What is 8/27 plus 8/21? (Answer: 128/189)

Exact Answer

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Problem: What is 8/27 plus 8/21?
Formula / Expression: 8/27 + 8/21
Final Answer: 128/189
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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 8/27 by 7, and multiply the numerator and denominator of 8/21 by 9 so both fractions share the common base 189.
Working: 8 × 7/27 × 7 = 56/189 and 8 × 9/21 × 9 = 72/189

Step 3: Add the Numerators
Now add the numerators (56 + 72 = 128) and keep the common denominator 189 unchanged.
Working: 56 + 72/189 = 128/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 128 and 189 is 1, confirming that 128/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 128/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 128 by denominator 189 produces a repeating decimal (approximately 0.677249, or 67.7249%).
Working: 128 ÷ 189 = 0.677249 (67.7249%)

Key Values:
- Simplified Fraction: 128/189
- Mixed Number Form: 128/189
- Decimal Value: 0.677249
- Percentage: 67.7249%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-27-plus-8-21/
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8/27 + 8/21 = 128/189

Simplified Fraction

128/189

Mixed Number

Proper (128/189)

Decimal Value

0.677249

Percentage

67.7249%

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Step-by-Step Solution: 8/27 + 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 8/27 by 7, and multiply the numerator and denominator of 8/21 by 9 so both fractions share the common base 189.

8 × 7/27 × 7 = 56/189 and 8 × 9/21 × 9 = 72/189

Step 3

Add the Numerators

Now add the numerators (56 + 72 = 128) and keep the common denominator 189 unchanged.

56 + 72/189 = 128/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 128 and 189 is 1, confirming that 128/189 cannot be reduced further—it is already in its simplest irreducible form.

128/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 128 by denominator 189 produces a repeating decimal (approximately 0.677249, or 67.7249%).

128 ÷ 189 = 0.677249 (67.7249%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`128/189`
Mixed Number Form	`128/189`
Decimal Form	`0.677249`
Percentage	`67.7249%`

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Frequently Asked Questions

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

8/27 + 8/21 in simplest fraction form is 128/189.

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

8/27 + 8/21 converted to a decimal is 0.677249.

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

8/27 + 8/21 expressed as a percentage is 67.7249%.

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

It results in a repeating decimal (approximately 0.677249...) because the denominator contains prime factors other than 2 and 5.