What is 4/9 divided by 7/21?
4/9 divided by 7/21 equals 4/3 (or 1 1/3 as a mixed number) (or 1.333333 in decimal form). Learn the step-by-step solution to divide 4/9 and 7/21 using Least Common Denominator and simplification.
Exact Answer
4/9 ÷ 7/21 = 4/3
Simplified Fraction
4/3
Mixed Number
1 1/3
Decimal Value
1.333333
Percentage
133.3333%
Step-by-Step Solution: 4/9 ÷ 7/21
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 7/21 to get 21/7.
4/9 ÷ 7/21 = 4/9 × 21/7
Step 2
Multiply the Numerators and Denominators
Multiply the new numerators (4 × 21 = 84) and denominators (9 × 7 = 63).
4 × 21/9 × 7 = 84/63
Step 3
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 63, which is 21. Divide both the numerator and denominator by 21.
84 ÷ 21/63 ÷ 21 = 4/3
Step 4
Convert Improper Fraction to a Mixed Number
Since the numerator (4) is greater than the denominator (3), divide 4 by 3: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/3.
4/3 = 11/3
Step 5
Decimal & Percentage Representation
Dividing the numerator 4 by denominator 3 produces a repeating decimal (approximately 1.333333, or 133.3333%).
4 ÷ 3 = 1.333333 (133.3333%)
Visual Representation
The diagram below illustrates 4/9 divided by 7/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 4/3 |
| Mixed Number Form | 1 1/3 |
| Decimal Form | 1.333333 |
| Percentage | 133.3333% |
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Frequently Asked Questions
What is 4/9 divided by 7/21 as a fraction?
4/9 ÷ 7/21 in simplest fraction form is 4/3 (or 1 1/3 as a mixed number).
What is 4/9 divided by 7/21 as a decimal?
4/9 ÷ 7/21 converted to a decimal is 1.333333.
What is 4/9 divided by 7/21 as a percentage?
4/9 ÷ 7/21 expressed as a percentage is 133.3333%.
How do you write 4/9 divided by 7/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 4/3 can be written as the mixed number 1 1/3.
Does 4/9 divided by 7/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.333333...) because the denominator contains prime factors other than 2 and 5.