What is 4/27 plus 5/21? (Answer: 73/189)

Exact Answer

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Problem: What is 4/27 plus 5/21?
Formula / Expression: 4/27 + 5/21
Final Answer: 73/189
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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 5/21 by 9 so both fractions share the common base 189.
Working: 4 × 7/27 × 7 = 28/189 and 5 × 9/21 × 9 = 45/189

Step 3: Add the Numerators
Now add the numerators (28 + 45 = 73) and keep the common denominator 189 unchanged.
Working: 28 + 45/189 = 73/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 189 is 1, confirming that 73/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 189 produces a repeating decimal (approximately 0.386243, or 38.6243%).
Working: 73 ÷ 189 = 0.386243 (38.6243%)

Key Values:
- Simplified Fraction: 73/189
- Mixed Number Form: 73/189
- Decimal Value: 0.386243
- Percentage: 38.6243%

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Solved with FractionsCalc:
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4/27 + 5/21 = 73/189

Simplified Fraction

73/189

Mixed Number

Proper (73/189)

Decimal Value

0.386243

Percentage

38.6243%

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Step-by-Step Solution: 4/27 + 5/21

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 5/21 by 9 so both fractions share the common base 189.

4 × 7/27 × 7 = 28/189 and 5 × 9/21 × 9 = 45/189

Step 3

Add the Numerators

Now add the numerators (28 + 45 = 73) and keep the common denominator 189 unchanged.

28 + 45/189 = 73/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 189 is 1, confirming that 73/189 cannot be reduced further—it is already in its simplest irreducible form.

73/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 189 produces a repeating decimal (approximately 0.386243, or 38.6243%).

73 ÷ 189 = 0.386243 (38.6243%)

Visual Representation

The diagram below illustrates 4/27 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/189`
Mixed Number Form	`73/189`
Decimal Form	`0.386243`
Percentage	`38.6243%`

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Frequently Asked Questions

What is 4/27 plus 5/21 as a fraction?

4/27 + 5/21 in simplest fraction form is 73/189.

What is 4/27 plus 5/21 as a decimal?

4/27 + 5/21 converted to a decimal is 0.386243.

What is 4/27 plus 5/21 as a percentage?

4/27 + 5/21 expressed as a percentage is 38.6243%.

Does 4/27 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.386243...) because the denominator contains prime factors other than 2 and 5.