What is 2/51 plus 6/21? (Answer: 116/357)

Exact Answer

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Problem: What is 2/51 plus 6/21?
Formula / Expression: 2/51 + 6/21
Final Answer: 116/357
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 51 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 51 × 21 = 1071, keeping the calculation simpler).
Working: LCD(51, 21) = 357

Step 2: Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 2/51 by 7, and multiply the numerator and denominator of 6/21 by 17 so both fractions share the common base 357.
Working: 2 × 7/51 × 7 = 14/357 and 6 × 17/21 × 17 = 102/357

Step 3: Add the Numerators
Now add the numerators (14 + 102 = 116) and keep the common denominator 357 unchanged.
Working: 14 + 102/357 = 116/357

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 116 and 357 is 1, confirming that 116/357 cannot be reduced further—it is already in its simplest irreducible form.
Working: 116/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 116 by denominator 357 produces a repeating decimal (approximately 0.32493, or 32.493%).
Working: 116 ÷ 357 = 0.32493 (32.493%)

Key Values:
- Simplified Fraction: 116/357
- Mixed Number Form: 116/357
- Decimal Value: 0.32493
- Percentage: 32.493%

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Solved with FractionsCalc:
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2/51 + 6/21 = 116/357

Simplified Fraction

116/357

Mixed Number

Proper (116/357)

Decimal Value

0.32493

Percentage

32.493%

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Step-by-Step Solution: 2/51 + 6/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 51 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 51 × 21 = 1071, keeping the calculation simpler).

LCD(51, 21) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

Multiply the numerator and denominator of 2/51 by 7, and multiply the numerator and denominator of 6/21 by 17 so both fractions share the common base 357.

2 × 7/51 × 7 = 14/357 and 6 × 17/21 × 17 = 102/357

Step 3

Add the Numerators

Now add the numerators (14 + 102 = 116) and keep the common denominator 357 unchanged.

14 + 102/357 = 116/357

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 116 and 357 is 1, confirming that 116/357 cannot be reduced further—it is already in its simplest irreducible form.

116/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 116 by denominator 357 produces a repeating decimal (approximately 0.32493, or 32.493%).

116 ÷ 357 = 0.32493 (32.493%)

Visual Representation

The diagram below illustrates 2/51 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`116/357`
Mixed Number Form	`116/357`
Decimal Form	`0.32493`
Percentage	`32.493%`

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Frequently Asked Questions

What is 2/51 plus 6/21 as a fraction?

2/51 + 6/21 in simplest fraction form is 116/357.

What is 2/51 plus 6/21 as a decimal?

2/51 + 6/21 converted to a decimal is 0.32493.

What is 2/51 plus 6/21 as a percentage?

2/51 + 6/21 expressed as a percentage is 32.493%.

Does 2/51 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.32493...) because the denominator contains prime factors other than 2 and 5.