What is 2/3 divided by 4/5? (Answer: 5/6)

Exact Answer

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Problem: What is 2/3 divided by 4/5?
Formula / Expression: 2/3 ÷ 4/5
Final Answer: 5/6
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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 4/5 to get 5/4.
Working: 2/3 ÷ 4/5 = 2/3 × 5/4

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 5 = 10) and denominators (3 × 4 = 12).
Working: 2 × 5/3 × 4 = 10/12

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 10 and 12, which is 2. Divide both the numerator and denominator by 2.
Working: 10 ÷ 2/12 ÷ 2 = 5/6

Step 4: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).
Working: 5 ÷ 6 = 0.833333 (83.3333%)

Key Values:
- Simplified Fraction: 5/6
- Mixed Number Form: 5/6
- Decimal Value: 0.833333
- Percentage: 83.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-3-divided-by-4-5/
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2/3 ÷ 4/5 = 5/6

Simplified Fraction

5/6

Mixed Number

Proper (5/6)

Decimal Value

0.833333

Percentage

83.3333%

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Step-by-Step Solution: 2/3 ÷ 4/5

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 4/5 to get 5/4.

2/3 ÷ 4/5 = 2/3 × 5/4

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 5 = 10) and denominators (3 × 4 = 12).

2 × 5/3 × 4 = 10/12

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 10 and 12, which is 2. Divide both the numerator and denominator by 2.

10 ÷ 2/12 ÷ 2 = 5/6

Step 4

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).

5 ÷ 6 = 0.833333 (83.3333%)

Visual Representation

The diagram below illustrates 2/3 divided by 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/6`
Mixed Number Form	`5/6`
Decimal Form	`0.833333`
Percentage	`83.3333%`

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Frequently Asked Questions

What is 2/3 divided by 4/5 as a fraction?

2/3 ÷ 4/5 in simplest fraction form is 5/6.

What is 2/3 divided by 4/5 as a decimal?

2/3 ÷ 4/5 converted to a decimal is 0.833333.

What is 2/3 divided by 4/5 as a percentage?

2/3 ÷ 4/5 expressed as a percentage is 83.3333%.

Does 2/3 divided by 4/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.833333...) because the denominator contains prime factors other than 2 and 5.