Finding the Number When Divided by 2 Gives 86 as the Answer

Often, we encounter mathematical problems that require us to use basic arithmetic operations such as division and multiplication to find an unknown number. In this article, we will solve a problem that asks us to find the number which, when divided by 2, gives 86 as the answer. This is a straightforward problem that can be easily solved using a linear equation.

Setting Up the Equation

To solve the problem, we need to set up an equation. Given that the unknown number x divided by 2 equals 86, we can write:

(frac{x}{2} 86)

Solving the Equation

The next step is to solve for x. To do this, we multiply both sides of the equation by 2 to isolate x:

(x 86 times 2)

Now, we calculate the value of x:

(x 172)

Therefore, the number we are looking for is 172. To verify this, we can check if dividing 172 by 2 indeed gives us 86:

(frac{172}{2} 86)

This confirms that our solution is correct.

Using Multiplication as the Opposite of Division

Multiplication can also be used to find the unknown number. Since division and multiplication are inverse operations, if we multiply 86 by 2, we should get the same result:

86 times 2 172)

Thus, multiplying 86 by 2 gives us 172, and dividing 172 by 2 indeed results in 86.

Generalizing the Solution

The method we used to solve this problem can be generalized for any similar problem. If you have an equation in the form of (frac{x}{n} m), the solution to find x is:

x m times n

For instance, if you need to find a number that, when divided by 3, gives 90 as the answer, you can set up the equation as:

(frac{x}{3} 90)

Multiplying both sides by 3:

x 90 times 3 270)

This method provides a straightforward approach to solving similar problems involving division and multiplication.

Conclusion

Solving problems like finding a number when divided by a certain value gives a particular result is a fundamental skill in mathematics. By using linear equations and understanding the inverse relationship between division and multiplication, you can easily find the solution to such problems. Whether you encounter this in a math class or in practical situations, the method explained here remains a reliable and efficient approach.

So, the number we are looking for, when divided by 2, gives 86 as the answer is 172.