What is 16/33 plus 11/21? (Answer: 233/231)

Exact Answer

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Problem: What is 16/33 plus 11/21?
Formula / Expression: 16/33 + 11/21
Final Answer: 1 2/231 (233/231)
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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 16/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.
Working: 16 × 7/33 × 7 = 112/231 and 11 × 11/21 × 11 = 121/231

Step 3: Add the Numerators
Now add the numerators (112 + 121 = 233) and keep the common denominator 231 unchanged.
Working: 112 + 121/231 = 233/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 233 and 231 is 1, confirming that 233/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 233/231

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (233) is greater than the denominator (231), divide 233 by 231: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/231.
Working: 233/231 = 1 2/231

Step 6: Decimal & Percentage Representation
Dividing the numerator 233 by denominator 231 produces a repeating decimal (approximately 1.008658, or 100.8658%).
Working: 233 ÷ 231 = 1.008658 (100.8658%)

Key Values:
- Simplified Fraction: 233/231
- Mixed Number Form: 1 2/231
- Decimal Value: 1.008658
- Percentage: 100.8658%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-33-plus-11-21/
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16/33 + 11/21 = 233/231

Simplified Fraction

233/231

Mixed Number

1 2/231

Decimal Value

1.008658

Percentage

100.8658%

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Step-by-Step Solution: 16/33 + 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 16/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.

16 × 7/33 × 7 = 112/231 and 11 × 11/21 × 11 = 121/231

Step 3

Add the Numerators

Now add the numerators (112 + 121 = 233) and keep the common denominator 231 unchanged.

112 + 121/231 = 233/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 233 and 231 is 1, confirming that 233/231 cannot be reduced further—it is already in its simplest irreducible form.

233/231

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (233) is greater than the denominator (231), divide 233 by 231: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/231.

233/231 = 12/231

Step 6

Decimal & Percentage Representation

Dividing the numerator 233 by denominator 231 produces a repeating decimal (approximately 1.008658, or 100.8658%).

233 ÷ 231 = 1.008658 (100.8658%)

Visual Representation

The diagram below illustrates 16/33 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`233/231`
Mixed Number Form	`1 2/231`
Decimal Form	`1.008658`
Percentage	`100.8658%`

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Frequently Asked Questions

What is 16/33 plus 11/21 as a fraction?

16/33 + 11/21 in simplest fraction form is 233/231 (or 1 2/231 as a mixed number).

What is 16/33 plus 11/21 as a decimal?

16/33 + 11/21 converted to a decimal is 1.008658.

What is 16/33 plus 11/21 as a percentage?

16/33 + 11/21 expressed as a percentage is 100.8658%.

How do you write 16/33 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 233/231 can be written as the mixed number 1 2/231.

Does 16/33 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.008658...) because the denominator contains prime factors other than 2 and 5.