What is 1/2 divided by 4/5? (Answer: 5/8)

Exact Answer

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Problem: What is 1/2 divided by 4/5?
Formula / Expression: 1/2 ÷ 4/5
Final Answer: 5/8
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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 4/5 to get 5/4.
Working: 1/2 ÷ 4/5 = 1/2 × 5/4

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (1 × 5 = 5) and denominators (2 × 4 = 8).
Working: 1 × 5/2 × 4 = 5/8

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 8 is 1, confirming that 5/8 cannot be reduced further—it is already in its simplest irreducible form.
Working: 5/8

Step 4: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).
Working: 5 ÷ 8 = 0.625 (62.5%)

Key Values:
- Simplified Fraction: 5/8
- Mixed Number Form: 5/8
- Decimal Value: 0.625
- Percentage: 62.5%

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Solved with FractionsCalc:
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1/2 ÷ 4/5 = 5/8

Simplified Fraction

5/8

Mixed Number

Proper (5/8)

Decimal Value

0.625

Percentage

62.5%

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Step-by-Step Solution: 1/2 ÷ 4/5

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 4/5 to get 5/4.

1/2 ÷ 4/5 = 1/2 × 5/4

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (1 × 5 = 5) and denominators (2 × 4 = 8).

1 × 5/2 × 4 = 5/8

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 8 is 1, confirming that 5/8 cannot be reduced further—it is already in its simplest irreducible form.

5/8

Step 4

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).

5 ÷ 8 = 0.625 (62.5%)

Visual Representation

The diagram below illustrates 1/2 divided by 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/8`
Mixed Number Form	`5/8`
Decimal Form	`0.625`
Percentage	`62.5%`

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Frequently Asked Questions

What is 1/2 divided by 4/5 as a fraction?

1/2 ÷ 4/5 in simplest fraction form is 5/8.

What is 1/2 divided by 4/5 as a decimal?

1/2 ÷ 4/5 converted to a decimal is 0.625.

What is 1/2 divided by 4/5 as a percentage?

1/2 ÷ 4/5 expressed as a percentage is 62.5%.

Does 1/2 divided by 4/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.625) because the denominator in simplest terms contains only prime factors 2 and/or 5.