What is 3/10 divided by 9/21?
3/10 divided by 9/21 equals 7/10 (or 0.7 in decimal form). Learn the step-by-step solution to divide 3/10 and 9/21 using Least Common Denominator and simplification.
Exact Answer
3/10 ÷ 9/21 = 7/10
Simplified Fraction
7/10
Mixed Number
Proper (7/10)
Decimal Value
0.7
Percentage
70%
Step-by-Step Solution: 3/10 ÷ 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.
3/10 ÷ 9/21 = 3/10 × 21/9
Step 2
Multiply the Numerators and Denominators
Multiply the new numerators (3 × 21 = 63) and denominators (10 × 9 = 90).
3 × 21/10 × 9 = 63/90
Step 3
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 90, which is 9. Divide both the numerator and denominator by 9.
63 ÷ 9/90 ÷ 9 = 7/10
Step 4
Decimal & Percentage Representation
Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).
7 ÷ 10 = 0.7 (70%)
Visual Representation
The diagram below illustrates 3/10 divided by 9/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 7/10 |
| Mixed Number Form | 7/10 |
| Decimal Form | 0.7 |
| Percentage | 70% |
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Frequently Asked Questions
What is 3/10 divided by 9/21 as a fraction?
3/10 ÷ 9/21 in simplest fraction form is 7/10.
What is 3/10 divided by 9/21 as a decimal?
3/10 ÷ 9/21 converted to a decimal is 0.7.
What is 3/10 divided by 9/21 as a percentage?
3/10 ÷ 9/21 expressed as a percentage is 70%.
Does 3/10 divided by 9/21 result in a terminating or repeating decimal?
It results in an exact terminating decimal (0.7) because the denominator in simplest terms contains only prime factors 2 and/or 5.