What is 9/57 plus 10/21? (Answer: 253/399)

Exact Answer

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Problem: What is 9/57 plus 10/21?
Formula / Expression: 9/57 + 10/21
Final Answer: 253/399
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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 9/57 by 7, and multiply the numerator and denominator of 10/21 by 19 so both fractions share the common base 399.
Working: 9 × 7/57 × 7 = 63/399 and 10 × 19/21 × 19 = 190/399

Step 3: Add the Numerators
Now add the numerators (63 + 190 = 253) and keep the common denominator 399 unchanged.
Working: 63 + 190/399 = 253/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 253 and 399 is 1, confirming that 253/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 253/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 253 by denominator 399 produces a repeating decimal (approximately 0.634085, or 63.4085%).
Working: 253 ÷ 399 = 0.634085 (63.4085%)

Key Values:
- Simplified Fraction: 253/399
- Mixed Number Form: 253/399
- Decimal Value: 0.634085
- Percentage: 63.4085%

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Solved with FractionsCalc:
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9/57 + 10/21 = 253/399

Simplified Fraction

253/399

Mixed Number

Proper (253/399)

Decimal Value

0.634085

Percentage

63.4085%

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Step-by-Step Solution: 9/57 + 10/21

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

9 × 7/57 × 7 = 63/399 and 10 × 19/21 × 19 = 190/399

Step 3

Add the Numerators

Now add the numerators (63 + 190 = 253) and keep the common denominator 399 unchanged.

63 + 190/399 = 253/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 253 and 399 is 1, confirming that 253/399 cannot be reduced further—it is already in its simplest irreducible form.

253/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 253 by denominator 399 produces a repeating decimal (approximately 0.634085, or 63.4085%).

253 ÷ 399 = 0.634085 (63.4085%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`253/399`
Mixed Number Form	`253/399`
Decimal Form	`0.634085`
Percentage	`63.4085%`

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Frequently Asked Questions

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

9/57 + 10/21 in simplest fraction form is 253/399.

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

9/57 + 10/21 converted to a decimal is 0.634085.

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

9/57 + 10/21 expressed as a percentage is 63.4085%.

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

It results in a repeating decimal (approximately 0.634085...) because the denominator contains prime factors other than 2 and 5.