What is 6/51 plus 6/21? (Answer: 48/119)

Exact Answer

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Problem: What is 6/51 plus 6/21?
Formula / Expression: 6/51 + 6/21
Final Answer: 48/119
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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 6/51 by 7, and multiply the numerator and denominator of 6/21 by 17 so both fractions share the common base 357.
Working: 6 × 7/51 × 7 = 42/357 and 6 × 17/21 × 17 = 102/357

Step 3: Add the Numerators
Now add the numerators (42 + 102 = 144) and keep the common denominator 357 unchanged.
Working: 42 + 102/357 = 144/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 144 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 144 ÷ 3/357 ÷ 3 = 48/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 48 by denominator 119 produces a repeating decimal (approximately 0.403361, or 40.3361%).
Working: 48 ÷ 119 = 0.403361 (40.3361%)

Key Values:
- Simplified Fraction: 48/119
- Mixed Number Form: 48/119
- Decimal Value: 0.403361
- Percentage: 40.3361%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-51-plus-6-21/
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6/51 + 6/21 = 48/119

Simplified Fraction

48/119

Mixed Number

Proper (48/119)

Decimal Value

0.403361

Percentage

40.3361%

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

6 × 7/51 × 7 = 42/357 and 6 × 17/21 × 17 = 102/357

Step 3

Add the Numerators

Now add the numerators (42 + 102 = 144) and keep the common denominator 357 unchanged.

42 + 102/357 = 144/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 144 and 357, which is 3. Divide both the numerator and denominator by 3.

144 ÷ 3/357 ÷ 3 = 48/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 48 by denominator 119 produces a repeating decimal (approximately 0.403361, or 40.3361%).

48 ÷ 119 = 0.403361 (40.3361%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`48/119`
Mixed Number Form	`48/119`
Decimal Form	`0.403361`
Percentage	`40.3361%`

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Frequently Asked Questions

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

6/51 + 6/21 in simplest fraction form is 48/119.

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

6/51 + 6/21 converted to a decimal is 0.403361.

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

6/51 + 6/21 expressed as a percentage is 40.3361%.

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

It results in a repeating decimal (approximately 0.403361...) because the denominator contains prime factors other than 2 and 5.