What is 11/33 plus 9/21? (Answer: 16/21)

Exact Answer

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Problem: What is 11/33 plus 9/21?
Formula / Expression: 11/33 + 9/21
Final Answer: 16/21
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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 11/33 by 7, and multiply the numerator and denominator of 9/21 by 11 so both fractions share the common base 231.
Working: 11 × 7/33 × 7 = 77/231 and 9 × 11/21 × 11 = 99/231

Step 3: Add the Numerators
Now add the numerators (77 + 99 = 176) and keep the common denominator 231 unchanged.
Working: 77 + 99/231 = 176/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 176 and 231, which is 11. Divide both the numerator and denominator by 11.
Working: 176 ÷ 11/231 ÷ 11 = 16/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-33-plus-9-21/
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11/33 + 9/21 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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Step-by-Step Solution: 11/33 + 9/21

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 11/33 by 7, and multiply the numerator and denominator of 9/21 by 11 so both fractions share the common base 231.

11 × 7/33 × 7 = 77/231 and 9 × 11/21 × 11 = 99/231

Step 3

Add the Numerators

Now add the numerators (77 + 99 = 176) and keep the common denominator 231 unchanged.

77 + 99/231 = 176/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 176 and 231, which is 11. Divide both the numerator and denominator by 11.

176 ÷ 11/231 ÷ 11 = 16/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

The diagram below illustrates 11/33 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

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Frequently Asked Questions

What is 11/33 plus 9/21 as a fraction?

11/33 + 9/21 in simplest fraction form is 16/21.

What is 11/33 plus 9/21 as a decimal?

11/33 + 9/21 converted to a decimal is 0.761905.

What is 11/33 plus 9/21 as a percentage?

11/33 + 9/21 expressed as a percentage is 76.1905%.

Does 11/33 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.