What is 10/27 plus 12/21? (Answer: 178/189)

Exact Answer

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Problem: What is 10/27 plus 12/21?
Formula / Expression: 10/27 + 12/21
Final Answer: 178/189
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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 10/27 by 7, and multiply the numerator and denominator of 12/21 by 9 so both fractions share the common base 189.
Working: 10 × 7/27 × 7 = 70/189 and 12 × 9/21 × 9 = 108/189

Step 3: Add the Numerators
Now add the numerators (70 + 108 = 178) and keep the common denominator 189 unchanged.
Working: 70 + 108/189 = 178/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 178 and 189 is 1, confirming that 178/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 178/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 178 by denominator 189 produces a repeating decimal (approximately 0.941799, or 94.1799%).
Working: 178 ÷ 189 = 0.941799 (94.1799%)

Key Values:
- Simplified Fraction: 178/189
- Mixed Number Form: 178/189
- Decimal Value: 0.941799
- Percentage: 94.1799%

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Solved with FractionsCalc:
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10/27 + 12/21 = 178/189

Simplified Fraction

178/189

Mixed Number

Proper (178/189)

Decimal Value

0.941799

Percentage

94.1799%

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Step-by-Step Solution: 10/27 + 12/21

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 10/27 by 7, and multiply the numerator and denominator of 12/21 by 9 so both fractions share the common base 189.

10 × 7/27 × 7 = 70/189 and 12 × 9/21 × 9 = 108/189

Step 3

Add the Numerators

Now add the numerators (70 + 108 = 178) and keep the common denominator 189 unchanged.

70 + 108/189 = 178/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 178 and 189 is 1, confirming that 178/189 cannot be reduced further—it is already in its simplest irreducible form.

178/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 178 by denominator 189 produces a repeating decimal (approximately 0.941799, or 94.1799%).

178 ÷ 189 = 0.941799 (94.1799%)

Visual Representation

The diagram below illustrates 10/27 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`178/189`
Mixed Number Form	`178/189`
Decimal Form	`0.941799`
Percentage	`94.1799%`

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Frequently Asked Questions

What is 10/27 plus 12/21 as a fraction?

10/27 + 12/21 in simplest fraction form is 178/189.

What is 10/27 plus 12/21 as a decimal?

10/27 + 12/21 converted to a decimal is 0.941799.

What is 10/27 plus 12/21 as a percentage?

10/27 + 12/21 expressed as a percentage is 94.1799%.

Does 10/27 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.941799...) because the denominator contains prime factors other than 2 and 5.