What is 4/9 divided by 9/21?
4/9 divided by 9/21 equals 28/27 (or 1 1/27 as a mixed number) (or 1.037037 in decimal form). Learn the step-by-step solution to divide 4/9 and 9/21 using Least Common Denominator and simplification.
Exact Answer
4/9 ÷ 9/21 = 28/27
Simplified Fraction
28/27
Mixed Number
1 1/27
Decimal Value
1.037037
Percentage
103.7037%
Step-by-Step Solution: 4/9 ÷ 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.
4/9 ÷ 9/21 = 4/9 × 21/9
Step 2
Multiply the Numerators and Denominators
Multiply the new numerators (4 × 21 = 84) and denominators (9 × 9 = 81).
4 × 21/9 × 9 = 84/81
Step 3
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 81, which is 3. Divide both the numerator and denominator by 3.
84 ÷ 3/81 ÷ 3 = 28/27
Step 4
Convert Improper Fraction to a Mixed Number
Since the numerator (28) is greater than the denominator (27), divide 28 by 27: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/27.
28/27 = 11/27
Step 5
Decimal & Percentage Representation
Dividing the numerator 28 by denominator 27 produces a repeating decimal (approximately 1.037037, or 103.7037%).
28 ÷ 27 = 1.037037 (103.7037%)
Visual Representation
The diagram below illustrates 4/9 divided by 9/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 28/27 |
| Mixed Number Form | 1 1/27 |
| Decimal Form | 1.037037 |
| Percentage | 103.7037% |
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Frequently Asked Questions
What is 4/9 divided by 9/21 as a fraction?
4/9 ÷ 9/21 in simplest fraction form is 28/27 (or 1 1/27 as a mixed number).
What is 4/9 divided by 9/21 as a decimal?
4/9 ÷ 9/21 converted to a decimal is 1.037037.
What is 4/9 divided by 9/21 as a percentage?
4/9 ÷ 9/21 expressed as a percentage is 103.7037%.
How do you write 4/9 divided by 9/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 28/27 can be written as the mixed number 1 1/27.
Does 4/9 divided by 9/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.037037...) because the denominator contains prime factors other than 2 and 5.