What is 17/57 plus 9/21? (Answer: 290/399)

Exact Answer

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Problem: What is 17/57 plus 9/21?
Formula / Expression: 17/57 + 9/21
Final Answer: 290/399
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).
Working: LCD(57, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 17/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.
Working: 17 × 7/57 × 7 = 119/399 and 9 × 19/21 × 19 = 171/399

Step 3: Add the Numerators
Now add the numerators (119 + 171 = 290) and keep the common denominator 399 unchanged.
Working: 119 + 171/399 = 290/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 290 and 399 is 1, confirming that 290/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 290/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 290 by denominator 399 produces a repeating decimal (approximately 0.726817, or 72.6817%).
Working: 290 ÷ 399 = 0.726817 (72.6817%)

Key Values:
- Simplified Fraction: 290/399
- Mixed Number Form: 290/399
- Decimal Value: 0.726817
- Percentage: 72.6817%

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Solved with FractionsCalc:
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17/57 + 9/21 = 290/399

Simplified Fraction

290/399

Mixed Number

Proper (290/399)

Decimal Value

0.726817

Percentage

72.6817%

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Step-by-Step Solution: 17/57 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).

LCD(57, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 17/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.

17 × 7/57 × 7 = 119/399 and 9 × 19/21 × 19 = 171/399

Step 3

Add the Numerators

Now add the numerators (119 + 171 = 290) and keep the common denominator 399 unchanged.

119 + 171/399 = 290/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 290 and 399 is 1, confirming that 290/399 cannot be reduced further—it is already in its simplest irreducible form.

290/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 290 by denominator 399 produces a repeating decimal (approximately 0.726817, or 72.6817%).

290 ÷ 399 = 0.726817 (72.6817%)

Visual Representation

The diagram below illustrates 17/57 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`290/399`
Mixed Number Form	`290/399`
Decimal Form	`0.726817`
Percentage	`72.6817%`

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Frequently Asked Questions

What is 17/57 plus 9/21 as a fraction?

17/57 + 9/21 in simplest fraction form is 290/399.

What is 17/57 plus 9/21 as a decimal?

17/57 + 9/21 converted to a decimal is 0.726817.

What is 17/57 plus 9/21 as a percentage?

17/57 + 9/21 expressed as a percentage is 72.6817%.

Does 17/57 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.726817...) because the denominator contains prime factors other than 2 and 5.