Work out the answers to:
a) $6 \times(-5)$
b) $(-5) \times 8$
c) $(-9) \times(-7)$
Answer (1)
Multiply 6 by -5: 6 × ( − 5 ) = − 30 .
Multiply -5 by 8: ( − 5 ) × 8 = − 40 .
Multiply -9 by -7: ( − 9 ) × ( − 7 ) = 63 .
The final answers are − 30 , − 40 , 63 .
Explanation
Understanding the Problem We need to calculate the results of three multiplication problems involving positive and negative numbers. Remember that multiplying a positive number by a negative number results in a negative number, and multiplying two negative numbers results in a positive number.
Calculating 6 x (-5) a) To calculate 6 × ( − 5 ) , we multiply the absolute values 6 and 5 , which gives us 30 . Since we are multiplying a positive number by a negative number, the result is negative. Therefore, 6 × ( − 5 ) = − 30 .
Calculating (-5) x 8 b) To calculate ( − 5 ) × 8 , we multiply the absolute values 5 and 8 , which gives us 40 . Since we are multiplying a negative number by a positive number, the result is negative. Therefore, ( − 5 ) × 8 = − 40 .
Calculating (-9) x (-7) c) To calculate ( − 9 ) × ( − 7 ) , we multiply the absolute values 9 and 7 , which gives us 63 . Since we are multiplying two negative numbers, the result is positive. Therefore, ( − 9 ) × ( − 7 ) = 63 .
Final Answer The answers to the three multiplication problems are: a) − 30 , b) − 40 , and c) 63 .
Examples
Understanding multiplication with negative numbers is crucial in many real-world scenarios. For example, if you have a debt of $5 (represented as -5) and you have this debt 6 times, your total debt is $6 \times (-5) = -$30. Similarly, if a stock price decreases by 5 e a c h d a y f or 8 d a ys , t h e t o t a l d ecre a se i s (-5) \times 8 = -$40. If you reduce spending by 9 e a c h d a y f or 7 d a ys , t h e t o t a l re d u c t i o nin s p e n d in g i s (-9) \times (-7) = $63, because reducing a negative is a positive.
