What is 2/33 divided by 2/21? (Answer: 7/11)

Exact Answer

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Problem: What is 2/33 divided by 2/21?
Formula / Expression: 2/33 ÷ 2/21
Final Answer: 7/11
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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 2/21 to get 21/2.
Working: 2/33 ÷ 2/21 = 2/33 × 21/2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (33 × 2 = 66).
Working: 2 × 21/33 × 2 = 42/66

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 66, which is 6. Divide both the numerator and denominator by 6.
Working: 42 ÷ 6/66 ÷ 6 = 7/11

Step 4: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 11 produces a repeating decimal (approximately 0.636364, or 63.6364%).
Working: 7 ÷ 11 = 0.636364 (63.6364%)

Key Values:
- Simplified Fraction: 7/11
- Mixed Number Form: 7/11
- Decimal Value: 0.636364
- Percentage: 63.6364%

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Solved with FractionsCalc:
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2/33 ÷ 2/21 = 7/11

Simplified Fraction

7/11

Mixed Number

Proper (7/11)

Decimal Value

0.636364

Percentage

63.6364%

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Step-by-Step Solution: 2/33 ÷ 2/21

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 2/21 to get 21/2.

2/33 ÷ 2/21 = 2/33 × 21/2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (33 × 2 = 66).

2 × 21/33 × 2 = 42/66

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 66, which is 6. Divide both the numerator and denominator by 6.

42 ÷ 6/66 ÷ 6 = 7/11

Step 4

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 11 produces a repeating decimal (approximately 0.636364, or 63.6364%).

7 ÷ 11 = 0.636364 (63.6364%)

Visual Representation

The diagram below illustrates 2/33 divided by 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/11`
Mixed Number Form	`7/11`
Decimal Form	`0.636364`
Percentage	`63.6364%`

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Frequently Asked Questions

What is 2/33 divided by 2/21 as a fraction?

2/33 ÷ 2/21 in simplest fraction form is 7/11.

What is 2/33 divided by 2/21 as a decimal?

2/33 ÷ 2/21 converted to a decimal is 0.636364.

What is 2/33 divided by 2/21 as a percentage?

2/33 ÷ 2/21 expressed as a percentage is 63.6364%.

Does 2/33 divided by 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.636364...) because the denominator contains prime factors other than 2 and 5.