What is 3/17 plus 8/21? (Answer: 199/357)

Exact Answer

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Problem: What is 3/17 plus 8/21?
Formula / Expression: 3/17 + 8/21
Final Answer: 199/357
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 21 = 357.
Working: LCD(17, 21) = 357

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 21 = 357.

LCD(17, 21) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

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

3 × 21/17 × 21 = 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 3/17 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 3/17 plus 8/21 as a fraction?

3/17 + 8/21 in simplest fraction form is 199/357.

What is 3/17 plus 8/21 as a decimal?

3/17 + 8/21 converted to a decimal is 0.557423.

What is 3/17 plus 8/21 as a percentage?

3/17 + 8/21 expressed as a percentage is 55.7423%.

Does 3/17 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.