What is 17/33 plus 12/21? (Answer: 251/231)

Exact Answer

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Problem: What is 17/33 plus 12/21?
Formula / Expression: 17/33 + 12/21
Final Answer: 1 20/231 (251/231)
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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 17/33 by 7, and multiply the numerator and denominator of 12/21 by 11 so both fractions share the common base 231.
Working: 17 × 7/33 × 7 = 119/231 and 12 × 11/21 × 11 = 132/231

Step 3: Add the Numerators
Now add the numerators (119 + 132 = 251) and keep the common denominator 231 unchanged.
Working: 119 + 132/231 = 251/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 251 and 231 is 1, confirming that 251/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 251/231

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (251) is greater than the denominator (231), divide 251 by 231: it goes in 1 whole time(s) with a remainder of 20, giving the mixed number 1 20/231.
Working: 251/231 = 1 20/231

Step 6: Decimal & Percentage Representation
Dividing the numerator 251 by denominator 231 produces a repeating decimal (approximately 1.08658, or 108.658%).
Working: 251 ÷ 231 = 1.08658 (108.658%)

Key Values:
- Simplified Fraction: 251/231
- Mixed Number Form: 1 20/231
- Decimal Value: 1.08658
- Percentage: 108.658%

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Solved with FractionsCalc:
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17/33 + 12/21 = 251/231

Simplified Fraction

251/231

Mixed Number

1 20/231

Decimal Value

1.08658

Percentage

108.658%

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Step-by-Step Solution: 17/33 + 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 17/33 by 7, and multiply the numerator and denominator of 12/21 by 11 so both fractions share the common base 231.

17 × 7/33 × 7 = 119/231 and 12 × 11/21 × 11 = 132/231

Step 3

Add the Numerators

Now add the numerators (119 + 132 = 251) and keep the common denominator 231 unchanged.

119 + 132/231 = 251/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 251 and 231 is 1, confirming that 251/231 cannot be reduced further—it is already in its simplest irreducible form.

251/231

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (251) is greater than the denominator (231), divide 251 by 231: it goes in 1 whole time(s) with a remainder of 20, giving the mixed number 1 20/231.

251/231 = 120/231

Step 6

Decimal & Percentage Representation

Dividing the numerator 251 by denominator 231 produces a repeating decimal (approximately 1.08658, or 108.658%).

251 ÷ 231 = 1.08658 (108.658%)

Visual Representation

The diagram below illustrates 17/33 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`251/231`
Mixed Number Form	`1 20/231`
Decimal Form	`1.08658`
Percentage	`108.658%`

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Frequently Asked Questions

What is 17/33 plus 12/21 as a fraction?

17/33 + 12/21 in simplest fraction form is 251/231 (or 1 20/231 as a mixed number).

What is 17/33 plus 12/21 as a decimal?

17/33 + 12/21 converted to a decimal is 1.08658.

What is 17/33 plus 12/21 as a percentage?

17/33 + 12/21 expressed as a percentage is 108.658%.

How do you write 17/33 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 251/231 can be written as the mixed number 1 20/231.

Does 17/33 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.08658...) because the denominator contains prime factors other than 2 and 5.