What is 11/27 plus 15/21? (Answer: 212/189)

Exact Answer

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Problem: What is 11/27 plus 15/21?
Formula / Expression: 11/27 + 15/21
Final Answer: 1 23/189 (212/189)
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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 11/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.
Working: 11 × 7/27 × 7 = 77/189 and 15 × 9/21 × 9 = 135/189

Step 3: Add the Numerators
Now add the numerators (77 + 135 = 212) and keep the common denominator 189 unchanged.
Working: 77 + 135/189 = 212/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 212 and 189 is 1, confirming that 212/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 212/189

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (212) is greater than the denominator (189), divide 212 by 189: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/189.
Working: 212/189 = 1 23/189

Step 6: Decimal & Percentage Representation
Dividing the numerator 212 by denominator 189 produces a repeating decimal (approximately 1.121693, or 112.1693%).
Working: 212 ÷ 189 = 1.121693 (112.1693%)

Key Values:
- Simplified Fraction: 212/189
- Mixed Number Form: 1 23/189
- Decimal Value: 1.121693
- Percentage: 112.1693%

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Solved with FractionsCalc:
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11/27 + 15/21 = 212/189

Simplified Fraction

212/189

Mixed Number

1 23/189

Decimal Value

1.121693

Percentage

112.1693%

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Step-by-Step Solution: 11/27 + 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 11/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.

11 × 7/27 × 7 = 77/189 and 15 × 9/21 × 9 = 135/189

Step 3

Add the Numerators

Now add the numerators (77 + 135 = 212) and keep the common denominator 189 unchanged.

77 + 135/189 = 212/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 212 and 189 is 1, confirming that 212/189 cannot be reduced further—it is already in its simplest irreducible form.

212/189

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (212) is greater than the denominator (189), divide 212 by 189: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/189.

212/189 = 123/189

Step 6

Decimal & Percentage Representation

Dividing the numerator 212 by denominator 189 produces a repeating decimal (approximately 1.121693, or 112.1693%).

212 ÷ 189 = 1.121693 (112.1693%)

Visual Representation

The diagram below illustrates 11/27 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`212/189`
Mixed Number Form	`1 23/189`
Decimal Form	`1.121693`
Percentage	`112.1693%`

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Frequently Asked Questions

What is 11/27 plus 15/21 as a fraction?

11/27 + 15/21 in simplest fraction form is 212/189 (or 1 23/189 as a mixed number).

What is 11/27 plus 15/21 as a decimal?

11/27 + 15/21 converted to a decimal is 1.121693.

What is 11/27 plus 15/21 as a percentage?

11/27 + 15/21 expressed as a percentage is 112.1693%.

How do you write 11/27 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 212/189 can be written as the mixed number 1 23/189.

Does 11/27 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.121693...) because the denominator contains prime factors other than 2 and 5.