Question

practice multiplying negative integers.
1 find each product. then describe any patterns you notice.
$3 \cdot (-7) = \underline{\quad\quad}$
$2 \cdot (-7) = \underline{\quad\quad}$
$1 \cdot (-7) = \underline{\quad\quad}$
$0 \cdot (-7) = \underline{\quad\quad}$
$(-1) \cdot (-7) = \underline{\quad\quad}$
$(-2) \cdot (-7) = \underline{\quad\quad}$
$(-3) \cdot (-7) = \underline{\quad\quad}$

Explanation:

Step1: Multiply 3 and -7

When multiplying a positive number and a negative number, the product is negative. So \(3 \cdot (-7) = -21\).

Step2: Multiply 2 and -7

Using the same rule as above, \(2 \cdot (-7) = -14\).

Step3: Multiply 1 and -7

\(1 \cdot (-7) = -7\) (positive times negative is negative).

Step4: Multiply 0 and -7

Any number multiplied by 0 is 0, so \(0 \cdot (-7) = 0\).

Step5: Multiply -1 and -7

When multiplying two negative numbers, the product is positive. So \((-1) \cdot (-7) = 7\).

Step6: Multiply -2 and -7

Using the rule for multiplying two negatives, \((-2) \cdot (-7) = 14\).

Step7: Multiply -3 and -7

\((-3) \cdot (-7) = 21\) (two negatives multiply to a positive).

Answer:

\(3 \cdot (-7) = -21\)
\(2 \cdot (-7) = -14\)
\(1 \cdot (-7) = -7\)
\(0 \cdot (-7) = 0\)
\((-1) \cdot (-7) = 7\)
\((-2) \cdot (-7) = 14\)
\((-3) \cdot (-7) = 21\)

Pattern: When multiplying by -7, as the first factor decreases by 1 (starting from 3, then 2, 1, 0, -1, -2, -3), the product increases by 7. Also, positive times negative is negative, negative times negative is positive, and any number times 0 is 0.