What is 9/51 plus 8/21? (Answer: 199/357)

Exact Answer

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Problem: What is 9/51 plus 8/21?
Formula / Expression: 9/51 + 8/21
Final Answer: 199/357
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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 9/51 by 7, and multiply the numerator and denominator of 8/21 by 17 so both fractions share the common base 357.
Working: 9 × 7/51 × 7 = 63/357 and 8 × 17/21 × 17 = 136/357

Step 3: Add the Numerators
Now add the numerators (63 + 136 = 199) and keep the common denominator 357 unchanged.
Working: 63 + 136/357 = 199/357

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 199 and 357 is 1, confirming that 199/357 cannot be reduced further—it is already in its simplest irreducible form.
Working: 199/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 199 by denominator 357 produces a repeating decimal (approximately 0.557423, or 55.7423%).
Working: 199 ÷ 357 = 0.557423 (55.7423%)

Key Values:
- Simplified Fraction: 199/357
- Mixed Number Form: 199/357
- Decimal Value: 0.557423
- Percentage: 55.7423%

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Solved with FractionsCalc:
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9/51 + 8/21 = 199/357

Simplified Fraction

199/357

Mixed Number

Proper (199/357)

Decimal Value

0.557423

Percentage

55.7423%

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Step-by-Step Solution: 9/51 + 8/21

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 9/51 by 7, and multiply the numerator and denominator of 8/21 by 17 so both fractions share the common base 357.

9 × 7/51 × 7 = 63/357 and 8 × 17/21 × 17 = 136/357

Step 3

Add the Numerators

Now add the numerators (63 + 136 = 199) and keep the common denominator 357 unchanged.

63 + 136/357 = 199/357

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 199 and 357 is 1, confirming that 199/357 cannot be reduced further—it is already in its simplest irreducible form.

199/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 199 by denominator 357 produces a repeating decimal (approximately 0.557423, or 55.7423%).

199 ÷ 357 = 0.557423 (55.7423%)

Visual Representation

The diagram below illustrates 9/51 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`199/357`
Mixed Number Form	`199/357`
Decimal Form	`0.557423`
Percentage	`55.7423%`

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Frequently Asked Questions

What is 9/51 plus 8/21 as a fraction?

9/51 + 8/21 in simplest fraction form is 199/357.

What is 9/51 plus 8/21 as a decimal?

9/51 + 8/21 converted to a decimal is 0.557423.

What is 9/51 plus 8/21 as a percentage?

9/51 + 8/21 expressed as a percentage is 55.7423%.

Does 9/51 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.557423...) because the denominator contains prime factors other than 2 and 5.