9514 1404 393
Answer:
-28/45
Step-by-step explanation:
Step 1, the sign
When the fractions have an odd number of minus signs (1, not 0 or 2), the result will be negative. This knowledge lets you ignore the sign while you do the rest of the arithmetic. The appropriate sign is applied to the final numbers.
Step 2, the formula
The ratio (a/b)÷(c/d) is (ad)/(bc). There are several ways you can get there:
⇒ "invert and multiply" or "swap dot"
[tex]\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\,\cdot\,\dfrac{d}{c}=\dfrac{ad}{bc} \quad\text{division is multiplication by the reciprocal}[/tex]
⇒ "numerators of a common denominator"
[tex]\dfrac{\left(\dfrac{a}{b}\right)}{\left(\dfrac{c}{d}\right)}=\dfrac{\left(\dfrac{ad}{bd}\right)}{\left(\dfrac{bc}{bd}\right)}=\dfrac{ad}{bc}[/tex]
⇒ "swapped denominators of a common numerator"
[tex]\dfrac{\left(\dfrac{a}{b}\right)}{\left(\dfrac{c}{d}\right)}=\dfrac{\left(\dfrac{ac}{bc}\right)}{\left(\dfrac{ac}{ad}\right)}=\dfrac{ad}{bc}[/tex]
The use of common numerators or common denominators is most often seen when the numerator or denominator of one fraction is a multiple of that in the other fraction. Example: (2/3)÷(1/6) = (4/6)÷(1/6) = 4/1 = 4
Step 3, reduce the result
Any of these fractions is reduced by cancelling common factors from numerator and denominator. Your fractions here don't have any common factors, so there is nothing to cancel.
_____
Your product is ...
(4/9) ÷ (-5/7) = -(4·7)/(9·5) = -28/45
