What is 2/5 divided by 11/21? (Answer: 42/55)

Exact Answer

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Problem: What is 2/5 divided by 11/21?
Formula / Expression: 2/5 ÷ 11/21
Final Answer: 42/55
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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: 2/5 ÷ 11/21 = 2/5 × 21/11

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (5 × 11 = 55).
Working: 2 × 21/5 × 11 = 42/55

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 42 and 55 is 1, confirming that 42/55 cannot be reduced further—it is already in its simplest irreducible form.
Working: 42/55

Step 4: Decimal & Percentage Representation
Dividing the numerator 42 by denominator 55 produces a repeating decimal (approximately 0.763636, or 76.3636%).
Working: 42 ÷ 55 = 0.763636 (76.3636%)

Key Values:
- Simplified Fraction: 42/55
- Mixed Number Form: 42/55
- Decimal Value: 0.763636
- Percentage: 76.3636%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-divided-by-11-21/
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2/5 ÷ 11/21 = 42/55

Simplified Fraction

42/55

Mixed Number

Proper (42/55)

Decimal Value

0.763636

Percentage

76.3636%

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Step-by-Step Solution: 2/5 ÷ 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.

2/5 ÷ 11/21 = 2/5 × 21/11

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (5 × 11 = 55).

2 × 21/5 × 11 = 42/55

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 42 and 55 is 1, confirming that 42/55 cannot be reduced further—it is already in its simplest irreducible form.

42/55

Step 4

Decimal & Percentage Representation

Dividing the numerator 42 by denominator 55 produces a repeating decimal (approximately 0.763636, or 76.3636%).

42 ÷ 55 = 0.763636 (76.3636%)

Visual Representation

The diagram below illustrates 2/5 divided by 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`42/55`
Mixed Number Form	`42/55`
Decimal Form	`0.763636`
Percentage	`76.3636%`

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Frequently Asked Questions

What is 2/5 divided by 11/21 as a fraction?

2/5 ÷ 11/21 in simplest fraction form is 42/55.

What is 2/5 divided by 11/21 as a decimal?

2/5 ÷ 11/21 converted to a decimal is 0.763636.

What is 2/5 divided by 11/21 as a percentage?

2/5 ÷ 11/21 expressed as a percentage is 76.3636%.

Does 2/5 divided by 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.763636...) because the denominator contains prime factors other than 2 and 5.