What is 4/21 plus 11/54? (Answer: 149/378)

Exact Answer

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Problem: What is 4/21 plus 11/54?
Formula / Expression: 4/21 + 11/54
Final Answer: 149/378
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 4/21 by 18, and multiply the numerator and denominator of 11/54 by 7 so both fractions share the common base 378.
Working: 4 × 18/21 × 18 = 72/378 and 11 × 7/54 × 7 = 77/378

Step 3: Add the Numerators
Now add the numerators (72 + 77 = 149) and keep the common denominator 378 unchanged.
Working: 72 + 77/378 = 149/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 149 and 378 is 1, confirming that 149/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 149/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 149 by denominator 378 produces a repeating decimal (approximately 0.39418, or 39.418%).
Working: 149 ÷ 378 = 0.39418 (39.418%)

Key Values:
- Simplified Fraction: 149/378
- Mixed Number Form: 149/378
- Decimal Value: 0.39418
- Percentage: 39.418%

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Solved with FractionsCalc:
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4/21 + 11/54 = 149/378

Simplified Fraction

149/378

Mixed Number

Proper (149/378)

Decimal Value

0.39418

Percentage

39.418%

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Step-by-Step Solution: 4/21 + 11/54

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 54) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 4/21 by 18, and multiply the numerator and denominator of 11/54 by 7 so both fractions share the common base 378.

4 × 18/21 × 18 = 72/378 and 11 × 7/54 × 7 = 77/378

Step 3

Add the Numerators

Now add the numerators (72 + 77 = 149) and keep the common denominator 378 unchanged.

72 + 77/378 = 149/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 149 and 378 is 1, confirming that 149/378 cannot be reduced further—it is already in its simplest irreducible form.

149/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 149 by denominator 378 produces a repeating decimal (approximately 0.39418, or 39.418%).

149 ÷ 378 = 0.39418 (39.418%)

Visual Representation

The diagram below illustrates 4/21 plus 11/54 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`149/378`
Mixed Number Form	`149/378`
Decimal Form	`0.39418`
Percentage	`39.418%`

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Frequently Asked Questions

What is 4/21 plus 11/54 as a fraction?

4/21 + 11/54 in simplest fraction form is 149/378.

What is 4/21 plus 11/54 as a decimal?

4/21 + 11/54 converted to a decimal is 0.39418.

What is 4/21 plus 11/54 as a percentage?

4/21 + 11/54 expressed as a percentage is 39.418%.

Does 4/21 plus 11/54 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.39418...) because the denominator contains prime factors other than 2 and 5.