What is 5/27 plus 8/21? (Answer: 107/189)

Exact Answer

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Problem: What is 5/27 plus 8/21?
Formula / Expression: 5/27 + 8/21
Final Answer: 107/189
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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 8/21 by 9 so both fractions share the common base 189.
Working: 5 × 7/27 × 7 = 35/189 and 8 × 9/21 × 9 = 72/189

Step 3: Add the Numerators
Now add the numerators (35 + 72 = 107) and keep the common denominator 189 unchanged.
Working: 35 + 72/189 = 107/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 189 is 1, confirming that 107/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 189 produces a repeating decimal (approximately 0.566138, or 56.6138%).
Working: 107 ÷ 189 = 0.566138 (56.6138%)

Key Values:
- Simplified Fraction: 107/189
- Mixed Number Form: 107/189
- Decimal Value: 0.566138
- Percentage: 56.6138%

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Solved with FractionsCalc:
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5/27 + 8/21 = 107/189

Simplified Fraction

107/189

Mixed Number

Proper (107/189)

Decimal Value

0.566138

Percentage

56.6138%

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Step-by-Step Solution: 5/27 + 8/21

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 8/21 by 9 so both fractions share the common base 189.

5 × 7/27 × 7 = 35/189 and 8 × 9/21 × 9 = 72/189

Step 3

Add the Numerators

Now add the numerators (35 + 72 = 107) and keep the common denominator 189 unchanged.

35 + 72/189 = 107/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 189 is 1, confirming that 107/189 cannot be reduced further—it is already in its simplest irreducible form.

107/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 189 produces a repeating decimal (approximately 0.566138, or 56.6138%).

107 ÷ 189 = 0.566138 (56.6138%)

Visual Representation

The diagram below illustrates 5/27 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/189`
Mixed Number Form	`107/189`
Decimal Form	`0.566138`
Percentage	`56.6138%`

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Frequently Asked Questions

What is 5/27 plus 8/21 as a fraction?

5/27 + 8/21 in simplest fraction form is 107/189.

What is 5/27 plus 8/21 as a decimal?

5/27 + 8/21 converted to a decimal is 0.566138.

What is 5/27 plus 8/21 as a percentage?

5/27 + 8/21 expressed as a percentage is 56.6138%.

Does 5/27 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.566138...) because the denominator contains prime factors other than 2 and 5.