add the Numerators
Now add the numerators (210 + 295 = 505) and keep the common denominator 1239 unchanged.
Working: 210 + 295/1239 = 505/1239

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 505 and 1239 is 1, confirming that 505/1239 cannot be reduced further—it is already in its simplest irreducible form.
Working: 505/1239

Step 5: Decimal & Percentage Representation
Dividing the numerator 505 by denominator 1239 produces a repeating decimal (approximately 0.407587, or 40.7587%).
Working: 505 ÷ 1239 = 0.407587 (40.7587%)

Key Values:
- Simplified Fraction: 505/1239
- Mixed Number Form: 505/1239
- Decimal Value: 0.407587
- Percentage: 40.7587%

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Solved with FractionsCalc:
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10/59 + 5/21 = 505/1239

Simplified Fraction

505/1239

Mixed Number

Proper (505/1239)

Decimal Value

0.407587

Percentage

40.7587%

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Step-by-Step Solution: 10/59 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 59 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 59 × 21 = 1239.

LCD(59, 21) = 1239

Step 2

Convert to Equivalent Fractions with Common Denominator 1239

Multiply the numerator and denominator of 10/59 by 21, and multiply the numerator and denominator of 5/21 by 59 so both fractions share the common base 1239.

10 × 21/59 × 21 = 210/1239 and 5 × 59/21 × 59 = 295/1239

Step 3

Add the Numerators

Now add the numerators (210 + 295 = 505) and keep the common denominator 1239 unchanged.

210 + 295/1239 = 505/1239

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 505 and 1239 is 1, confirming that 505/1239 cannot be reduced further—it is already in its simplest irreducible form.

505/1239

Step 5

Decimal & Percentage Representation

Dividing the numerator 505 by denominator 1239 produces a repeating decimal (approximately 0.407587, or 40.7587%).

505 ÷ 1239 = 0.407587 (40.7587%)

Visual Representation

The diagram below illustrates 10/59 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`505/1239`
Mixed Number Form	`505/1239`
Decimal Form	`0.407587`
Percentage	`40.7587%`

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Frequently Asked Questions

What is 10/59 plus 5/21 as a fraction?

10/59 + 5/21 in simplest fraction form is 505/1239.

What is 10/59 plus 5/21 as a decimal?

10/59 + 5/21 converted to a decimal is 0.407587.

What is 10/59 plus 5/21 as a percentage?

10/59 + 5/21 expressed as a percentage is 40.7587%.

Does 10/59 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.407587...) because the denominator contains prime factors other than 2 and 5.