What is 5/54 plus 3/21? (Answer: 89/378)

Exact Answer

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Problem: What is 5/54 plus 3/21?
Formula / Expression: 5/54 + 3/21
Final Answer: 89/378
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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 5/54 by 7, and multiply the numerator and denominator of 3/21 by 18 so both fractions share the common base 378.
Working: 5 × 7/54 × 7 = 35/378 and 3 × 18/21 × 18 = 54/378

Step 3: Add the Numerators
Now add the numerators (35 + 54 = 89) and keep the common denominator 378 unchanged.
Working: 35 + 54/378 = 89/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 378 is 1, confirming that 89/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 378 produces a repeating decimal (approximately 0.23545, or 23.545%).
Working: 89 ÷ 378 = 0.23545 (23.545%)

Key Values:
- Simplified Fraction: 89/378
- Mixed Number Form: 89/378
- Decimal Value: 0.23545
- Percentage: 23.545%

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Solved with FractionsCalc:
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5/54 + 3/21 = 89/378

Simplified Fraction

89/378

Mixed Number

Proper (89/378)

Decimal Value

0.23545

Percentage

23.545%

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Step-by-Step Solution: 5/54 + 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 5/54 by 7, and multiply the numerator and denominator of 3/21 by 18 so both fractions share the common base 378.

5 × 7/54 × 7 = 35/378 and 3 × 18/21 × 18 = 54/378

Step 3

Add the Numerators

Now add the numerators (35 + 54 = 89) and keep the common denominator 378 unchanged.

35 + 54/378 = 89/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 378 is 1, confirming that 89/378 cannot be reduced further—it is already in its simplest irreducible form.

89/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 378 produces a repeating decimal (approximately 0.23545, or 23.545%).

89 ÷ 378 = 0.23545 (23.545%)

Visual Representation

The diagram below illustrates 5/54 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/378`
Mixed Number Form	`89/378`
Decimal Form	`0.23545`
Percentage	`23.545%`

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Frequently Asked Questions

What is 5/54 plus 3/21 as a fraction?

5/54 + 3/21 in simplest fraction form is 89/378.

What is 5/54 plus 3/21 as a decimal?

5/54 + 3/21 converted to a decimal is 0.23545.

What is 5/54 plus 3/21 as a percentage?

5/54 + 3/21 expressed as a percentage is 23.545%.

Does 5/54 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.23545...) because the denominator contains prime factors other than 2 and 5.