What is 1/5 divided by 9/21?
1/5 divided by 9/21 equals 7/15 (or 0.466667 in decimal form). Learn the step-by-step solution to divide 1/5 and 9/21 using Least Common Denominator and simplification.
Exact Answer
1/5 ÷ 9/21 = 7/15
Simplified Fraction
7/15
Mixed Number
Proper (7/15)
Decimal Value
0.466667
Percentage
46.6667%
Step-by-Step Solution: 1/5 ÷ 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.
1/5 ÷ 9/21 = 1/5 × 21/9
Step 2
Multiply the Numerators and Denominators
Multiply the new numerators (1 × 21 = 21) and denominators (5 × 9 = 45).
1 × 21/5 × 9 = 21/45
Step 3
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 21 and 45, which is 3. Divide both the numerator and denominator by 3.
21 ÷ 3/45 ÷ 3 = 7/15
Step 4
Decimal & Percentage Representation
Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).
7 ÷ 15 = 0.466667 (46.6667%)
Visual Representation
The diagram below illustrates 1/5 divided by 9/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 7/15 |
| Mixed Number Form | 7/15 |
| Decimal Form | 0.466667 |
| Percentage | 46.6667% |
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Frequently Asked Questions
What is 1/5 divided by 9/21 as a fraction?
1/5 ÷ 9/21 in simplest fraction form is 7/15.
What is 1/5 divided by 9/21 as a decimal?
1/5 ÷ 9/21 converted to a decimal is 0.466667.
What is 1/5 divided by 9/21 as a percentage?
1/5 ÷ 9/21 expressed as a percentage is 46.6667%.
Does 1/5 divided by 9/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.466667...) because the denominator contains prime factors other than 2 and 5.