What is 3/51 plus 5/21? (Answer: 106/357)

Exact Answer

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Problem: What is 3/51 plus 5/21?
Formula / Expression: 3/51 + 5/21
Final Answer: 106/357
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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 3/51 by 7, and multiply the numerator and denominator of 5/21 by 17 so both fractions share the common base 357.
Working: 3 × 7/51 × 7 = 21/357 and 5 × 17/21 × 17 = 85/357

Step 3: Add the Numerators
Now add the numerators (21 + 85 = 106) and keep the common denominator 357 unchanged.
Working: 21 + 85/357 = 106/357

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 106 and 357 is 1, confirming that 106/357 cannot be reduced further—it is already in its simplest irreducible form.
Working: 106/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 106 by denominator 357 produces a repeating decimal (approximately 0.296919, or 29.6919%).
Working: 106 ÷ 357 = 0.296919 (29.6919%)

Key Values:
- Simplified Fraction: 106/357
- Mixed Number Form: 106/357
- Decimal Value: 0.296919
- Percentage: 29.6919%

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3/51 + 5/21 = 106/357

Simplified Fraction

106/357

Mixed Number

Proper (106/357)

Decimal Value

0.296919

Percentage

29.6919%

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Step-by-Step Solution: 3/51 + 5/21

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 5/21 by 17 so both fractions share the common base 357.

3 × 7/51 × 7 = 21/357 and 5 × 17/21 × 17 = 85/357

Step 3

Add the Numerators

Now add the numerators (21 + 85 = 106) and keep the common denominator 357 unchanged.

21 + 85/357 = 106/357

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 106 and 357 is 1, confirming that 106/357 cannot be reduced further—it is already in its simplest irreducible form.

106/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 106 by denominator 357 produces a repeating decimal (approximately 0.296919, or 29.6919%).

106 ÷ 357 = 0.296919 (29.6919%)

Visual Representation

The diagram below illustrates 3/51 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`106/357`
Mixed Number Form	`106/357`
Decimal Form	`0.296919`
Percentage	`29.6919%`

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Frequently Asked Questions

What is 3/51 plus 5/21 as a fraction?

3/51 + 5/21 in simplest fraction form is 106/357.

What is 3/51 plus 5/21 as a decimal?

3/51 + 5/21 converted to a decimal is 0.296919.

What is 3/51 plus 5/21 as a percentage?

3/51 + 5/21 expressed as a percentage is 29.6919%.

Does 3/51 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.296919...) because the denominator contains prime factors other than 2 and 5.