109. Observe the following patterns and fill in the blanks to make the statements true:
(a)
−5 × 4 = −20
−5 × 3 = −15 = −20 − (−5)
−5 × 2 = ______ = −15 − (−5)
−5 × 1 = ______ = ______
−5 × 0 = 0 = ______
−5 × −1 = 5 = ______
−5 × −2 = ______ = ______
(b)
7 × 4 = 28
7 × 3 = ______ = 28 − 7
7 × 2 = ______ = ______ − 7
7 × 1 = 7 = ______ − 7
7 × 0 = ______ = ______ − ______
7 × −1 = −7 = ______ − ______
7 × −2 = ______ = ______ − ______
7 × −3 = ______ = ______ − ______
(a) −5 × 2 = −10 = −15 − (−5)
−5 × 1 = −5 = −10 − (−5)
−5 × 0 = 0 = −5 − (−5)
−5 × −1 = 5 = 0 − (−5)
−5 × −2 = 10 = 5 − (−5)
(b) 7 × 3 = 21 = 28 − 7
7 × 2 = 14 = 21 − 7
7 × 1 = 7 = 14 − 7
7 × 0 = 0 = 7 − 7
7 × −1 = −7 = 0 − 7
7 × −2 = −14 = −7 − 7
7 × −3 = −21 = −14 − 7
Successive products change by adding (or subtracting) the multiplicand. Extending this pattern across 0 and into negatives gives the filled values.