What is 4/27 plus 6/21? (Answer: 82/189)

Exact Answer

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Problem: What is 4/27 plus 6/21?
Formula / Expression: 4/27 + 6/21
Final Answer: 82/189
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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 4/27 by 7, and multiply the numerator and denominator of 6/21 by 9 so both fractions share the common base 189.
Working: 4 × 7/27 × 7 = 28/189 and 6 × 9/21 × 9 = 54/189

Step 3: Add the Numerators
Now add the numerators (28 + 54 = 82) and keep the common denominator 189 unchanged.
Working: 28 + 54/189 = 82/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 82 and 189 is 1, confirming that 82/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 82/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 189 produces a repeating decimal (approximately 0.433862, or 43.3862%).
Working: 82 ÷ 189 = 0.433862 (43.3862%)

Key Values:
- Simplified Fraction: 82/189
- Mixed Number Form: 82/189
- Decimal Value: 0.433862
- Percentage: 43.3862%

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Solved with FractionsCalc:
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4/27 + 6/21 = 82/189

Simplified Fraction

82/189

Mixed Number

Proper (82/189)

Decimal Value

0.433862

Percentage

43.3862%

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Step-by-Step Solution: 4/27 + 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 4/27 by 7, and multiply the numerator and denominator of 6/21 by 9 so both fractions share the common base 189.

4 × 7/27 × 7 = 28/189 and 6 × 9/21 × 9 = 54/189

Step 3

Add the Numerators

Now add the numerators (28 + 54 = 82) and keep the common denominator 189 unchanged.

28 + 54/189 = 82/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 82 and 189 is 1, confirming that 82/189 cannot be reduced further—it is already in its simplest irreducible form.

82/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 189 produces a repeating decimal (approximately 0.433862, or 43.3862%).

82 ÷ 189 = 0.433862 (43.3862%)

Visual Representation

The diagram below illustrates 4/27 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/189`
Mixed Number Form	`82/189`
Decimal Form	`0.433862`
Percentage	`43.3862%`

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Frequently Asked Questions

What is 4/27 plus 6/21 as a fraction?

4/27 + 6/21 in simplest fraction form is 82/189.

What is 4/27 plus 6/21 as a decimal?

4/27 + 6/21 converted to a decimal is 0.433862.

What is 4/27 plus 6/21 as a percentage?

4/27 + 6/21 expressed as a percentage is 43.3862%.

Does 4/27 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.433862...) because the denominator contains prime factors other than 2 and 5.