What is 11/54 plus 9/21? (Answer: 239/378)

Exact Answer

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Problem: What is 11/54 plus 9/21?
Formula / Expression: 11/54 + 9/21
Final Answer: 239/378
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).
Working: LCD(54, 21) = 378

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 11/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.
Working: 11 × 7/54 × 7 = 77/378 and 9 × 18/21 × 18 = 162/378

Step 3: Add the Numerators
Now add the numerators (77 + 162 = 239) and keep the common denominator 378 unchanged.
Working: 77 + 162/378 = 239/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 239 and 378 is 1, confirming that 239/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 239/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 239 by denominator 378 produces a repeating decimal (approximately 0.632275, or 63.2275%).
Working: 239 ÷ 378 = 0.632275 (63.2275%)

Key Values:
- Simplified Fraction: 239/378
- Mixed Number Form: 239/378
- Decimal Value: 0.632275
- Percentage: 63.2275%

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Solved with FractionsCalc:
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11/54 + 9/21 = 239/378

Simplified Fraction

239/378

Mixed Number

Proper (239/378)

Decimal Value

0.632275

Percentage

63.2275%

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Step-by-Step Solution: 11/54 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).

LCD(54, 21) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 11/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.

11 × 7/54 × 7 = 77/378 and 9 × 18/21 × 18 = 162/378

Step 3

Add the Numerators

Now add the numerators (77 + 162 = 239) and keep the common denominator 378 unchanged.

77 + 162/378 = 239/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 239 and 378 is 1, confirming that 239/378 cannot be reduced further—it is already in its simplest irreducible form.

239/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 239 by denominator 378 produces a repeating decimal (approximately 0.632275, or 63.2275%).

239 ÷ 378 = 0.632275 (63.2275%)

Visual Representation

The diagram below illustrates 11/54 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`239/378`
Mixed Number Form	`239/378`
Decimal Form	`0.632275`
Percentage	`63.2275%`

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Frequently Asked Questions

What is 11/54 plus 9/21 as a fraction?

11/54 + 9/21 in simplest fraction form is 239/378.

What is 11/54 plus 9/21 as a decimal?

11/54 + 9/21 converted to a decimal is 0.632275.

What is 11/54 plus 9/21 as a percentage?

11/54 + 9/21 expressed as a percentage is 63.2275%.

Does 11/54 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.632275...) because the denominator contains prime factors other than 2 and 5.