What is 5/51 plus 10/21? (Answer: 205/357)

Exact Answer

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Problem: What is 5/51 plus 10/21?
Formula / Expression: 5/51 + 10/21
Final Answer: 205/357
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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 5/51 by 7, and multiply the numerator and denominator of 10/21 by 17 so both fractions share the common base 357.
Working: 5 × 7/51 × 7 = 35/357 and 10 × 17/21 × 17 = 170/357

Step 3: Add the Numerators
Now add the numerators (35 + 170 = 205) and keep the common denominator 357 unchanged.
Working: 35 + 170/357 = 205/357

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 205 and 357 is 1, confirming that 205/357 cannot be reduced further—it is already in its simplest irreducible form.
Working: 205/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 205 by denominator 357 produces a repeating decimal (approximately 0.57423, or 57.423%).
Working: 205 ÷ 357 = 0.57423 (57.423%)

Key Values:
- Simplified Fraction: 205/357
- Mixed Number Form: 205/357
- Decimal Value: 0.57423
- Percentage: 57.423%

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Solved with FractionsCalc:
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5/51 + 10/21 = 205/357

Simplified Fraction

205/357

Mixed Number

Proper (205/357)

Decimal Value

0.57423

Percentage

57.423%

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Step-by-Step Solution: 5/51 + 10/21

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 5/51 by 7, and multiply the numerator and denominator of 10/21 by 17 so both fractions share the common base 357.

5 × 7/51 × 7 = 35/357 and 10 × 17/21 × 17 = 170/357

Step 3

Add the Numerators

Now add the numerators (35 + 170 = 205) and keep the common denominator 357 unchanged.

35 + 170/357 = 205/357

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 205 and 357 is 1, confirming that 205/357 cannot be reduced further—it is already in its simplest irreducible form.

205/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 205 by denominator 357 produces a repeating decimal (approximately 0.57423, or 57.423%).

205 ÷ 357 = 0.57423 (57.423%)

Visual Representation

The diagram below illustrates 5/51 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`205/357`
Mixed Number Form	`205/357`
Decimal Form	`0.57423`
Percentage	`57.423%`

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Frequently Asked Questions

What is 5/51 plus 10/21 as a fraction?

5/51 + 10/21 in simplest fraction form is 205/357.

What is 5/51 plus 10/21 as a decimal?

5/51 + 10/21 converted to a decimal is 0.57423.

What is 5/51 plus 10/21 as a percentage?

5/51 + 10/21 expressed as a percentage is 57.423%.

Does 5/51 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.57423...) because the denominator contains prime factors other than 2 and 5.