What is 2/5 divided by 7/9? (Answer: 18/35)

Exact Answer

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Problem: What is 2/5 divided by 7/9?
Formula / Expression: 2/5 ÷ 7/9
Final Answer: 18/35
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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 7/9 to get 9/7.
Working: 2/5 ÷ 7/9 = 2/5 × 9/7

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 9 = 18) and denominators (5 × 7 = 35).
Working: 2 × 9/5 × 7 = 18/35

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 18 and 35 is 1, confirming that 18/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 18/35

Step 4: Decimal & Percentage Representation
Dividing the numerator 18 by denominator 35 produces a repeating decimal (approximately 0.514286, or 51.4286%).
Working: 18 ÷ 35 = 0.514286 (51.4286%)

Key Values:
- Simplified Fraction: 18/35
- Mixed Number Form: 18/35
- Decimal Value: 0.514286
- Percentage: 51.4286%

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2/5 ÷ 7/9 = 18/35

Simplified Fraction

18/35

Mixed Number

Proper (18/35)

Decimal Value

0.514286

Percentage

51.4286%

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Step-by-Step Solution: 2/5 ÷ 7/9

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 7/9 to get 9/7.

2/5 ÷ 7/9 = 2/5 × 9/7

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 9 = 18) and denominators (5 × 7 = 35).

2 × 9/5 × 7 = 18/35

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 18 and 35 is 1, confirming that 18/35 cannot be reduced further—it is already in its simplest irreducible form.

18/35

Step 4

Decimal & Percentage Representation

Dividing the numerator 18 by denominator 35 produces a repeating decimal (approximately 0.514286, or 51.4286%).

18 ÷ 35 = 0.514286 (51.4286%)

Visual Representation

The diagram below illustrates 2/5 divided by 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`18/35`
Mixed Number Form	`18/35`
Decimal Form	`0.514286`
Percentage	`51.4286%`

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Frequently Asked Questions

What is 2/5 divided by 7/9 as a fraction?

2/5 ÷ 7/9 in simplest fraction form is 18/35.

What is 2/5 divided by 7/9 as a decimal?

2/5 ÷ 7/9 converted to a decimal is 0.514286.

What is 2/5 divided by 7/9 as a percentage?

2/5 ÷ 7/9 expressed as a percentage is 51.4286%.

Does 2/5 divided by 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.514286...) because the denominator contains prime factors other than 2 and 5.