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" ... multiply by the RECIPROCAL of the divisor.
When a fraction is simplified, it is made into an equivalent fraction with no common divisor between the numerator and denominator.
Fractions where both the numerator and divisor are rational numbers are always rational numbers.
It is easier to multiply or divide fractions than to add or subtract fractions because in multiplication, you just have to multiply the numerator by the numerator and the denominator by the denominator. Same applies with division of fractions, except that you have to reciprocate the fraction you're dividing with (divisor) then proceed to multiplication. Whereas, in addition and subtraction of fractions, you still have to get their Least Common Denominator (LCD).
When you divide fractions you need to multiply by the reciprocal of the divisor. You would also use it anytime the multiplicative inverse is required.