What is 2/3 divided by 3/5? (Answer: 10/9)

Exact Answer

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Problem: What is 2/3 divided by 3/5?
Formula / Expression: 2/3 ÷ 3/5
Final Answer: 1 1/9 (10/9)
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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: 2/3 ÷ 3/5 = 2/3 × 5/3

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 5 = 10) and denominators (3 × 3 = 9).
Working: 2 × 5/3 × 3 = 10/9

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 10 and 9 is 1, confirming that 10/9 cannot be reduced further—it is already in its simplest irreducible form.
Working: 10/9

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (10) is greater than the denominator (9), divide 10 by 9: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/9.
Working: 10/9 = 1 1/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 9 produces a repeating decimal (approximately 1.111111, or 111.1111%).
Working: 10 ÷ 9 = 1.111111 (111.1111%)

Key Values:
- Simplified Fraction: 10/9
- Mixed Number Form: 1 1/9
- Decimal Value: 1.111111
- Percentage: 111.1111%

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2/3 ÷ 3/5 = 10/9

Simplified Fraction

10/9

Mixed Number

1 1/9

Decimal Value

1.111111

Percentage

111.1111%

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Step-by-Step Solution: 2/3 ÷ 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.

2/3 ÷ 3/5 = 2/3 × 5/3

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 5 = 10) and denominators (3 × 3 = 9).

2 × 5/3 × 3 = 10/9

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 10 and 9 is 1, confirming that 10/9 cannot be reduced further—it is already in its simplest irreducible form.

10/9

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (10) is greater than the denominator (9), divide 10 by 9: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/9.

10/9 = 11/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 9 produces a repeating decimal (approximately 1.111111, or 111.1111%).

10 ÷ 9 = 1.111111 (111.1111%)

Visual Representation

The diagram below illustrates 2/3 divided by 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/9`
Mixed Number Form	`1 1/9`
Decimal Form	`1.111111`
Percentage	`111.1111%`

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Frequently Asked Questions

What is 2/3 divided by 3/5 as a fraction?

2/3 ÷ 3/5 in simplest fraction form is 10/9 (or 1 1/9 as a mixed number).

What is 2/3 divided by 3/5 as a decimal?

2/3 ÷ 3/5 converted to a decimal is 1.111111.

What is 2/3 divided by 3/5 as a percentage?

2/3 ÷ 3/5 expressed as a percentage is 111.1111%.

How do you write 2/3 divided by 3/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 10/9 can be written as the mixed number 1 1/9.

Does 2/3 divided by 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.111111...) because the denominator contains prime factors other than 2 and 5.