Algebra Foundations for Normal People by Gabriel Beguerie - HTML preview
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Chapter 2
Worked example (no skipped steps)
2.1 Compute 7 − 12.
7 − 12 = 7 + (−12) = −5
137
Worked example (no skipped steps)
2.2 Compute −9 + 4.
Starting at −9 and moving 4 units right gives −5.
Worked example (no skipped steps)
2.3 Compute −6 − 5.
−6 − 5 = −6 + (−5) = −11
Worked example (no skipped steps)
2.4 Compute −8 − (−3).
−8 − (−3) = −8 + 3 = −5
Worked example (no skipped steps)
2.5 Compute (−5)(−6).
Same signs give positive:
(−5)(−6) = 30
Worked example (no skipped steps)
2.6 Compute (−4)(9).
Different signs give negative:
(−4)(9) = −36
Worked example (no skipped steps)
2.7 Compute −21 .
7
Different signs give negative:
−21 = −3
7
Worked example (no skipped steps)
2.8 Compute −24 .
−6
Same signs give positive:
−24 = 4
−6
Step-by-step solutions
Worked example (no skipped steps)
2.9 Compute −7 + 15.
Starting at −7 and moving 15 units right lands at:
8
Answer: 8.
Worked example (no skipped steps)
2.10 Compute −11 − (−4).
Subtracting a negative means adding the opposite:
−11 − (−4) = −11 + 4
Now add:
−11 + 4 = −7
Answer: −7.
Worked example (no skipped steps)
2.11 Compute (−8)(−7).
Same signs give a positive product. Multiply the absolute values: 8 · 7 = 56
So:
(−8)(−7) = 56
Answer: 56.
Worked example (no skipped steps)
2.12 Compute 36 .
−9
Different signs give a negative quotient. Then divide the absolute values: 36 ÷ 9 = 4
So:
36 = −4
−9
Answer: −4.
139
Worked example (no skipped steps)
2.13 Compute −4 + (−9).
Adding a negative means moving left:
−4 + (−9) = −13
Answer: −13.
Worked example (no skipped steps)
2.14 Compute 13 − (−6).
Subtracting a negative means adding:
13 − (−6) = 13 + 6 = 19
Answer: 19.
Worked example (no skipped steps)
2.15 Compute (−8)(−5).
Two negatives multiply to a positive:
(−8)(−5) = 40
Answer: 40.
Worked example (no skipped steps)
2.16 Compute 42 ÷ (−7).
Positive divided by negative gives negative:
42 ÷ (−7) = −6
Answer: −6.
Worked example (no skipped steps)
2.17 Compute −18 ÷ (−3).
Negative divided by negative gives positive:
−18 ÷ (−3) = 6
Answer: 6.
Step-by-step solutions
Worked example (no skipped steps)
2.18 Compute −9 + 14.
Different signs mean subtract the absolute values:
14 − 9 = 5
Keep the sign of the larger absolute value, which is positive. Answer: 5.
Worked example (no skipped steps)
2.19 Compute −3 − 11.
Move 11 more units left:
−3 − 11 = −14
Answer: −14.
Worked example (no skipped steps)
2.20 Compute (−6)(4).
Negative times positive is negative:
(−6)(4) = −24
Answer: −24.