What is 1/2 divided by 8/9? (Answer: 9/16)

Exact Answer

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Problem: What is 1/2 divided by 8/9?
Formula / Expression: 1/2 ÷ 8/9
Final Answer: 9/16
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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 8/9 to get 9/8.
Working: 1/2 ÷ 8/9 = 1/2 × 9/8

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (1 × 9 = 9) and denominators (2 × 8 = 16).
Working: 1 × 9/2 × 8 = 9/16

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 9 and 16 is 1, confirming that 9/16 cannot be reduced further—it is already in its simplest irreducible form.
Working: 9/16

Step 4: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 16 yields an exact terminating decimal of 0.5625 (or 56.25%).
Working: 9 ÷ 16 = 0.5625 (56.25%)

Key Values:
- Simplified Fraction: 9/16
- Mixed Number Form: 9/16
- Decimal Value: 0.5625
- Percentage: 56.25%

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1/2 ÷ 8/9 = 9/16

Simplified Fraction

9/16

Mixed Number

Proper (9/16)

Decimal Value

0.5625

Percentage

56.25%

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Step-by-Step Solution: 1/2 ÷ 8/9

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 8/9 to get 9/8.

1/2 ÷ 8/9 = 1/2 × 9/8

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (1 × 9 = 9) and denominators (2 × 8 = 16).

1 × 9/2 × 8 = 9/16

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 9 and 16 is 1, confirming that 9/16 cannot be reduced further—it is already in its simplest irreducible form.

9/16

Step 4

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 16 yields an exact terminating decimal of 0.5625 (or 56.25%).

9 ÷ 16 = 0.5625 (56.25%)

Visual Representation

The diagram below illustrates 1/2 divided by 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/16`
Mixed Number Form	`9/16`
Decimal Form	`0.5625`
Percentage	`56.25%`

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Frequently Asked Questions

What is 1/2 divided by 8/9 as a fraction?

1/2 ÷ 8/9 in simplest fraction form is 9/16.

What is 1/2 divided by 8/9 as a decimal?

1/2 ÷ 8/9 converted to a decimal is 0.5625.

What is 1/2 divided by 8/9 as a percentage?

1/2 ÷ 8/9 expressed as a percentage is 56.25%.

Does 1/2 divided by 8/9 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5625) because the denominator in simplest terms contains only prime factors 2 and/or 5.