What is 3/21 plus 4/27? (Answer: 55/189)

Exact Answer

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Problem: What is 3/21 plus 4/27?
Formula / Expression: 3/21 + 4/27
Final Answer: 55/189
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 3/21 by 9, and multiply the numerator and denominator of 4/27 by 7 so both fractions share the common base 189.
Working: 3 × 9/21 × 9 = 27/189 and 4 × 7/27 × 7 = 28/189

Step 3: Add the Numerators
Now add the numerators (27 + 28 = 55) and keep the common denominator 189 unchanged.
Working: 27 + 28/189 = 55/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 189 is 1, confirming that 55/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 189 produces a repeating decimal (approximately 0.291005, or 29.1005%).
Working: 55 ÷ 189 = 0.291005 (29.1005%)

Key Values:
- Simplified Fraction: 55/189
- Mixed Number Form: 55/189
- Decimal Value: 0.291005
- Percentage: 29.1005%

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Solved with FractionsCalc:
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3/21 + 4/27 = 55/189

Simplified Fraction

55/189

Mixed Number

Proper (55/189)

Decimal Value

0.291005

Percentage

29.1005%

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Step-by-Step Solution: 3/21 + 4/27

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 27) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 3/21 by 9, and multiply the numerator and denominator of 4/27 by 7 so both fractions share the common base 189.

3 × 9/21 × 9 = 27/189 and 4 × 7/27 × 7 = 28/189

Step 3

Add the Numerators

Now add the numerators (27 + 28 = 55) and keep the common denominator 189 unchanged.

27 + 28/189 = 55/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 189 is 1, confirming that 55/189 cannot be reduced further—it is already in its simplest irreducible form.

55/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 189 produces a repeating decimal (approximately 0.291005, or 29.1005%).

55 ÷ 189 = 0.291005 (29.1005%)

Visual Representation

The diagram below illustrates 3/21 plus 4/27 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/189`
Mixed Number Form	`55/189`
Decimal Form	`0.291005`
Percentage	`29.1005%`

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Frequently Asked Questions

What is 3/21 plus 4/27 as a fraction?

3/21 + 4/27 in simplest fraction form is 55/189.

What is 3/21 plus 4/27 as a decimal?

3/21 + 4/27 converted to a decimal is 0.291005.

What is 3/21 plus 4/27 as a percentage?

3/21 + 4/27 expressed as a percentage is 29.1005%.

Does 3/21 plus 4/27 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.291005...) because the denominator contains prime factors other than 2 and 5.