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

Exact Answer

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Problem: What is 2/5 divided by 2/3?
Formula / Expression: 2/5 ÷ 2/3
Final Answer: 3/5
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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: 2/5 ÷ 2/3 = 2/5 × 3/2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 3 = 6) and denominators (5 × 2 = 10).
Working: 2 × 3/5 × 2 = 6/10

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 6 and 10, which is 2. Divide both the numerator and denominator by 2.
Working: 6 ÷ 2/10 ÷ 2 = 3/5

Step 4: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).
Working: 3 ÷ 5 = 0.6 (60%)

Key Values:
- Simplified Fraction: 3/5
- Mixed Number Form: 3/5
- Decimal Value: 0.6
- Percentage: 60%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-divided-by-2-3/
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2/5 ÷ 2/3 = 3/5

Simplified Fraction

3/5

Mixed Number

Proper (3/5)

Decimal Value

0.6

Percentage

60%

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Step-by-Step Solution: 2/5 ÷ 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.

2/5 ÷ 2/3 = 2/5 × 3/2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 3 = 6) and denominators (5 × 2 = 10).

2 × 3/5 × 2 = 6/10

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 6 and 10, which is 2. Divide both the numerator and denominator by 2.

6 ÷ 2/10 ÷ 2 = 3/5

Step 4

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).

3 ÷ 5 = 0.6 (60%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/5`
Mixed Number Form	`3/5`
Decimal Form	`0.6`
Percentage	`60%`

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Frequently Asked Questions

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

2/5 ÷ 2/3 in simplest fraction form is 3/5.

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

2/5 ÷ 2/3 converted to a decimal is 0.6.

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

2/5 ÷ 2/3 expressed as a percentage is 60%.

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

It results in an exact terminating decimal (0.6) because the denominator in simplest terms contains only prime factors 2 and/or 5.