Q. Which expression is equivalent to −3.7−54.7 ?54.7−(−3.7)−54.7+3.73.7+(−54.7)−3.7+(−54.7)
Understand the problem: Understand the problem.We need to find the expression that is equivalent to the subtraction of −3.7 from −54.7.
Analyze given expressions: Analyze the given expressions to see which one is equivalent to −3.7−54.7. We will compare each expression with −3.7−54.7 to find the equivalent one.
Evaluate first expression: Evaluate the first expression 54.7−(−3.7). Subtracting a negative is the same as adding a positive, so this is equivalent to 54.7+3.7.
Calculate 54.7+3.7: Calculate 54.7+3.7.54.7+3.7=58.4 This is not equivalent to −3.7−54.7 because the signs are different and the result is positive.
Evaluate second expression: Evaluate the second expression −54.7+3.7. This is subtracting a smaller positive number from a larger negative number.
Calculate −54.7+3.7: Calculate −54.7+3.7.−54.7+3.7=−51.0This is not equivalent to −3.7−54.7 because the order of subtraction matters, and this result is not the same as subtracting −3.7 from −54.7.
Evaluate third expression: Evaluate the third expression 3.7+(−54.7). This is adding a negative number to a positive number, which is the same as subtracting the positive value of the negative number from the positive number.
Calculate 3.7+(−54.7): Calculate 3.7+(−54.7).3.7+(−54.7)=3.7−54.7=−51.0This is not equivalent to −3.7−54.7 because the result is not the same as subtracting −3.7 from −54.7.
Evaluate fourth expression: Evaluate the fourth expression −3.7+(−54.7). This is adding two negative numbers together.
Calculate −3.7+(−54.7): Calculate −3.7+(−54.7).−3.7+(−54.7)=−(3.7+54.7)=−58.4This is equivalent to −3.7−54.7 because adding two negative numbers is the same as subtracting the second number from the first when both are negative.