What is 2/21 plus 6/54? (Answer: 13/63)

Exact Answer

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Problem: What is 2/21 plus 6/54?
Formula / Expression: 2/21 + 6/54
Final Answer: 13/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 54 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 21 × 54 = 1134, keeping the calculation simpler).
Working: LCD(21, 54) = 378

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 2/21 by 18, and multiply the numerator and denominator of 6/54 by 7 so both fractions share the common base 378.
Working: 2 × 18/21 × 18 = 36/378 and 6 × 7/54 × 7 = 42/378

Step 3: Add the Numerators
Now add the numerators (36 + 42 = 78) and keep the common denominator 378 unchanged.
Working: 36 + 42/378 = 78/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 378, which is 6. Divide both the numerator and denominator by 6.
Working: 78 ÷ 6/378 ÷ 6 = 13/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 63 produces a repeating decimal (approximately 0.206349, or 20.6349%).
Working: 13 ÷ 63 = 0.206349 (20.6349%)

Key Values:
- Simplified Fraction: 13/63
- Mixed Number Form: 13/63
- Decimal Value: 0.206349
- Percentage: 20.6349%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-6-54/
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2/21 + 6/54 = 13/63

Simplified Fraction

13/63

Mixed Number

Proper (13/63)

Decimal Value

0.206349

Percentage

20.6349%

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Step-by-Step Solution: 2/21 + 6/54

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 54 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 21 × 54 = 1134, keeping the calculation simpler).

LCD(21, 54) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 2/21 by 18, and multiply the numerator and denominator of 6/54 by 7 so both fractions share the common base 378.

2 × 18/21 × 18 = 36/378 and 6 × 7/54 × 7 = 42/378

Step 3

Add the Numerators

Now add the numerators (36 + 42 = 78) and keep the common denominator 378 unchanged.

36 + 42/378 = 78/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 378, which is 6. Divide both the numerator and denominator by 6.

78 ÷ 6/378 ÷ 6 = 13/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 63 produces a repeating decimal (approximately 0.206349, or 20.6349%).

13 ÷ 63 = 0.206349 (20.6349%)

Visual Representation

The diagram below illustrates 2/21 plus 6/54 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/63`
Mixed Number Form	`13/63`
Decimal Form	`0.206349`
Percentage	`20.6349%`

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Frequently Asked Questions

What is 2/21 plus 6/54 as a fraction?

2/21 + 6/54 in simplest fraction form is 13/63.

What is 2/21 plus 6/54 as a decimal?

2/21 + 6/54 converted to a decimal is 0.206349.

What is 2/21 plus 6/54 as a percentage?

2/21 + 6/54 expressed as a percentage is 20.6349%.

Does 2/21 plus 6/54 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.206349...) because the denominator contains prime factors other than 2 and 5.