What is 5/21 plus 13/52? (Answer: 41/84)

Exact Answer

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Problem: What is 5/21 plus 13/52?
Formula / Expression: 5/21 + 13/52
Final Answer: 41/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 52 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 52 = 1092.
Working: LCD(21, 52) = 1092

Step 2: Convert to Equivalent Fractions with Common Denominator 1092
Multiply the numerator and denominator of 5/21 by 52, and multiply the numerator and denominator of 13/52 by 21 so both fractions share the common base 1092.
Working: 5 × 52/21 × 52 = 260/1092 and 13 × 21/52 × 21 = 273/1092

Step 3: Add the Numerators
Now add the numerators (260 + 273 = 533) and keep the common denominator 1092 unchanged.
Working: 260 + 273/1092 = 533/1092

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 533 and 1092, which is 13. Divide both the numerator and denominator by 13.
Working: 533 ÷ 13/1092 ÷ 13 = 41/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 84 produces a repeating decimal (approximately 0.488095, or 48.8095%).
Working: 41 ÷ 84 = 0.488095 (48.8095%)

Key Values:
- Simplified Fraction: 41/84
- Mixed Number Form: 41/84
- Decimal Value: 0.488095
- Percentage: 48.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-21-plus-13-52/
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5/21 + 13/52 = 41/84

Simplified Fraction

41/84

Mixed Number

Proper (41/84)

Decimal Value

0.488095

Percentage

48.8095%

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Step-by-Step Solution: 5/21 + 13/52

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 52 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 52 = 1092.

LCD(21, 52) = 1092

Step 2

Convert to Equivalent Fractions with Common Denominator 1092

Multiply the numerator and denominator of 5/21 by 52, and multiply the numerator and denominator of 13/52 by 21 so both fractions share the common base 1092.

5 × 52/21 × 52 = 260/1092 and 13 × 21/52 × 21 = 273/1092

Step 3

Add the Numerators

Now add the numerators (260 + 273 = 533) and keep the common denominator 1092 unchanged.

260 + 273/1092 = 533/1092

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 533 and 1092, which is 13. Divide both the numerator and denominator by 13.

533 ÷ 13/1092 ÷ 13 = 41/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 84 produces a repeating decimal (approximately 0.488095, or 48.8095%).

41 ÷ 84 = 0.488095 (48.8095%)

Visual Representation

The diagram below illustrates 5/21 plus 13/52 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/84`
Mixed Number Form	`41/84`
Decimal Form	`0.488095`
Percentage	`48.8095%`

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Frequently Asked Questions

What is 5/21 plus 13/52 as a fraction?

5/21 + 13/52 in simplest fraction form is 41/84.

What is 5/21 plus 13/52 as a decimal?

5/21 + 13/52 converted to a decimal is 0.488095.

What is 5/21 plus 13/52 as a percentage?

5/21 + 13/52 expressed as a percentage is 48.8095%.

Does 5/21 plus 13/52 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.488095...) because the denominator contains prime factors other than 2 and 5.