What is 4/17 plus 10/21? (Answer: 254/357)

Exact Answer

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Problem: What is 4/17 plus 10/21?
Formula / Expression: 4/17 + 10/21
Final Answer: 254/357
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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 4/17 by 21, and multiply the numerator and denominator of 10/21 by 17 so both fractions share the common base 357.
Working: 4 × 21/17 × 21 = 84/357 and 10 × 17/21 × 17 = 170/357

Step 3: Add the Numerators
Now add the numerators (84 + 170 = 254) and keep the common denominator 357 unchanged.
Working: 84 + 170/357 = 254/357

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 254 and 357 is 1, confirming that 254/357 cannot be reduced further—it is already in its simplest irreducible form.
Working: 254/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 254 by denominator 357 produces a repeating decimal (approximately 0.711485, or 71.1485%).
Working: 254 ÷ 357 = 0.711485 (71.1485%)

Key Values:
- Simplified Fraction: 254/357
- Mixed Number Form: 254/357
- Decimal Value: 0.711485
- Percentage: 71.1485%

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4/17 + 10/21 = 254/357

Simplified Fraction

254/357

Mixed Number

Proper (254/357)

Decimal Value

0.711485

Percentage

71.1485%

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Step-by-Step Solution: 4/17 + 10/21

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 4/17 by 21, and multiply the numerator and denominator of 10/21 by 17 so both fractions share the common base 357.

4 × 21/17 × 21 = 84/357 and 10 × 17/21 × 17 = 170/357

Step 3

Add the Numerators

Now add the numerators (84 + 170 = 254) and keep the common denominator 357 unchanged.

84 + 170/357 = 254/357

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 254 and 357 is 1, confirming that 254/357 cannot be reduced further—it is already in its simplest irreducible form.

254/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 254 by denominator 357 produces a repeating decimal (approximately 0.711485, or 71.1485%).

254 ÷ 357 = 0.711485 (71.1485%)

Visual Representation

The diagram below illustrates 4/17 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`254/357`
Mixed Number Form	`254/357`
Decimal Form	`0.711485`
Percentage	`71.1485%`

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Frequently Asked Questions

What is 4/17 plus 10/21 as a fraction?

4/17 + 10/21 in simplest fraction form is 254/357.

What is 4/17 plus 10/21 as a decimal?

4/17 + 10/21 converted to a decimal is 0.711485.

What is 4/17 plus 10/21 as a percentage?

4/17 + 10/21 expressed as a percentage is 71.1485%.

Does 4/17 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.711485...) because the denominator contains prime factors other than 2 and 5.