What is 3/54 plus 6/21? (Answer: 43/126)

Exact Answer

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Problem: What is 3/54 plus 6/21?
Formula / Expression: 3/54 + 6/21
Final Answer: 43/126
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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 6/21 by 18 so both fractions share the common base 378.
Working: 3 × 7/54 × 7 = 21/378 and 6 × 18/21 × 18 = 108/378

Step 3: Add the Numerators
Now add the numerators (21 + 108 = 129) and keep the common denominator 378 unchanged.
Working: 21 + 108/378 = 129/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 378, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/378 ÷ 3 = 43/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 126 produces a repeating decimal (approximately 0.34127, or 34.127%).
Working: 43 ÷ 126 = 0.34127 (34.127%)

Key Values:
- Simplified Fraction: 43/126
- Mixed Number Form: 43/126
- Decimal Value: 0.34127
- Percentage: 34.127%

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Solved with FractionsCalc:
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3/54 + 6/21 = 43/126

Simplified Fraction

43/126

Mixed Number

Proper (43/126)

Decimal Value

0.34127

Percentage

34.127%

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Step-by-Step Solution: 3/54 + 6/21

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 6/21 by 18 so both fractions share the common base 378.

3 × 7/54 × 7 = 21/378 and 6 × 18/21 × 18 = 108/378

Step 3

Add the Numerators

Now add the numerators (21 + 108 = 129) and keep the common denominator 378 unchanged.

21 + 108/378 = 129/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 378, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/378 ÷ 3 = 43/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 126 produces a repeating decimal (approximately 0.34127, or 34.127%).

43 ÷ 126 = 0.34127 (34.127%)

Visual Representation

The diagram below illustrates 3/54 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/126`
Mixed Number Form	`43/126`
Decimal Form	`0.34127`
Percentage	`34.127%`

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Frequently Asked Questions

What is 3/54 plus 6/21 as a fraction?

3/54 + 6/21 in simplest fraction form is 43/126.

What is 3/54 plus 6/21 as a decimal?

3/54 + 6/21 converted to a decimal is 0.34127.

What is 3/54 plus 6/21 as a percentage?

3/54 + 6/21 expressed as a percentage is 34.127%.

Does 3/54 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.34127...) because the denominator contains prime factors other than 2 and 5.