What is 2/21 plus 6/57? (Answer: 80/399)

Exact Answer

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Problem: What is 2/21 plus 6/57?
Formula / Expression: 2/21 + 6/57
Final Answer: 80/399
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 2/21 by 19, and multiply the numerator and denominator of 6/57 by 7 so both fractions share the common base 399.
Working: 2 × 19/21 × 19 = 38/399 and 6 × 7/57 × 7 = 42/399

Step 3: Add the Numerators
Now add the numerators (38 + 42 = 80) and keep the common denominator 399 unchanged.
Working: 38 + 42/399 = 80/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 80 and 399 is 1, confirming that 80/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 80/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 80 by denominator 399 produces a repeating decimal (approximately 0.200501, or 20.0501%).
Working: 80 ÷ 399 = 0.200501 (20.0501%)

Key Values:
- Simplified Fraction: 80/399
- Mixed Number Form: 80/399
- Decimal Value: 0.200501
- Percentage: 20.0501%

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Solved with FractionsCalc:
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2/21 + 6/57 = 80/399

Simplified Fraction

80/399

Mixed Number

Proper (80/399)

Decimal Value

0.200501

Percentage

20.0501%

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Step-by-Step Solution: 2/21 + 6/57

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 57) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 2/21 by 19, and multiply the numerator and denominator of 6/57 by 7 so both fractions share the common base 399.

2 × 19/21 × 19 = 38/399 and 6 × 7/57 × 7 = 42/399

Step 3

Add the Numerators

Now add the numerators (38 + 42 = 80) and keep the common denominator 399 unchanged.

38 + 42/399 = 80/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 80 and 399 is 1, confirming that 80/399 cannot be reduced further—it is already in its simplest irreducible form.

80/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 80 by denominator 399 produces a repeating decimal (approximately 0.200501, or 20.0501%).

80 ÷ 399 = 0.200501 (20.0501%)

Visual Representation

The diagram below illustrates 2/21 plus 6/57 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`80/399`
Mixed Number Form	`80/399`
Decimal Form	`0.200501`
Percentage	`20.0501%`

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Frequently Asked Questions

What is 2/21 plus 6/57 as a fraction?

2/21 + 6/57 in simplest fraction form is 80/399.

What is 2/21 plus 6/57 as a decimal?

2/21 + 6/57 converted to a decimal is 0.200501.

What is 2/21 plus 6/57 as a percentage?

2/21 + 6/57 expressed as a percentage is 20.0501%.

Does 2/21 plus 6/57 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.200501...) because the denominator contains prime factors other than 2 and 5.