What is 10/33 plus 12/21? (Answer: 202/231)

Exact Answer

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Problem: What is 10/33 plus 12/21?
Formula / Expression: 10/33 + 12/21
Final Answer: 202/231
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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 12/21 by 11 so both fractions share the common base 231.
Working: 10 × 7/33 × 7 = 70/231 and 12 × 11/21 × 11 = 132/231

Step 3: Add the Numerators
Now add the numerators (70 + 132 = 202) and keep the common denominator 231 unchanged.
Working: 70 + 132/231 = 202/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 202 and 231 is 1, confirming that 202/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 202/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 202 by denominator 231 produces a repeating decimal (approximately 0.874459, or 87.4459%).
Working: 202 ÷ 231 = 0.874459 (87.4459%)

Key Values:
- Simplified Fraction: 202/231
- Mixed Number Form: 202/231
- Decimal Value: 0.874459
- Percentage: 87.4459%

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10/33 + 12/21 = 202/231

Simplified Fraction

202/231

Mixed Number

Proper (202/231)

Decimal Value

0.874459

Percentage

87.4459%

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Step-by-Step Solution: 10/33 + 12/21

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 12/21 by 11 so both fractions share the common base 231.

10 × 7/33 × 7 = 70/231 and 12 × 11/21 × 11 = 132/231

Step 3

Add the Numerators

Now add the numerators (70 + 132 = 202) and keep the common denominator 231 unchanged.

70 + 132/231 = 202/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 202 and 231 is 1, confirming that 202/231 cannot be reduced further—it is already in its simplest irreducible form.

202/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 202 by denominator 231 produces a repeating decimal (approximately 0.874459, or 87.4459%).

202 ÷ 231 = 0.874459 (87.4459%)

Visual Representation

The diagram below illustrates 10/33 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`202/231`
Mixed Number Form	`202/231`
Decimal Form	`0.874459`
Percentage	`87.4459%`

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Frequently Asked Questions

What is 10/33 plus 12/21 as a fraction?

10/33 + 12/21 in simplest fraction form is 202/231.

What is 10/33 plus 12/21 as a decimal?

10/33 + 12/21 converted to a decimal is 0.874459.

What is 10/33 plus 12/21 as a percentage?

10/33 + 12/21 expressed as a percentage is 87.4459%.

Does 10/33 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.874459...) because the denominator contains prime factors other than 2 and 5.