What is 8/27 plus 15/21? (Answer: 191/189)

Exact Answer

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Problem: What is 8/27 plus 15/21?
Formula / Expression: 8/27 + 15/21
Final Answer: 1 2/189 (191/189)
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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 15/21 by 9 so both fractions share the common base 189.
Working: 8 × 7/27 × 7 = 56/189 and 15 × 9/21 × 9 = 135/189

Step 3: Add the Numerators
Now add the numerators (56 + 135 = 191) and keep the common denominator 189 unchanged.
Working: 56 + 135/189 = 191/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 191 and 189 is 1, confirming that 191/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 191/189

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (191) is greater than the denominator (189), divide 191 by 189: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/189.
Working: 191/189 = 1 2/189

Step 6: Decimal & Percentage Representation
Dividing the numerator 191 by denominator 189 produces a repeating decimal (approximately 1.010582, or 101.0582%).
Working: 191 ÷ 189 = 1.010582 (101.0582%)

Key Values:
- Simplified Fraction: 191/189
- Mixed Number Form: 1 2/189
- Decimal Value: 1.010582
- Percentage: 101.0582%

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Solved with FractionsCalc:
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8/27 + 15/21 = 191/189

Simplified Fraction

191/189

Mixed Number

1 2/189

Decimal Value

1.010582

Percentage

101.0582%

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Step-by-Step Solution: 8/27 + 15/21

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 15/21 by 9 so both fractions share the common base 189.

8 × 7/27 × 7 = 56/189 and 15 × 9/21 × 9 = 135/189

Step 3

Add the Numerators

Now add the numerators (56 + 135 = 191) and keep the common denominator 189 unchanged.

56 + 135/189 = 191/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 191 and 189 is 1, confirming that 191/189 cannot be reduced further—it is already in its simplest irreducible form.

191/189

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (191) is greater than the denominator (189), divide 191 by 189: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/189.

191/189 = 12/189

Step 6

Decimal & Percentage Representation

Dividing the numerator 191 by denominator 189 produces a repeating decimal (approximately 1.010582, or 101.0582%).

191 ÷ 189 = 1.010582 (101.0582%)

Visual Representation

The diagram below illustrates 8/27 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`191/189`
Mixed Number Form	`1 2/189`
Decimal Form	`1.010582`
Percentage	`101.0582%`

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Frequently Asked Questions

What is 8/27 plus 15/21 as a fraction?

8/27 + 15/21 in simplest fraction form is 191/189 (or 1 2/189 as a mixed number).

What is 8/27 plus 15/21 as a decimal?

8/27 + 15/21 converted to a decimal is 1.010582.

What is 8/27 plus 15/21 as a percentage?

8/27 + 15/21 expressed as a percentage is 101.0582%.

How do you write 8/27 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 191/189 can be written as the mixed number 1 2/189.

Does 8/27 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.010582...) because the denominator contains prime factors other than 2 and 5.