What is 3/51 plus 6/21? (Answer: 41/119)

Exact Answer

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Problem: What is 3/51 plus 6/21?
Formula / Expression: 3/51 + 6/21
Final Answer: 41/119
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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 3/51 by 7, and multiply the numerator and denominator of 6/21 by 17 so both fractions share the common base 357.
Working: 3 × 7/51 × 7 = 21/357 and 6 × 17/21 × 17 = 102/357

Step 3: Add the Numerators
Now add the numerators (21 + 102 = 123) and keep the common denominator 357 unchanged.
Working: 21 + 102/357 = 123/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/357 ÷ 3 = 41/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 119 produces a repeating decimal (approximately 0.344538, or 34.4538%).
Working: 41 ÷ 119 = 0.344538 (34.4538%)

Key Values:
- Simplified Fraction: 41/119
- Mixed Number Form: 41/119
- Decimal Value: 0.344538
- Percentage: 34.4538%

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Solved with FractionsCalc:
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3/51 + 6/21 = 41/119

Simplified Fraction

41/119

Mixed Number

Proper (41/119)

Decimal Value

0.344538

Percentage

34.4538%

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Step-by-Step Solution: 3/51 + 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 3/51 by 7, and multiply the numerator and denominator of 6/21 by 17 so both fractions share the common base 357.

3 × 7/51 × 7 = 21/357 and 6 × 17/21 × 17 = 102/357

Step 3

Add the Numerators

Now add the numerators (21 + 102 = 123) and keep the common denominator 357 unchanged.

21 + 102/357 = 123/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 357, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/357 ÷ 3 = 41/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 119 produces a repeating decimal (approximately 0.344538, or 34.4538%).

41 ÷ 119 = 0.344538 (34.4538%)

Visual Representation

The diagram below illustrates 3/51 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/119`
Mixed Number Form	`41/119`
Decimal Form	`0.344538`
Percentage	`34.4538%`

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Frequently Asked Questions

What is 3/51 plus 6/21 as a fraction?

3/51 + 6/21 in simplest fraction form is 41/119.

What is 3/51 plus 6/21 as a decimal?

3/51 + 6/21 converted to a decimal is 0.344538.

What is 3/51 plus 6/21 as a percentage?

3/51 + 6/21 expressed as a percentage is 34.4538%.

Does 3/51 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.344538...) because the denominator contains prime factors other than 2 and 5.