What is 10/21 plus 13/27? (Answer: 181/189)

Exact Answer

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Problem: What is 10/21 plus 13/27?
Formula / Expression: 10/21 + 13/27
Final Answer: 181/189
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 27 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 21 × 27 = 567, keeping the calculation simpler).
Working: LCD(21, 27) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 10/21 by 9, and multiply the numerator and denominator of 13/27 by 7 so both fractions share the common base 189.
Working: 10 × 9/21 × 9 = 90/189 and 13 × 7/27 × 7 = 91/189

Step 3: Add the Numerators
Now add the numerators (90 + 91 = 181) and keep the common denominator 189 unchanged.
Working: 90 + 91/189 = 181/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 189 is 1, confirming that 181/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 189 produces a repeating decimal (approximately 0.957672, or 95.7672%).
Working: 181 ÷ 189 = 0.957672 (95.7672%)

Key Values:
- Simplified Fraction: 181/189
- Mixed Number Form: 181/189
- Decimal Value: 0.957672
- Percentage: 95.7672%

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Solved with FractionsCalc:
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10/21 + 13/27 = 181/189

Simplified Fraction

181/189

Mixed Number

Proper (181/189)

Decimal Value

0.957672

Percentage

95.7672%

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Step-by-Step Solution: 10/21 + 13/27

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 27 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 21 × 27 = 567, keeping the calculation simpler).

LCD(21, 27) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 10/21 by 9, and multiply the numerator and denominator of 13/27 by 7 so both fractions share the common base 189.

10 × 9/21 × 9 = 90/189 and 13 × 7/27 × 7 = 91/189

Step 3

Add the Numerators

Now add the numerators (90 + 91 = 181) and keep the common denominator 189 unchanged.

90 + 91/189 = 181/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 189 is 1, confirming that 181/189 cannot be reduced further—it is already in its simplest irreducible form.

181/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 189 produces a repeating decimal (approximately 0.957672, or 95.7672%).

181 ÷ 189 = 0.957672 (95.7672%)

Visual Representation

The diagram below illustrates 10/21 plus 13/27 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/189`
Mixed Number Form	`181/189`
Decimal Form	`0.957672`
Percentage	`95.7672%`

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Frequently Asked Questions

What is 10/21 plus 13/27 as a fraction?

10/21 + 13/27 in simplest fraction form is 181/189.

What is 10/21 plus 13/27 as a decimal?

10/21 + 13/27 converted to a decimal is 0.957672.

What is 10/21 plus 13/27 as a percentage?

10/21 + 13/27 expressed as a percentage is 95.7672%.

Does 10/21 plus 13/27 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.957672...) because the denominator contains prime factors other than 2 and 5.