What is 1/9 divided by 8/21?
1/9 divided by 8/21 equals 7/24 (or 0.291667 in decimal form). Learn the step-by-step solution to divide 1/9 and 8/21 using Least Common Denominator and simplification.
Exact Answer
1/9 ÷ 8/21 = 7/24
Simplified Fraction
7/24
Mixed Number
Proper (7/24)
Decimal Value
0.291667
Percentage
29.1667%
Step-by-Step Solution: 1/9 ÷ 8/21
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 8/21 to get 21/8.
1/9 ÷ 8/21 = 1/9 × 21/8
Step 2
Multiply the Numerators and Denominators
Multiply the new numerators (1 × 21 = 21) and denominators (9 × 8 = 72).
1 × 21/9 × 8 = 21/72
Step 3
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 21 and 72, which is 3. Divide both the numerator and denominator by 3.
21 ÷ 3/72 ÷ 3 = 7/24
Step 4
Decimal & Percentage Representation
Dividing the numerator 7 by denominator 24 produces a repeating decimal (approximately 0.291667, or 29.1667%).
7 ÷ 24 = 0.291667 (29.1667%)
Visual Representation
The diagram below illustrates 1/9 divided by 8/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 7/24 |
| Mixed Number Form | 7/24 |
| Decimal Form | 0.291667 |
| Percentage | 29.1667% |
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Frequently Asked Questions
What is 1/9 divided by 8/21 as a fraction?
1/9 ÷ 8/21 in simplest fraction form is 7/24.
What is 1/9 divided by 8/21 as a decimal?
1/9 ÷ 8/21 converted to a decimal is 0.291667.
What is 1/9 divided by 8/21 as a percentage?
1/9 ÷ 8/21 expressed as a percentage is 29.1667%.
Does 1/9 divided by 8/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.291667...) because the denominator contains prime factors other than 2 and 5.