What is 4/54 plus 4/21? (Answer: 50/189)

Exact Answer

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Problem: What is 4/54 plus 4/21?
Formula / Expression: 4/54 + 4/21
Final Answer: 50/189
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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 4/21 by 18 so both fractions share the common base 378.
Working: 4 × 7/54 × 7 = 28/378 and 4 × 18/21 × 18 = 72/378

Step 3: Add the Numerators
Now add the numerators (28 + 72 = 100) and keep the common denominator 378 unchanged.
Working: 28 + 72/378 = 100/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 100 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 100 ÷ 2/378 ÷ 2 = 50/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 50 by denominator 189 produces a repeating decimal (approximately 0.26455, or 26.455%).
Working: 50 ÷ 189 = 0.26455 (26.455%)

Key Values:
- Simplified Fraction: 50/189
- Mixed Number Form: 50/189
- Decimal Value: 0.26455
- Percentage: 26.455%

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Solved with FractionsCalc:
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4/54 + 4/21 = 50/189

Simplified Fraction

50/189

Mixed Number

Proper (50/189)

Decimal Value

0.26455

Percentage

26.455%

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

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 4/21 by 18 so both fractions share the common base 378.

4 × 7/54 × 7 = 28/378 and 4 × 18/21 × 18 = 72/378

Step 3

Add the Numerators

Now add the numerators (28 + 72 = 100) and keep the common denominator 378 unchanged.

28 + 72/378 = 100/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 100 and 378, which is 2. Divide both the numerator and denominator by 2.

100 ÷ 2/378 ÷ 2 = 50/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 50 by denominator 189 produces a repeating decimal (approximately 0.26455, or 26.455%).

50 ÷ 189 = 0.26455 (26.455%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`50/189`
Mixed Number Form	`50/189`
Decimal Form	`0.26455`
Percentage	`26.455%`

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Frequently Asked Questions

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

4/54 + 4/21 in simplest fraction form is 50/189.

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

4/54 + 4/21 converted to a decimal is 0.26455.

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

4/54 + 4/21 expressed as a percentage is 26.455%.

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

It results in a repeating decimal (approximately 0.26455...) because the denominator contains prime factors other than 2 and 5.