What is 5/9 divided by 9/21? (Answer: 35/27)

Exact Answer

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Problem: What is 5/9 divided by 9/21?
Formula / Expression: 5/9 ÷ 9/21
Final Answer: 1 8/27 (35/27)
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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 9/21 to get 21/9.
Working: 5/9 ÷ 9/21 = 5/9 × 21/9

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (5 × 21 = 105) and denominators (9 × 9 = 81).
Working: 5 × 21/9 × 9 = 105/81

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 105 and 81, which is 3. Divide both the numerator and denominator by 3.
Working: 105 ÷ 3/81 ÷ 3 = 35/27

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (35) is greater than the denominator (27), divide 35 by 27: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/27.
Working: 35/27 = 1 8/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 27 produces a repeating decimal (approximately 1.296296, or 129.6296%).
Working: 35 ÷ 27 = 1.296296 (129.6296%)

Key Values:
- Simplified Fraction: 35/27
- Mixed Number Form: 1 8/27
- Decimal Value: 1.296296
- Percentage: 129.6296%

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5/9 ÷ 9/21 = 35/27

Simplified Fraction

35/27

Mixed Number

1 8/27

Decimal Value

1.296296

Percentage

129.6296%

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Step-by-Step Solution: 5/9 ÷ 9/21

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 9/21 to get 21/9.

5/9 ÷ 9/21 = 5/9 × 21/9

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (5 × 21 = 105) and denominators (9 × 9 = 81).

5 × 21/9 × 9 = 105/81

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 105 and 81, which is 3. Divide both the numerator and denominator by 3.

105 ÷ 3/81 ÷ 3 = 35/27

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (35) is greater than the denominator (27), divide 35 by 27: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/27.

35/27 = 18/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 27 produces a repeating decimal (approximately 1.296296, or 129.6296%).

35 ÷ 27 = 1.296296 (129.6296%)

Visual Representation

The diagram below illustrates 5/9 divided by 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/27`
Mixed Number Form	`1 8/27`
Decimal Form	`1.296296`
Percentage	`129.6296%`

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Frequently Asked Questions

What is 5/9 divided by 9/21 as a fraction?

5/9 ÷ 9/21 in simplest fraction form is 35/27 (or 1 8/27 as a mixed number).

What is 5/9 divided by 9/21 as a decimal?

5/9 ÷ 9/21 converted to a decimal is 1.296296.

What is 5/9 divided by 9/21 as a percentage?

5/9 ÷ 9/21 expressed as a percentage is 129.6296%.

How do you write 5/9 divided by 9/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 35/27 can be written as the mixed number 1 8/27.

Does 5/9 divided by 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.296296...) because the denominator contains prime factors other than 2 and 5.