What is 13/57 plus 9/21? (Answer: 262/399)

Exact Answer

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Problem: What is 13/57 plus 9/21?
Formula / Expression: 13/57 + 9/21
Final Answer: 262/399
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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 13/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.
Working: 13 × 7/57 × 7 = 91/399 and 9 × 19/21 × 19 = 171/399

Step 3: Add the Numerators
Now add the numerators (91 + 171 = 262) and keep the common denominator 399 unchanged.
Working: 91 + 171/399 = 262/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 262 and 399 is 1, confirming that 262/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 262/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 262 by denominator 399 produces a repeating decimal (approximately 0.656642, or 65.6642%).
Working: 262 ÷ 399 = 0.656642 (65.6642%)

Key Values:
- Simplified Fraction: 262/399
- Mixed Number Form: 262/399
- Decimal Value: 0.656642
- Percentage: 65.6642%

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Solved with FractionsCalc:
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13/57 + 9/21 = 262/399

Simplified Fraction

262/399

Mixed Number

Proper (262/399)

Decimal Value

0.656642

Percentage

65.6642%

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Step-by-Step Solution: 13/57 + 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 13/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.

13 × 7/57 × 7 = 91/399 and 9 × 19/21 × 19 = 171/399

Step 3

Add the Numerators

Now add the numerators (91 + 171 = 262) and keep the common denominator 399 unchanged.

91 + 171/399 = 262/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 262 and 399 is 1, confirming that 262/399 cannot be reduced further—it is already in its simplest irreducible form.

262/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 262 by denominator 399 produces a repeating decimal (approximately 0.656642, or 65.6642%).

262 ÷ 399 = 0.656642 (65.6642%)

Visual Representation

The diagram below illustrates 13/57 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`262/399`
Mixed Number Form	`262/399`
Decimal Form	`0.656642`
Percentage	`65.6642%`

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Frequently Asked Questions

What is 13/57 plus 9/21 as a fraction?

13/57 + 9/21 in simplest fraction form is 262/399.

What is 13/57 plus 9/21 as a decimal?

13/57 + 9/21 converted to a decimal is 0.656642.

What is 13/57 plus 9/21 as a percentage?

13/57 + 9/21 expressed as a percentage is 65.6642%.

Does 13/57 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.656642...) because the denominator contains prime factors other than 2 and 5.