To find the number that, when multiplied by 6, results in 42, we can use basic arithmetic operations and algebraic equations. Let’s denote the unknown number as “x”.
We can set up an equation to represent the problem:
6x = 42
To solve for “x”, we need to isolate it on one side of the equation.
One way to do this is by dividing both sides of the equation by 6, since division is the inverse operation of multiplication.
6x / 6 = 42 / 6
This simplifies to:
x = 7
So, the number that, when multiplied by 6, gives us 42 is 7.
Now let’s explain the solution in detail.
Multiplication is the mathematical operation of repeated addition. In this case, we are multiplying a number “x” by 6, which means we are adding “x” to itself six times.
The equation 6x = 42 can be interpreted as “6 times some unknown number ‘x’ is equal to 42”. Our goal is to find the value of “x” that satisfies this equation.
To solve for “x”, we need to isolate it on one side of the equation. We can do this by using the inverse operation of multiplication, which is division. By dividing both sides of the equation by 6, we are essentially undoing the multiplication by 6, and “x” will be left alone on the left-hand side of the equation.
Dividing both sides of the equation by 6, we get:
6x / 6 = 42 / 6
The left-hand side simplifies to just “x”, since 6 divided by 6 is 1. The right-hand side simplifies to 7, since 42 divided by 6 is 7.
So we have:
x = 7
This tells us that the unknown number “x” is equal to 7.
We can check our solution by substituting “x” with 7 in the original equation:
6(7) = 42
6 times 7 is indeed equal to 42, so our solution is correct.
In conclusion, the number that, when multiplied by 6, gives us 42 is 7. We arrived at this solution by setting up an equation, dividing both sides by 6 to isolate “x”, and simplifying the expression to find the value of “x”. It’s important to remember that equations are a way to represent mathematical relationships, and solving them involves using inverse operations to isolate the unknown variable on one side of the equation.
