What is 2/11 divided by 9/21? (Answer: 14/33)

Exact Answer

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Problem: What is 2/11 divided by 9/21?
Formula / Expression: 2/11 ÷ 9/21
Final Answer: 14/33
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Step-by-Step Solution:

Step 1: Find the Reciprocal of the Second Fraction
Dividing by a fraction is equivalent to multiplying by its reciprocal ("Keep, Change, Flip"). Invert the second fraction 9/21 to get 21/9.
Working: 2/11 ÷ 9/21 = 2/11 × 21/9

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (11 × 9 = 99).
Working: 2 × 21/11 × 9 = 42/99

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 99, which is 3. Divide both the numerator and denominator by 3.
Working: 42 ÷ 3/99 ÷ 3 = 14/33

Step 4: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 33 produces a repeating decimal (approximately 0.424242, or 42.4242%).
Working: 14 ÷ 33 = 0.424242 (42.4242%)

Key Values:
- Simplified Fraction: 14/33
- Mixed Number Form: 14/33
- Decimal Value: 0.424242
- Percentage: 42.4242%

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2/11 ÷ 9/21 = 14/33

Simplified Fraction

14/33

Mixed Number

Proper (14/33)

Decimal Value

0.424242

Percentage

42.4242%

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Step-by-Step Solution: 2/11 ÷ 9/21

Step 1

Find the Reciprocal of the Second Fraction

Dividing by a fraction is equivalent to multiplying by its reciprocal ("Keep, Change, Flip"). Invert the second fraction 9/21 to get 21/9.

2/11 ÷ 9/21 = 2/11 × 21/9

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (11 × 9 = 99).

2 × 21/11 × 9 = 42/99

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 99, which is 3. Divide both the numerator and denominator by 3.

42 ÷ 3/99 ÷ 3 = 14/33

Step 4

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 33 produces a repeating decimal (approximately 0.424242, or 42.4242%).

14 ÷ 33 = 0.424242 (42.4242%)

Visual Representation

The diagram below illustrates 2/11 divided by 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/33`
Mixed Number Form	`14/33`
Decimal Form	`0.424242`
Percentage	`42.4242%`

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Frequently Asked Questions

What is 2/11 divided by 9/21 as a fraction?

2/11 ÷ 9/21 in simplest fraction form is 14/33.

What is 2/11 divided by 9/21 as a decimal?

2/11 ÷ 9/21 converted to a decimal is 0.424242.

What is 2/11 divided by 9/21 as a percentage?

2/11 ÷ 9/21 expressed as a percentage is 42.4242%.

Does 2/11 divided by 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.424242...) because the denominator contains prime factors other than 2 and 5.