What is 2/21 plus 3/27? (Answer: 13/63)

Exact Answer

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Problem: What is 2/21 plus 3/27?
Formula / Expression: 2/21 + 3/27
Final Answer: 13/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 27 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 21 × 27 = 567, keeping the calculation simpler).
Working: LCD(21, 27) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 2/21 by 9, and multiply the numerator and denominator of 3/27 by 7 so both fractions share the common base 189.
Working: 2 × 9/21 × 9 = 18/189 and 3 × 7/27 × 7 = 21/189

Step 3: Add the Numerators
Now add the numerators (18 + 21 = 39) and keep the common denominator 189 unchanged.
Working: 18 + 21/189 = 39/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 189, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/189 ÷ 3 = 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:
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2/21 + 3/27 = 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 + 3/27

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 27 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 21 × 27 = 567, keeping the calculation simpler).

LCD(21, 27) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 2/21 by 9, and multiply the numerator and denominator of 3/27 by 7 so both fractions share the common base 189.

2 × 9/21 × 9 = 18/189 and 3 × 7/27 × 7 = 21/189

Step 3

Add the Numerators

Now add the numerators (18 + 21 = 39) and keep the common denominator 189 unchanged.

18 + 21/189 = 39/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 189, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/189 ÷ 3 = 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 3/27 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 3/27 as a fraction?

2/21 + 3/27 in simplest fraction form is 13/63.

What is 2/21 plus 3/27 as a decimal?

2/21 + 3/27 converted to a decimal is 0.206349.

What is 2/21 plus 3/27 as a percentage?

2/21 + 3/27 expressed as a percentage is 20.6349%.

Does 2/21 plus 3/27 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.