P divided by 5 equals 3
The Correct Answer and Explanation is:
To solve the equation ( P \div 5 = 3 ), we need to isolate the variable ( P ). To do this, we can multiply both sides of the equation by 5. This will allow us to eliminate the division by 5.
Step-by-Step Solution
- Start with the original equation:
[
P \div 5 = 3
] - Multiply both sides by 5:
[
P \div 5 \times 5 = 3 \times 5
] Here, when we multiply ( P \div 5 ) by 5, the 5s cancel out. This simplifies the left side to ( P ): [
P = 15
]
Explanation of the Steps
- Understanding Division: The operation ( P \div 5 ) can be thought of as asking, “What number, when divided by 5, gives 3?” In simpler terms, we want to find a number ( P ) such that if we take that number and split it into 5 equal parts, each part equals 3.
- Inverses: To solve for ( P ), we use the inverse operation of division, which is multiplication. By multiplying both sides by 5, we effectively reverse the division operation. This is a crucial property in algebra, where whatever operation is performed on one side of an equation must also be performed on the other side to maintain equality.
- Final Result: After performing the multiplication, we find that ( P ) equals 15. This means that if you take the number 15 and divide it by 5, the result will indeed be 3, confirming that our solution is correct.
Conclusion
The solution to the equation ( P \div 5 = 3 ) is ( P = 15 ). This example illustrates the importance of understanding inverse operations in algebra, as well as the fundamental principles of maintaining equality when solving equations. It also emphasizes the role of multiplication as a method to isolate variables and solve for unknowns.