What is 4/54 plus 3/21? (Answer: 41/189)

Exact Answer

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Problem: What is 4/54 plus 3/21?
Formula / Expression: 4/54 + 3/21
Final Answer: 41/189
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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 4/54 by 7, and multiply the numerator and denominator of 3/21 by 18 so both fractions share the common base 378.
Working: 4 × 7/54 × 7 = 28/378 and 3 × 18/21 × 18 = 54/378

Step 3: Add the Numerators
Now add the numerators (28 + 54 = 82) and keep the common denominator 378 unchanged.
Working: 28 + 54/378 = 82/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/378 ÷ 2 = 41/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 189 produces a repeating decimal (approximately 0.216931, or 21.6931%).
Working: 41 ÷ 189 = 0.216931 (21.6931%)

Key Values:
- Simplified Fraction: 41/189
- Mixed Number Form: 41/189
- Decimal Value: 0.216931
- Percentage: 21.6931%

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Solved with FractionsCalc:
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4/54 + 3/21 = 41/189

Simplified Fraction

41/189

Mixed Number

Proper (41/189)

Decimal Value

0.216931

Percentage

21.6931%

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Step-by-Step Solution: 4/54 + 3/21

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 4/54 by 7, and multiply the numerator and denominator of 3/21 by 18 so both fractions share the common base 378.

4 × 7/54 × 7 = 28/378 and 3 × 18/21 × 18 = 54/378

Step 3

Add the Numerators

Now add the numerators (28 + 54 = 82) and keep the common denominator 378 unchanged.

28 + 54/378 = 82/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 378, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/378 ÷ 2 = 41/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 189 produces a repeating decimal (approximately 0.216931, or 21.6931%).

41 ÷ 189 = 0.216931 (21.6931%)

Visual Representation

The diagram below illustrates 4/54 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/189`
Mixed Number Form	`41/189`
Decimal Form	`0.216931`
Percentage	`21.6931%`

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Frequently Asked Questions

What is 4/54 plus 3/21 as a fraction?

4/54 + 3/21 in simplest fraction form is 41/189.

What is 4/54 plus 3/21 as a decimal?

4/54 + 3/21 converted to a decimal is 0.216931.

What is 4/54 plus 3/21 as a percentage?

4/54 + 3/21 expressed as a percentage is 21.6931%.

Does 4/54 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.216931...) because the denominator contains prime factors other than 2 and 5.