In simplest form, what is 210/385?
A6/11
B3/11
C6/7
D2/11
Answer & Solution
Correct answer: A. 6/11
1. Factor the numerator into primes: 210 = 2 x 3 x 5 x 7.
2. Factor the denominator into primes: 385 = 5 x 7 x 11.
3. Both the numerator and denominator share the factors 5 and 7.
4. Divide out the common factors of 5 and 7, leaving 2 x 3 over 11.
5. Multiplying the remaining factors gives 6/11.
6. 3/11 comes from dropping an extra factor of 2, and 6/7 comes from cancelling 11 instead of leaving it in the denominator.
_Source: OpenStax Prealgebra (CC BY 4.0), Ch 4 "Fractions", section 4.2 Multiply and Divide Fractions_
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