What is 3/27 plus 6/21? (Answer: 25/63)

Exact Answer

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Problem: What is 3/27 plus 6/21?
Formula / Expression: 3/27 + 6/21
Final Answer: 25/63
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 3/27 by 7, and multiply the numerator and denominator of 6/21 by 9 so both fractions share the common base 189.
Working: 3 × 7/27 × 7 = 21/189 and 6 × 9/21 × 9 = 54/189

Step 3: Add the Numerators
Now add the numerators (21 + 54 = 75) and keep the common denominator 189 unchanged.
Working: 21 + 54/189 = 75/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 189, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/189 ÷ 3 = 25/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 63 produces a repeating decimal (approximately 0.396825, or 39.6825%).
Working: 25 ÷ 63 = 0.396825 (39.6825%)

Key Values:
- Simplified Fraction: 25/63
- Mixed Number Form: 25/63
- Decimal Value: 0.396825
- Percentage: 39.6825%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-27-plus-6-21/
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3/27 + 6/21 = 25/63

Simplified Fraction

25/63

Mixed Number

Proper (25/63)

Decimal Value

0.396825

Percentage

39.6825%

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Step-by-Step Solution: 3/27 + 6/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 3/27 by 7, and multiply the numerator and denominator of 6/21 by 9 so both fractions share the common base 189.

3 × 7/27 × 7 = 21/189 and 6 × 9/21 × 9 = 54/189

Step 3

Add the Numerators

Now add the numerators (21 + 54 = 75) and keep the common denominator 189 unchanged.

21 + 54/189 = 75/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 189, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/189 ÷ 3 = 25/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 63 produces a repeating decimal (approximately 0.396825, or 39.6825%).

25 ÷ 63 = 0.396825 (39.6825%)

Visual Representation

The diagram below illustrates 3/27 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/63`
Mixed Number Form	`25/63`
Decimal Form	`0.396825`
Percentage	`39.6825%`

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Frequently Asked Questions

What is 3/27 plus 6/21 as a fraction?

3/27 + 6/21 in simplest fraction form is 25/63.

What is 3/27 plus 6/21 as a decimal?

3/27 + 6/21 converted to a decimal is 0.396825.

What is 3/27 plus 6/21 as a percentage?

3/27 + 6/21 expressed as a percentage is 39.6825%.

Does 3/27 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.396825...) because the denominator contains prime factors other than 2 and 5.