What is 6/27 plus 9/21? (Answer: 41/63)

Exact Answer

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Problem: What is 6/27 plus 9/21?
Formula / Expression: 6/27 + 9/21
Final Answer: 41/63
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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 6/27 by 7, and multiply the numerator and denominator of 9/21 by 9 so both fractions share the common base 189.
Working: 6 × 7/27 × 7 = 42/189 and 9 × 9/21 × 9 = 81/189

Step 3: Add the Numerators
Now add the numerators (42 + 81 = 123) and keep the common denominator 189 unchanged.
Working: 42 + 81/189 = 123/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 189, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/189 ÷ 3 = 41/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).
Working: 41 ÷ 63 = 0.650794 (65.0794%)

Key Values:
- Simplified Fraction: 41/63
- Mixed Number Form: 41/63
- Decimal Value: 0.650794
- Percentage: 65.0794%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-27-plus-9-21/
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6/27 + 9/21 = 41/63

Simplified Fraction

41/63

Mixed Number

Proper (41/63)

Decimal Value

0.650794

Percentage

65.0794%

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Step-by-Step Solution: 6/27 + 9/21

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

6 × 7/27 × 7 = 42/189 and 9 × 9/21 × 9 = 81/189

Step 3

Add the Numerators

Now add the numerators (42 + 81 = 123) and keep the common denominator 189 unchanged.

42 + 81/189 = 123/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 189, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/189 ÷ 3 = 41/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).

41 ÷ 63 = 0.650794 (65.0794%)

Visual Representation

The diagram below illustrates 6/27 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/63`
Mixed Number Form	`41/63`
Decimal Form	`0.650794`
Percentage	`65.0794%`

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Frequently Asked Questions

What is 6/27 plus 9/21 as a fraction?

6/27 + 9/21 in simplest fraction form is 41/63.

What is 6/27 plus 9/21 as a decimal?

6/27 + 9/21 converted to a decimal is 0.650794.

What is 6/27 plus 9/21 as a percentage?

6/27 + 9/21 expressed as a percentage is 65.0794%.

Does 6/27 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.650794...) because the denominator contains prime factors other than 2 and 5.