What is 4/9 divided by 2/3? (Answer: 2/3)

Exact Answer

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Problem: What is 4/9 divided by 2/3?
Formula / Expression: 4/9 ÷ 2/3
Final Answer: 2/3
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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 2/3 to get 3/2.
Working: 4/9 ÷ 2/3 = 4/9 × 3/2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (4 × 3 = 12) and denominators (9 × 2 = 18).
Working: 4 × 3/9 × 2 = 12/18

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 12 and 18, which is 6. Divide both the numerator and denominator by 6.
Working: 12 ÷ 6/18 ÷ 6 = 2/3

Step 4: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
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4/9 ÷ 2/3 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 4/9 ÷ 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.

4/9 ÷ 2/3 = 4/9 × 3/2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (4 × 3 = 12) and denominators (9 × 2 = 18).

4 × 3/9 × 2 = 12/18

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 12 and 18, which is 6. Divide both the numerator and denominator by 6.

12 ÷ 6/18 ÷ 6 = 2/3

Step 4

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 4/9 divided by 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 4/9 divided by 2/3 as a fraction?

4/9 ÷ 2/3 in simplest fraction form is 2/3.

What is 4/9 divided by 2/3 as a decimal?

4/9 ÷ 2/3 converted to a decimal is 0.666667.

What is 4/9 divided by 2/3 as a percentage?

4/9 ÷ 2/3 expressed as a percentage is 66.6667%.

Does 4/9 divided by 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.