What is 10/33 plus 11/21? (Answer: 191/231)

Exact Answer

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Problem: What is 10/33 plus 11/21?
Formula / Expression: 10/33 + 11/21
Final Answer: 191/231
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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 10/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.
Working: 10 × 7/33 × 7 = 70/231 and 11 × 11/21 × 11 = 121/231

Step 3: Add the Numerators
Now add the numerators (70 + 121 = 191) and keep the common denominator 231 unchanged.
Working: 70 + 121/231 = 191/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 191 and 231 is 1, confirming that 191/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 191/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 191 by denominator 231 produces a repeating decimal (approximately 0.82684, or 82.684%).
Working: 191 ÷ 231 = 0.82684 (82.684%)

Key Values:
- Simplified Fraction: 191/231
- Mixed Number Form: 191/231
- Decimal Value: 0.82684
- Percentage: 82.684%

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Solved with FractionsCalc:
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10/33 + 11/21 = 191/231

Simplified Fraction

191/231

Mixed Number

Proper (191/231)

Decimal Value

0.82684

Percentage

82.684%

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Step-by-Step Solution: 10/33 + 11/21

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

10 × 7/33 × 7 = 70/231 and 11 × 11/21 × 11 = 121/231

Step 3

Add the Numerators

Now add the numerators (70 + 121 = 191) and keep the common denominator 231 unchanged.

70 + 121/231 = 191/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 191 and 231 is 1, confirming that 191/231 cannot be reduced further—it is already in its simplest irreducible form.

191/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 191 by denominator 231 produces a repeating decimal (approximately 0.82684, or 82.684%).

191 ÷ 231 = 0.82684 (82.684%)

Visual Representation

The diagram below illustrates 10/33 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`191/231`
Mixed Number Form	`191/231`
Decimal Form	`0.82684`
Percentage	`82.684%`

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Frequently Asked Questions

What is 10/33 plus 11/21 as a fraction?

10/33 + 11/21 in simplest fraction form is 191/231.

What is 10/33 plus 11/21 as a decimal?

10/33 + 11/21 converted to a decimal is 0.82684.

What is 10/33 plus 11/21 as a percentage?

10/33 + 11/21 expressed as a percentage is 82.684%.

Does 10/33 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.82684...) because the denominator contains prime factors other than 2 and 5.