Which inverse operation would be used to verify the following equation?
[tex]$102 \div 3=34$[/tex]
A) [tex]$34 \times 3=102$[/tex]
B) [tex]$3+34=37$[/tex]
C) [tex]$34-3=31$[/tex]
D) [tex]$102 \div 34=3$[/tex]
Answer (1)
The inverse operation of division is multiplication.
Check the options to see which one uses multiplication to verify the equation.
Option A, 34 × 3 = 102 , correctly uses multiplication to verify the equation.
Therefore, the answer is A
Explanation
Understanding Inverse Operations To verify the equation 102 ÷ 3 = 34 , we need to use the inverse operation of division, which is multiplication. We need to check which of the given options correctly uses multiplication to verify the equation.
Checking Option A Option A states 34 × 3 = 102 . This is the correct inverse operation because when we multiply the quotient (34) by the divisor (3), we get the dividend (102).
Checking Option B Option B states 3 + 34 = 37 . This uses addition, which is not the inverse operation of division.
Checking Option C Option C states 34 − 3 = 31 . This uses subtraction, which is not the inverse operation of division.
Checking Option D Option D states 102 ÷ 34 = 3 . This uses division, which can be used as an inverse operation by swapping the quotient and divisor. In this case, it is also a valid way to verify the original equation.
Determining the Best Answer Both options A and D are valid inverse operations. However, since the question asks for the inverse operation, and option A directly uses multiplication (the inverse of division), it is the more straightforward and conventional way to verify the equation.
Final Answer Therefore, the inverse operation that would be used to verify the equation 102 ÷ 3 = 34 is 34 × 3 = 102 .
Examples
In real life, inverse operations are used to check calculations. For example, if you divide a total bill of $102 among 3 people and each person owes $34, you can multiply $34 by 3 to verify that the total bill was indeed $102. This ensures accuracy in everyday calculations and helps to avoid errors.
