What is 11/27 plus 10/21? (Answer: 167/189)

Exact Answer

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Problem: What is 11/27 plus 10/21?
Formula / Expression: 11/27 + 10/21
Final Answer: 167/189
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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 10/21 by 9 so both fractions share the common base 189.
Working: 11 × 7/27 × 7 = 77/189 and 10 × 9/21 × 9 = 90/189

Step 3: Add the Numerators
Now add the numerators (77 + 90 = 167) and keep the common denominator 189 unchanged.
Working: 77 + 90/189 = 167/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 167 and 189 is 1, confirming that 167/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 167/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 167 by denominator 189 produces a repeating decimal (approximately 0.883598, or 88.3598%).
Working: 167 ÷ 189 = 0.883598 (88.3598%)

Key Values:
- Simplified Fraction: 167/189
- Mixed Number Form: 167/189
- Decimal Value: 0.883598
- Percentage: 88.3598%

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Solved with FractionsCalc:
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11/27 + 10/21 = 167/189

Simplified Fraction

167/189

Mixed Number

Proper (167/189)

Decimal Value

0.883598

Percentage

88.3598%

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Step-by-Step Solution: 11/27 + 10/21

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 10/21 by 9 so both fractions share the common base 189.

11 × 7/27 × 7 = 77/189 and 10 × 9/21 × 9 = 90/189

Step 3

Add the Numerators

Now add the numerators (77 + 90 = 167) and keep the common denominator 189 unchanged.

77 + 90/189 = 167/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 167 and 189 is 1, confirming that 167/189 cannot be reduced further—it is already in its simplest irreducible form.

167/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 167 by denominator 189 produces a repeating decimal (approximately 0.883598, or 88.3598%).

167 ÷ 189 = 0.883598 (88.3598%)

Visual Representation

The diagram below illustrates 11/27 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`167/189`
Mixed Number Form	`167/189`
Decimal Form	`0.883598`
Percentage	`88.3598%`

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Frequently Asked Questions

What is 11/27 plus 10/21 as a fraction?

11/27 + 10/21 in simplest fraction form is 167/189.

What is 11/27 plus 10/21 as a decimal?

11/27 + 10/21 converted to a decimal is 0.883598.

What is 11/27 plus 10/21 as a percentage?

11/27 + 10/21 expressed as a percentage is 88.3598%.

Does 11/27 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.883598...) because the denominator contains prime factors other than 2 and 5.