What is 2/7 divided by 11/21? (Answer: 6/11)

Exact Answer

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Problem: What is 2/7 divided by 11/21?
Formula / Expression: 2/7 ÷ 11/21
Final Answer: 6/11
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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 11/21 to get 21/11.
Working: 2/7 ÷ 11/21 = 2/7 × 21/11

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (7 × 11 = 77).
Working: 2 × 21/7 × 11 = 42/77

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 77, which is 7. Divide both the numerator and denominator by 7.
Working: 42 ÷ 7/77 ÷ 7 = 6/11

Step 4: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 11 produces a repeating decimal (approximately 0.545455, or 54.5455%).
Working: 6 ÷ 11 = 0.545455 (54.5455%)

Key Values:
- Simplified Fraction: 6/11
- Mixed Number Form: 6/11
- Decimal Value: 0.545455
- Percentage: 54.5455%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-divided-by-11-21/
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2/7 ÷ 11/21 = 6/11

Simplified Fraction

6/11

Mixed Number

Proper (6/11)

Decimal Value

0.545455

Percentage

54.5455%

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Step-by-Step Solution: 2/7 ÷ 11/21

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 11/21 to get 21/11.

2/7 ÷ 11/21 = 2/7 × 21/11

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (7 × 11 = 77).

2 × 21/7 × 11 = 42/77

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 77, which is 7. Divide both the numerator and denominator by 7.

42 ÷ 7/77 ÷ 7 = 6/11

Step 4

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 11 produces a repeating decimal (approximately 0.545455, or 54.5455%).

6 ÷ 11 = 0.545455 (54.5455%)

Visual Representation

The diagram below illustrates 2/7 divided by 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/11`
Mixed Number Form	`6/11`
Decimal Form	`0.545455`
Percentage	`54.5455%`

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Frequently Asked Questions

What is 2/7 divided by 11/21 as a fraction?

2/7 ÷ 11/21 in simplest fraction form is 6/11.

What is 2/7 divided by 11/21 as a decimal?

2/7 ÷ 11/21 converted to a decimal is 0.545455.

What is 2/7 divided by 11/21 as a percentage?

2/7 ÷ 11/21 expressed as a percentage is 54.5455%.

Does 2/7 divided by 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.545455...) because the denominator contains prime factors other than 2 and 5.