What is 1/5 divided by 1/2? (Answer: 2/5)

Exact Answer

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Problem: What is 1/5 divided by 1/2?
Formula / Expression: 1/5 ÷ 1/2
Final Answer: 2/5
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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 1/2 to get 2/1.
Working: 1/5 ÷ 1/2 = 1/5 × 2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (1 × 2 = 2) and denominators (5 × 1 = 5).
Working: 1 × 2/5 × 1 = 2/5

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 2 and 5 is 1, confirming that 2/5 cannot be reduced further—it is already in its simplest irreducible form.
Working: 2/5

Step 4: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).
Working: 2 ÷ 5 = 0.4 (40%)

Key Values:
- Simplified Fraction: 2/5
- Mixed Number Form: 2/5
- Decimal Value: 0.4
- Percentage: 40%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-5-divided-by-1-2/
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1/5 ÷ 1/2 = 2/5

Simplified Fraction

2/5

Mixed Number

Proper (2/5)

Decimal Value

0.4

Percentage

40%

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Step-by-Step Solution: 1/5 ÷ 1/2

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 1/2 to get 2/1.

1/5 ÷ 1/2 = 1/5 × 2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (1 × 2 = 2) and denominators (5 × 1 = 5).

1 × 2/5 × 1 = 2/5

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 2 and 5 is 1, confirming that 2/5 cannot be reduced further—it is already in its simplest irreducible form.

2/5

Step 4

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).

2 ÷ 5 = 0.4 (40%)

Visual Representation

The diagram below illustrates 1/5 divided by 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/5`
Mixed Number Form	`2/5`
Decimal Form	`0.4`
Percentage	`40%`

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Frequently Asked Questions

What is 1/5 divided by 1/2 as a fraction?

1/5 ÷ 1/2 in simplest fraction form is 2/5.

What is 1/5 divided by 1/2 as a decimal?

1/5 ÷ 1/2 converted to a decimal is 0.4.

What is 1/5 divided by 1/2 as a percentage?

1/5 ÷ 1/2 expressed as a percentage is 40%.

Does 1/5 divided by 1/2 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.4) because the denominator in simplest terms contains only prime factors 2 and/or 5.