Q. Which expression is equivalent to −47.7−64.5 ?−64.5+47.747.7+(−64.5)−47.7+(−64.5)64.5−(−47.7)
Identify Given Expression: Identify the given expression and the list of possible equivalent expressions.The given expression is −47.7−64.5. We need to find which of the following is equivalent:−64.5+47.747.7+(−64.5)−47.7+(−64.5)64.5−(−47.7)
Analyze First Option: Analyze the first option: −64.5+47.7. This expression changes the order of the numbers in the original expression but keeps their signs the same. According to the commutative property of addition, changing the order of the numbers does not change the sum. Therefore, this expression is equivalent to the original expression. −64.5+47.7=−47.7−64.5
Analyze Second Option: Analyze the second option: 47.7+(−64.5).This expression also changes the order of the numbers and represents the second number as an addition of a negative, which is the same as subtraction. This expression is equivalent to the original expression.47.7+(−64.5)=−47.7−64.5
Analyze Third Option: Analyze the third option: −47.7+(−64.5).This expression keeps the first number the same and represents the second number as an addition of a negative, which is the same as subtraction. This expression is equivalent to the original expression.−47.7+(−64.5)=−47.7−64.5
Analyze Fourth Option: Analyze the fourth option: 64.5−(−47.7). This expression changes the subtraction to addition by subtracting a negative number, which is not equivalent to the original expression of subtracting two negative numbers. 64.5−(−47.7)=−47.7−64.5