What is 5/27 plus 4/21? (Answer: 71/189)

Exact Answer

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Problem: What is 5/27 plus 4/21?
Formula / Expression: 5/27 + 4/21
Final Answer: 71/189
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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 5/27 by 7, and multiply the numerator and denominator of 4/21 by 9 so both fractions share the common base 189.
Working: 5 × 7/27 × 7 = 35/189 and 4 × 9/21 × 9 = 36/189

Step 3: Add the Numerators
Now add the numerators (35 + 36 = 71) and keep the common denominator 189 unchanged.
Working: 35 + 36/189 = 71/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 189 is 1, confirming that 71/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 189 produces a repeating decimal (approximately 0.375661, or 37.5661%).
Working: 71 ÷ 189 = 0.375661 (37.5661%)

Key Values:
- Simplified Fraction: 71/189
- Mixed Number Form: 71/189
- Decimal Value: 0.375661
- Percentage: 37.5661%

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Solved with FractionsCalc:
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5/27 + 4/21 = 71/189

Simplified Fraction

71/189

Mixed Number

Proper (71/189)

Decimal Value

0.375661

Percentage

37.5661%

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

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 5/27 by 7, and multiply the numerator and denominator of 4/21 by 9 so both fractions share the common base 189.

5 × 7/27 × 7 = 35/189 and 4 × 9/21 × 9 = 36/189

Step 3

Add the Numerators

Now add the numerators (35 + 36 = 71) and keep the common denominator 189 unchanged.

35 + 36/189 = 71/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 189 is 1, confirming that 71/189 cannot be reduced further—it is already in its simplest irreducible form.

71/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 189 produces a repeating decimal (approximately 0.375661, or 37.5661%).

71 ÷ 189 = 0.375661 (37.5661%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/189`
Mixed Number Form	`71/189`
Decimal Form	`0.375661`
Percentage	`37.5661%`

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Frequently Asked Questions

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

5/27 + 4/21 in simplest fraction form is 71/189.

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

5/27 + 4/21 converted to a decimal is 0.375661.

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

5/27 + 4/21 expressed as a percentage is 37.5661%.

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

It results in a repeating decimal (approximately 0.375661...) because the denominator contains prime factors other than 2 and 5.