What is 10/57 plus 9/21? (Answer: 241/399)

Exact Answer

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Problem: What is 10/57 plus 9/21?
Formula / Expression: 10/57 + 9/21
Final Answer: 241/399
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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 10/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.
Working: 10 × 7/57 × 7 = 70/399 and 9 × 19/21 × 19 = 171/399

Step 3: Add the Numerators
Now add the numerators (70 + 171 = 241) and keep the common denominator 399 unchanged.
Working: 70 + 171/399 = 241/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 241 and 399 is 1, confirming that 241/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 241/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 241 by denominator 399 produces a repeating decimal (approximately 0.60401, or 60.401%).
Working: 241 ÷ 399 = 0.60401 (60.401%)

Key Values:
- Simplified Fraction: 241/399
- Mixed Number Form: 241/399
- Decimal Value: 0.60401
- Percentage: 60.401%

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Solved with FractionsCalc:
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10/57 + 9/21 = 241/399

Simplified Fraction

241/399

Mixed Number

Proper (241/399)

Decimal Value

0.60401

Percentage

60.401%

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Step-by-Step Solution: 10/57 + 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 10/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.

10 × 7/57 × 7 = 70/399 and 9 × 19/21 × 19 = 171/399

Step 3

Add the Numerators

Now add the numerators (70 + 171 = 241) and keep the common denominator 399 unchanged.

70 + 171/399 = 241/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 241 and 399 is 1, confirming that 241/399 cannot be reduced further—it is already in its simplest irreducible form.

241/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 241 by denominator 399 produces a repeating decimal (approximately 0.60401, or 60.401%).

241 ÷ 399 = 0.60401 (60.401%)

Visual Representation

The diagram below illustrates 10/57 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`241/399`
Mixed Number Form	`241/399`
Decimal Form	`0.60401`
Percentage	`60.401%`

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Frequently Asked Questions

What is 10/57 plus 9/21 as a fraction?

10/57 + 9/21 in simplest fraction form is 241/399.

What is 10/57 plus 9/21 as a decimal?

10/57 + 9/21 converted to a decimal is 0.60401.

What is 10/57 plus 9/21 as a percentage?

10/57 + 9/21 expressed as a percentage is 60.401%.

Does 10/57 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.60401...) because the denominator contains prime factors other than 2 and 5.