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

Exact Answer

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Problem: What is 2/3 divided by 1/2?
Formula / Expression: 2/3 ÷ 1/2
Final Answer: 1 1/3 (4/3)
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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: 2/3 ÷ 1/2 = 2/3 × 2

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

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

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (4) is greater than the denominator (3), divide 4 by 3: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/3.
Working: 4/3 = 1 1/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 3 produces a repeating decimal (approximately 1.333333, or 133.3333%).
Working: 4 ÷ 3 = 1.333333 (133.3333%)

Key Values:
- Simplified Fraction: 4/3
- Mixed Number Form: 1 1/3
- Decimal Value: 1.333333
- Percentage: 133.3333%

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2/3 ÷ 1/2 = 4/3

Simplified Fraction

4/3

Mixed Number

1 1/3

Decimal Value

1.333333

Percentage

133.3333%

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Step-by-Step Solution: 2/3 ÷ 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.

2/3 ÷ 1/2 = 2/3 × 2

Step 2

Multiply the Numerators and Denominators

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

2 × 2/3 × 1 = 4/3

Step 3

Check if the Fraction Can Be Simplified

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

4/3

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (4) is greater than the denominator (3), divide 4 by 3: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/3.

4/3 = 11/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 3 produces a repeating decimal (approximately 1.333333, or 133.3333%).

4 ÷ 3 = 1.333333 (133.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/3`
Mixed Number Form	`1 1/3`
Decimal Form	`1.333333`
Percentage	`133.3333%`

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Frequently Asked Questions

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

2/3 ÷ 1/2 in simplest fraction form is 4/3 (or 1 1/3 as a mixed number).

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

2/3 ÷ 1/2 converted to a decimal is 1.333333.

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

2/3 ÷ 1/2 expressed as a percentage is 133.3333%.

How do you write 2/3 divided by 1/2 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 4/3 can be written as the mixed number 1 1/3.

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

It results in a repeating decimal (approximately 1.333333...) because the denominator contains prime factors other than 2 and 5.