What is 8/33 plus 10/21? (Answer: 166/231)

Exact Answer

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Problem: What is 8/33 plus 10/21?
Formula / Expression: 8/33 + 10/21
Final Answer: 166/231
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).
Working: LCD(33, 21) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 8/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.
Working: 8 × 7/33 × 7 = 56/231 and 10 × 11/21 × 11 = 110/231

Step 3: Add the Numerators
Now add the numerators (56 + 110 = 166) and keep the common denominator 231 unchanged.
Working: 56 + 110/231 = 166/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 166 and 231 is 1, confirming that 166/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 166/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 166 by denominator 231 produces a repeating decimal (approximately 0.718615, or 71.8615%).
Working: 166 ÷ 231 = 0.718615 (71.8615%)

Key Values:
- Simplified Fraction: 166/231
- Mixed Number Form: 166/231
- Decimal Value: 0.718615
- Percentage: 71.8615%

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Solved with FractionsCalc:
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8/33 + 10/21 = 166/231

Simplified Fraction

166/231

Mixed Number

Proper (166/231)

Decimal Value

0.718615

Percentage

71.8615%

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Step-by-Step Solution: 8/33 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 8/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.

8 × 7/33 × 7 = 56/231 and 10 × 11/21 × 11 = 110/231

Step 3

Add the Numerators

Now add the numerators (56 + 110 = 166) and keep the common denominator 231 unchanged.

56 + 110/231 = 166/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 166 and 231 is 1, confirming that 166/231 cannot be reduced further—it is already in its simplest irreducible form.

166/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 166 by denominator 231 produces a repeating decimal (approximately 0.718615, or 71.8615%).

166 ÷ 231 = 0.718615 (71.8615%)

Visual Representation

The diagram below illustrates 8/33 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`166/231`
Mixed Number Form	`166/231`
Decimal Form	`0.718615`
Percentage	`71.8615%`

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Frequently Asked Questions

What is 8/33 plus 10/21 as a fraction?

8/33 + 10/21 in simplest fraction form is 166/231.

What is 8/33 plus 10/21 as a decimal?

8/33 + 10/21 converted to a decimal is 0.718615.

What is 8/33 plus 10/21 as a percentage?

8/33 + 10/21 expressed as a percentage is 71.8615%.

Does 8/33 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.718615...) because the denominator contains prime factors other than 2 and 5.