What is 1/51 plus 2/21? (Answer: 41/357)

Exact Answer

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Problem: What is 1/51 plus 2/21?
Formula / Expression: 1/51 + 2/21
Final Answer: 41/357
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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 1/51 by 7, and multiply the numerator and denominator of 2/21 by 17 so both fractions share the common base 357.
Working: 1 × 7/51 × 7 = 7/357 and 2 × 17/21 × 17 = 34/357

Step 3: Add the Numerators
Now add the numerators (7 + 34 = 41) and keep the common denominator 357 unchanged.
Working: 7 + 34/357 = 41/357

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 357 is 1, confirming that 41/357 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 357 produces a repeating decimal (approximately 0.114846, or 11.4846%).
Working: 41 ÷ 357 = 0.114846 (11.4846%)

Key Values:
- Simplified Fraction: 41/357
- Mixed Number Form: 41/357
- Decimal Value: 0.114846
- Percentage: 11.4846%

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Solved with FractionsCalc:
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1/51 + 2/21 = 41/357

Simplified Fraction

41/357

Mixed Number

Proper (41/357)

Decimal Value

0.114846

Percentage

11.4846%

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Step-by-Step Solution: 1/51 + 2/21

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 1/51 by 7, and multiply the numerator and denominator of 2/21 by 17 so both fractions share the common base 357.

1 × 7/51 × 7 = 7/357 and 2 × 17/21 × 17 = 34/357

Step 3

Add the Numerators

Now add the numerators (7 + 34 = 41) and keep the common denominator 357 unchanged.

7 + 34/357 = 41/357

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 357 is 1, confirming that 41/357 cannot be reduced further—it is already in its simplest irreducible form.

41/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 357 produces a repeating decimal (approximately 0.114846, or 11.4846%).

41 ÷ 357 = 0.114846 (11.4846%)

Visual Representation

The diagram below illustrates 1/51 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/357`
Mixed Number Form	`41/357`
Decimal Form	`0.114846`
Percentage	`11.4846%`

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Frequently Asked Questions

What is 1/51 plus 2/21 as a fraction?

1/51 + 2/21 in simplest fraction form is 41/357.

What is 1/51 plus 2/21 as a decimal?

1/51 + 2/21 converted to a decimal is 0.114846.

What is 1/51 plus 2/21 as a percentage?

1/51 + 2/21 expressed as a percentage is 11.4846%.

Does 1/51 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.114846...) because the denominator contains prime factors other than 2 and 5.