What is 2/57 plus 8/21? (Answer: 166/399)

Exact Answer

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Problem: What is 2/57 plus 8/21?
Formula / Expression: 2/57 + 8/21
Final Answer: 166/399
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).
Working: LCD(57, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 2/57 by 7, and multiply the numerator and denominator of 8/21 by 19 so both fractions share the common base 399.
Working: 2 × 7/57 × 7 = 14/399 and 8 × 19/21 × 19 = 152/399

Step 3: Add the Numerators
Now add the numerators (14 + 152 = 166) and keep the common denominator 399 unchanged.
Working: 14 + 152/399 = 166/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 166 and 399 is 1, confirming that 166/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 166/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 166 by denominator 399 produces a repeating decimal (approximately 0.41604, or 41.604%).
Working: 166 ÷ 399 = 0.41604 (41.604%)

Key Values:
- Simplified Fraction: 166/399
- Mixed Number Form: 166/399
- Decimal Value: 0.41604
- Percentage: 41.604%

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Solved with FractionsCalc:
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2/57 + 8/21 = 166/399

Simplified Fraction

166/399

Mixed Number

Proper (166/399)

Decimal Value

0.41604

Percentage

41.604%

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Step-by-Step Solution: 2/57 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).

LCD(57, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 2/57 by 7, and multiply the numerator and denominator of 8/21 by 19 so both fractions share the common base 399.

2 × 7/57 × 7 = 14/399 and 8 × 19/21 × 19 = 152/399

Step 3

Add the Numerators

Now add the numerators (14 + 152 = 166) and keep the common denominator 399 unchanged.

14 + 152/399 = 166/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 166 and 399 is 1, confirming that 166/399 cannot be reduced further—it is already in its simplest irreducible form.

166/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 166 by denominator 399 produces a repeating decimal (approximately 0.41604, or 41.604%).

166 ÷ 399 = 0.41604 (41.604%)

Visual Representation

The diagram below illustrates 2/57 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`166/399`
Mixed Number Form	`166/399`
Decimal Form	`0.41604`
Percentage	`41.604%`

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Frequently Asked Questions

What is 2/57 plus 8/21 as a fraction?

2/57 + 8/21 in simplest fraction form is 166/399.

What is 2/57 plus 8/21 as a decimal?

2/57 + 8/21 converted to a decimal is 0.41604.

What is 2/57 plus 8/21 as a percentage?

2/57 + 8/21 expressed as a percentage is 41.604%.

Does 2/57 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.41604...) because the denominator contains prime factors other than 2 and 5.