What is 1/3 divided by 3/5? (Answer: 5/9)

Exact Answer

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Problem: What is 1/3 divided by 3/5?
Formula / Expression: 1/3 ÷ 3/5
Final Answer: 5/9
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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 3/5 to get 5/3.
Working: 1/3 ÷ 3/5 = 1/3 × 5/3

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (1 × 5 = 5) and denominators (3 × 3 = 9).
Working: 1 × 5/3 × 3 = 5/9

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 9 is 1, confirming that 5/9 cannot be reduced further—it is already in its simplest irreducible form.
Working: 5/9

Step 4: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).
Working: 5 ÷ 9 = 0.555556 (55.5556%)

Key Values:
- Simplified Fraction: 5/9
- Mixed Number Form: 5/9
- Decimal Value: 0.555556
- Percentage: 55.5556%

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1/3 ÷ 3/5 = 5/9

Simplified Fraction

5/9

Mixed Number

Proper (5/9)

Decimal Value

0.555556

Percentage

55.5556%

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Step-by-Step Solution: 1/3 ÷ 3/5

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 3/5 to get 5/3.

1/3 ÷ 3/5 = 1/3 × 5/3

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (1 × 5 = 5) and denominators (3 × 3 = 9).

1 × 5/3 × 3 = 5/9

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 9 is 1, confirming that 5/9 cannot be reduced further—it is already in its simplest irreducible form.

5/9

Step 4

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).

5 ÷ 9 = 0.555556 (55.5556%)

Visual Representation

The diagram below illustrates 1/3 divided by 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/9`
Mixed Number Form	`5/9`
Decimal Form	`0.555556`
Percentage	`55.5556%`

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Frequently Asked Questions

What is 1/3 divided by 3/5 as a fraction?

1/3 ÷ 3/5 in simplest fraction form is 5/9.

What is 1/3 divided by 3/5 as a decimal?

1/3 ÷ 3/5 converted to a decimal is 0.555556.

What is 1/3 divided by 3/5 as a percentage?

1/3 ÷ 3/5 expressed as a percentage is 55.5556%.

Does 1/3 divided by 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.555556...) because the denominator contains prime factors other than 2 and 5.