What is 8/21 plus 2/5? (Answer: 82/105)

Exact Answer

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Problem: What is 8/21 plus 2/5?
Formula / Expression: 8/21 + 2/5
Final Answer: 82/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 5 = 105.
Working: LCD(21, 5) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 8/21 by 5, and multiply the numerator and denominator of 2/5 by 21 so both fractions share the common base 105.
Working: 8 × 5/21 × 5 = 40/105 and 2 × 21/5 × 21 = 42/105

Step 3: Add the Numerators
Now add the numerators (40 + 42 = 82) and keep the common denominator 105 unchanged.
Working: 40 + 42/105 = 82/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 82 and 105 is 1, confirming that 82/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 82/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 105 produces a repeating decimal (approximately 0.780952, or 78.0952%).
Working: 82 ÷ 105 = 0.780952 (78.0952%)

Key Values:
- Simplified Fraction: 82/105
- Mixed Number Form: 82/105
- Decimal Value: 0.780952
- Percentage: 78.0952%

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Solved with FractionsCalc:
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8/21 + 2/5 = 82/105

Simplified Fraction

82/105

Mixed Number

Proper (82/105)

Decimal Value

0.780952

Percentage

78.0952%

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Step-by-Step Solution: 8/21 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 5 = 105.

LCD(21, 5) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 8/21 by 5, and multiply the numerator and denominator of 2/5 by 21 so both fractions share the common base 105.

8 × 5/21 × 5 = 40/105 and 2 × 21/5 × 21 = 42/105

Step 3

Add the Numerators

Now add the numerators (40 + 42 = 82) and keep the common denominator 105 unchanged.

40 + 42/105 = 82/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 82 and 105 is 1, confirming that 82/105 cannot be reduced further—it is already in its simplest irreducible form.

82/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 105 produces a repeating decimal (approximately 0.780952, or 78.0952%).

82 ÷ 105 = 0.780952 (78.0952%)

Visual Representation

The diagram below illustrates 8/21 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/105`
Mixed Number Form	`82/105`
Decimal Form	`0.780952`
Percentage	`78.0952%`

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Frequently Asked Questions

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

8/21 + 2/5 in simplest fraction form is 82/105.

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

8/21 + 2/5 converted to a decimal is 0.780952.

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

8/21 + 2/5 expressed as a percentage is 78.0952%.

Does 8/21 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.780952...) because the denominator contains prime factors other than 2 and 5.