What is 8/27 plus 10/21? (Answer: 146/189)

Exact Answer

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Problem: What is 8/27 plus 10/21?
Formula / Expression: 8/27 + 10/21
Final Answer: 146/189
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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 10/21 by 9 so both fractions share the common base 189.
Working: 8 × 7/27 × 7 = 56/189 and 10 × 9/21 × 9 = 90/189

Step 3: Add the Numerators
Now add the numerators (56 + 90 = 146) and keep the common denominator 189 unchanged.
Working: 56 + 90/189 = 146/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 146 and 189 is 1, confirming that 146/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 146/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 146 by denominator 189 produces a repeating decimal (approximately 0.772487, or 77.2487%).
Working: 146 ÷ 189 = 0.772487 (77.2487%)

Key Values:
- Simplified Fraction: 146/189
- Mixed Number Form: 146/189
- Decimal Value: 0.772487
- Percentage: 77.2487%

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Solved with FractionsCalc:
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8/27 + 10/21 = 146/189

Simplified Fraction

146/189

Mixed Number

Proper (146/189)

Decimal Value

0.772487

Percentage

77.2487%

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Step-by-Step Solution: 8/27 + 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 8/27 by 7, and multiply the numerator and denominator of 10/21 by 9 so both fractions share the common base 189.

8 × 7/27 × 7 = 56/189 and 10 × 9/21 × 9 = 90/189

Step 3

Add the Numerators

Now add the numerators (56 + 90 = 146) and keep the common denominator 189 unchanged.

56 + 90/189 = 146/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 146 and 189 is 1, confirming that 146/189 cannot be reduced further—it is already in its simplest irreducible form.

146/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 146 by denominator 189 produces a repeating decimal (approximately 0.772487, or 77.2487%).

146 ÷ 189 = 0.772487 (77.2487%)

Visual Representation

The diagram below illustrates 8/27 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`146/189`
Mixed Number Form	`146/189`
Decimal Form	`0.772487`
Percentage	`77.2487%`

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Frequently Asked Questions

What is 8/27 plus 10/21 as a fraction?

8/27 + 10/21 in simplest fraction form is 146/189.

What is 8/27 plus 10/21 as a decimal?

8/27 + 10/21 converted to a decimal is 0.772487.

What is 8/27 plus 10/21 as a percentage?

8/27 + 10/21 expressed as a percentage is 77.2487%.

Does 8/27 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.772487...) because the denominator contains prime factors other than 2 and 5.