What is 1/2 divided by 2/3? (Answer: 3/4)

Exact Answer

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Problem: What is 1/2 divided by 2/3?
Formula / Expression: 1/2 ÷ 2/3
Final Answer: 3/4
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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 2/3 to get 3/2.
Working: 1/2 ÷ 2/3 = 1/2 × 3/2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (1 × 3 = 3) and denominators (2 × 2 = 4).
Working: 1 × 3/2 × 2 = 3/4

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 3 and 4 is 1, confirming that 3/4 cannot be reduced further—it is already in its simplest irreducible form.
Working: 3/4

Step 4: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).
Working: 3 ÷ 4 = 0.75 (75%)

Key Values:
- Simplified Fraction: 3/4
- Mixed Number Form: 3/4
- Decimal Value: 0.75
- Percentage: 75%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-divided-by-2-3/
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1/2 ÷ 2/3 = 3/4

Simplified Fraction

3/4

Mixed Number

Proper (3/4)

Decimal Value

0.75

Percentage

75%

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Step-by-Step Solution: 1/2 ÷ 2/3

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 2/3 to get 3/2.

1/2 ÷ 2/3 = 1/2 × 3/2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (1 × 3 = 3) and denominators (2 × 2 = 4).

1 × 3/2 × 2 = 3/4

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 3 and 4 is 1, confirming that 3/4 cannot be reduced further—it is already in its simplest irreducible form.

3/4

Step 4

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).

3 ÷ 4 = 0.75 (75%)

Visual Representation

The diagram below illustrates 1/2 divided by 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/4`
Mixed Number Form	`3/4`
Decimal Form	`0.75`
Percentage	`75%`

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Frequently Asked Questions

What is 1/2 divided by 2/3 as a fraction?

1/2 ÷ 2/3 in simplest fraction form is 3/4.

What is 1/2 divided by 2/3 as a decimal?

1/2 ÷ 2/3 converted to a decimal is 0.75.

What is 1/2 divided by 2/3 as a percentage?

1/2 ÷ 2/3 expressed as a percentage is 75%.

Does 1/2 divided by 2/3 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.75) because the denominator in simplest terms contains only prime factors 2 and/or 5.