Question

which of the following statements is true regarding multiplying or dividing signed numbers? (check all that apply.)

• multiply or divide as normal first. then, if the signs of the two original numbers are the same, the result is positive.
• multiply or divide as normal first. then, if the signs of the two original numbers are the opposite, the result is the same as the sign of the larger number.
• multiply or divide as normal first. then, if the signs of the two original numbers are the same, the result is the same as the sign of the larger number.
• multiply or divide as normal first. then, if the signs of the two original numbers are the opposite, the result is negative.

Explanation:

• For the first statement: When multiplying or dividing two signed numbers with the same sign (both positive or both negative), the result is positive. For example, \(2\times3 = 6\) (both positive) and \((-2)\times(-3)=6\) (both negative). So this statement is true.
• For the second statement: When the signs are opposite, the result should be negative, not related to the sign of the larger number. For example, \(2\times(-3)= - 6\) (positive times negative gives negative), regardless of the size of the numbers. So this statement is false.
• For the third statement: When signs are the same, the result is positive, not related to the sign of the larger number (since both have the same sign). For example, \((-5)\times(-2) = 10\) (both negative, result positive) and \(4\times5=20\) (both positive, result positive). So this statement is false.
• For the fourth statement: When multiplying or dividing two signed numbers with opposite signs (one positive and one negative), the result is negative. For example, \(2\times(-3)=-6\) and \((-2)\times3 = - 6\). So this statement is true.

Answer:

• Multiply or divide as normal first. Then, if the signs of the two original numbers are the SAME, the result is positive.
• Multiply or divide as normal first. Then, if the signs of the two original numbers are the OPPOSITE, the result is negative.