What is 5/21 plus 2/8? (Answer: 41/84)

Exact Answer

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Problem: What is 5/21 plus 2/8?
Formula / Expression: 5/21 + 2/8
Final Answer: 41/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 8 = 168.
Working: LCD(21, 8) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 5/21 by 8, and multiply the numerator and denominator of 2/8 by 21 so both fractions share the common base 168.
Working: 5 × 8/21 × 8 = 40/168 and 2 × 21/8 × 21 = 42/168

Step 3: Add the Numerators
Now add the numerators (40 + 42 = 82) and keep the common denominator 168 unchanged.
Working: 40 + 42/168 = 82/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/168 ÷ 2 = 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-2-8/
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5/21 + 2/8 = 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 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 8 = 168.

LCD(21, 8) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 5/21 by 8, and multiply the numerator and denominator of 2/8 by 21 so both fractions share the common base 168.

5 × 8/21 × 8 = 40/168 and 2 × 21/8 × 21 = 42/168

Step 3

Add the Numerators

Now add the numerators (40 + 42 = 82) and keep the common denominator 168 unchanged.

40 + 42/168 = 82/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 168, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/168 ÷ 2 = 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 2/8 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 2/8 as a fraction?

5/21 + 2/8 in simplest fraction form is 41/84.

What is 5/21 plus 2/8 as a decimal?

5/21 + 2/8 converted to a decimal is 0.488095.

What is 5/21 plus 2/8 as a percentage?

5/21 + 2/8 expressed as a percentage is 48.8095%.

Does 5/21 plus 2/8 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.