What is 3/21 plus 8/51? (Answer: 107/357)

Exact Answer

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Problem: What is 3/21 plus 8/51?
Formula / Expression: 3/21 + 8/51
Final Answer: 107/357
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 3/21 by 17, and multiply the numerator and denominator of 8/51 by 7 so both fractions share the common base 357.
Working: 3 × 17/21 × 17 = 51/357 and 8 × 7/51 × 7 = 56/357

Step 3: Add the Numerators
Now add the numerators (51 + 56 = 107) and keep the common denominator 357 unchanged.
Working: 51 + 56/357 = 107/357

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 357 is 1, confirming that 107/357 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 357 produces a repeating decimal (approximately 0.29972, or 29.972%).
Working: 107 ÷ 357 = 0.29972 (29.972%)

Key Values:
- Simplified Fraction: 107/357
- Mixed Number Form: 107/357
- Decimal Value: 0.29972
- Percentage: 29.972%

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Solved with FractionsCalc:
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3/21 + 8/51 = 107/357

Simplified Fraction

107/357

Mixed Number

Proper (107/357)

Decimal Value

0.29972

Percentage

29.972%

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Step-by-Step Solution: 3/21 + 8/51

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 51) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

Multiply the numerator and denominator of 3/21 by 17, and multiply the numerator and denominator of 8/51 by 7 so both fractions share the common base 357.

3 × 17/21 × 17 = 51/357 and 8 × 7/51 × 7 = 56/357

Step 3

Add the Numerators

Now add the numerators (51 + 56 = 107) and keep the common denominator 357 unchanged.

51 + 56/357 = 107/357

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 357 is 1, confirming that 107/357 cannot be reduced further—it is already in its simplest irreducible form.

107/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 357 produces a repeating decimal (approximately 0.29972, or 29.972%).

107 ÷ 357 = 0.29972 (29.972%)

Visual Representation

The diagram below illustrates 3/21 plus 8/51 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/357`
Mixed Number Form	`107/357`
Decimal Form	`0.29972`
Percentage	`29.972%`

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Frequently Asked Questions

What is 3/21 plus 8/51 as a fraction?

3/21 + 8/51 in simplest fraction form is 107/357.

What is 3/21 plus 8/51 as a decimal?

3/21 + 8/51 converted to a decimal is 0.29972.

What is 3/21 plus 8/51 as a percentage?

3/21 + 8/51 expressed as a percentage is 29.972%.

Does 3/21 plus 8/51 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.29972...) because the denominator contains prime factors other than 2 and 5.