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Question 1.
Answer:
Negative: 3/-7, -6/25, -41/32
Positive: 17/20, -11/-25, -17/-85
Explanation:
The negative numbers will only have one negative sign, either in the numerator or denominator.
On the other hand, the positive numbers will either have no negativity at all or will have the negative sign in both the numerator and denominator. For the latter, we will cancel by -1 to prove that it is after all, positive.
Question 2.
Answer and explanation:
(a) -14/6, -21/9, -28/12 (multiplying the rational number by 2/2, 3/3 and 4/4)
(b) 4/26, 6/39, 8/52 (multiplying the rational number by 2/2, 3/3 and 4/4)
(c) 32/-50, 48/-75, 64/-100 (multiplying the rational number by 2/2, 3/3 and 4/4)
In this case, it would be better to write them as -32/50, -48/75, -64/100, because it's a better practice to write negative numerators than denominators.
(d) Let's convert -9/-12 into 9/12 by dividing both the numerator and denominator by -1. So, now we deal with the rational number 9/12.
3/4, 6/8, 18/24 (dividing the rational number by 3/3, then multiplying the resultant by 2/2 and 3/3)
(e) 2/16, 1/8, 10/80 (dividing the rational number by 10/10, then further dividing the resultant by 2/2 and then finally multiplying that new resultant by 10/10)
Question 3.
Answer and explanation:
(a) Cancelling with 8, we have -4/5
(b) Cancelling with 25, we have -1/2
(c) Cancelling with 6, we have 3/-7
Now, multiplying both numerator and denominator by -1, we have -3/7
(d) Cancelling with -24, we have 9/23
(e) Cancelling with 10, we have -13/30
Question 4.
Answer and explanation:
I will be taking all the unknowns to be x.
(a) 5/x = 90/216
=> x = (216 × 5)/90 = 12
(b) 2/x = 90/135
=> x = (135 × 2)/90 = 3
(c) 9/16 = 90/x
=> x = (90 × 16)/9 = 160
(d) x/4 = 90/120
=> x = (90 × 4)/120 = 3
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