What is 3/54 plus 3/21? (Answer: 25/126)

Exact Answer

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Problem: What is 3/54 plus 3/21?
Formula / Expression: 3/54 + 3/21
Final Answer: 25/126
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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 3/54 by 7, and multiply the numerator and denominator of 3/21 by 18 so both fractions share the common base 378.
Working: 3 × 7/54 × 7 = 21/378 and 3 × 18/21 × 18 = 54/378

Step 3: Add the Numerators
Now add the numerators (21 + 54 = 75) and keep the common denominator 378 unchanged.
Working: 21 + 54/378 = 75/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 378, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/378 ÷ 3 = 25/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 126 produces a repeating decimal (approximately 0.198413, or 19.8413%).
Working: 25 ÷ 126 = 0.198413 (19.8413%)

Key Values:
- Simplified Fraction: 25/126
- Mixed Number Form: 25/126
- Decimal Value: 0.198413
- Percentage: 19.8413%

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3/54 + 3/21 = 25/126

Simplified Fraction

25/126

Mixed Number

Proper (25/126)

Decimal Value

0.198413

Percentage

19.8413%

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

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

Step 3

Add the Numerators

Now add the numerators (21 + 54 = 75) and keep the common denominator 378 unchanged.

21 + 54/378 = 75/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 378, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/378 ÷ 3 = 25/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 126 produces a repeating decimal (approximately 0.198413, or 19.8413%).

25 ÷ 126 = 0.198413 (19.8413%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/126`
Mixed Number Form	`25/126`
Decimal Form	`0.198413`
Percentage	`19.8413%`

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Frequently Asked Questions

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

3/54 + 3/21 in simplest fraction form is 25/126.

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

3/54 + 3/21 converted to a decimal is 0.198413.

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

3/54 + 3/21 expressed as a percentage is 19.8413%.

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

It results in a repeating decimal (approximately 0.198413...) because the denominator contains prime factors other than 2 and 5.