What is 4/27 plus 9/21? (Answer: 109/189)

Exact Answer

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Problem: What is 4/27 plus 9/21?
Formula / Expression: 4/27 + 9/21
Final Answer: 109/189
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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 9/21 by 9 so both fractions share the common base 189.
Working: 4 × 7/27 × 7 = 28/189 and 9 × 9/21 × 9 = 81/189

Step 3: Add the Numerators
Now add the numerators (28 + 81 = 109) and keep the common denominator 189 unchanged.
Working: 28 + 81/189 = 109/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 189 is 1, confirming that 109/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 189 produces a repeating decimal (approximately 0.57672, or 57.672%).
Working: 109 ÷ 189 = 0.57672 (57.672%)

Key Values:
- Simplified Fraction: 109/189
- Mixed Number Form: 109/189
- Decimal Value: 0.57672
- Percentage: 57.672%

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Solved with FractionsCalc:
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4/27 + 9/21 = 109/189

Simplified Fraction

109/189

Mixed Number

Proper (109/189)

Decimal Value

0.57672

Percentage

57.672%

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

4 × 7/27 × 7 = 28/189 and 9 × 9/21 × 9 = 81/189

Step 3

Add the Numerators

Now add the numerators (28 + 81 = 109) and keep the common denominator 189 unchanged.

28 + 81/189 = 109/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 189 is 1, confirming that 109/189 cannot be reduced further—it is already in its simplest irreducible form.

109/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 189 produces a repeating decimal (approximately 0.57672, or 57.672%).

109 ÷ 189 = 0.57672 (57.672%)

Visual Representation

The diagram below illustrates 4/27 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/189`
Mixed Number Form	`109/189`
Decimal Form	`0.57672`
Percentage	`57.672%`

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Frequently Asked Questions

What is 4/27 plus 9/21 as a fraction?

4/27 + 9/21 in simplest fraction form is 109/189.

What is 4/27 plus 9/21 as a decimal?

4/27 + 9/21 converted to a decimal is 0.57672.

What is 4/27 plus 9/21 as a percentage?

4/27 + 9/21 expressed as a percentage is 57.672%.

Does 4/27 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.57672...) because the denominator contains prime factors other than 2 and 5.