What is 8/21 plus 5/13? (Answer: 209/273)

Exact Answer

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Problem: What is 8/21 plus 5/13?
Formula / Expression: 8/21 + 5/13
Final Answer: 209/273
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 13 = 273.
Working: LCD(21, 13) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 8/21 by 13, and multiply the numerator and denominator of 5/13 by 21 so both fractions share the common base 273.
Working: 8 × 13/21 × 13 = 104/273 and 5 × 21/13 × 21 = 105/273

Step 3: Add the Numerators
Now add the numerators (104 + 105 = 209) and keep the common denominator 273 unchanged.
Working: 104 + 105/273 = 209/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 273 is 1, confirming that 209/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 273 produces a repeating decimal (approximately 0.765568, or 76.5568%).
Working: 209 ÷ 273 = 0.765568 (76.5568%)

Key Values:
- Simplified Fraction: 209/273
- Mixed Number Form: 209/273
- Decimal Value: 0.765568
- Percentage: 76.5568%

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Solved with FractionsCalc:
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8/21 + 5/13 = 209/273

Simplified Fraction

209/273

Mixed Number

Proper (209/273)

Decimal Value

0.765568

Percentage

76.5568%

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Step-by-Step Solution: 8/21 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 13 = 273.

LCD(21, 13) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 8/21 by 13, and multiply the numerator and denominator of 5/13 by 21 so both fractions share the common base 273.

8 × 13/21 × 13 = 104/273 and 5 × 21/13 × 21 = 105/273

Step 3

Add the Numerators

Now add the numerators (104 + 105 = 209) and keep the common denominator 273 unchanged.

104 + 105/273 = 209/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 273 is 1, confirming that 209/273 cannot be reduced further—it is already in its simplest irreducible form.

209/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 273 produces a repeating decimal (approximately 0.765568, or 76.5568%).

209 ÷ 273 = 0.765568 (76.5568%)

Visual Representation

The diagram below illustrates 8/21 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/273`
Mixed Number Form	`209/273`
Decimal Form	`0.765568`
Percentage	`76.5568%`

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Frequently Asked Questions

What is 8/21 plus 5/13 as a fraction?

8/21 + 5/13 in simplest fraction form is 209/273.

What is 8/21 plus 5/13 as a decimal?

8/21 + 5/13 converted to a decimal is 0.765568.

What is 8/21 plus 5/13 as a percentage?

8/21 + 5/13 expressed as a percentage is 76.5568%.

Does 8/21 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.765568...) because the denominator contains prime factors other than 2 and 5.