Find The Value Of Y In This Equation 16y 164
Finding the value ofy in this equation 16y 164 is a fundamental algebraic task that involves isolating the variable through inverse operations. This article will walk you through each step of the process, ensuring clarity and understanding for readers of all levels.
Introduction to Solving Linear Equations
At its core, solving an equation like 16y = 164 requires understanding the relationship between variables and constants. In this case, y is the unknown value we need to determine, while 16 and 164 are known numerical coefficients. The goal is to manipulate the equation to isolate y on one side, allowing us to calculate its exact value. This process is rooted in the principles of equality, where any operation performed on one side of the equation must be mirrored on the other to maintain balance. By applying these rules systematically, even seemingly complex equations can be resolved with precision.
Step-by-Step Guide to Solving 16y = 164
Step 1: Understand the Equation
The equation 16y = 164 states that 16 multiplied by an unknown number y equals 164. To find y, we need to reverse the multiplication operation. This is where the concept of inverse operations comes into play. Since multiplication is being used to combine 16 and y, division—its inverse—will be used to isolate y.
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Step 2: Apply the Inverse Operation
To isolate y, divide both sides of the equation by 16. This ensures the equation remains balanced while simplifying the left side to just y. The operation looks like this:
$
\frac{16y}{16} = \frac{164}{16}
$
On the left side, 16 cancels out, leaving y. On the right side, we perform the division:
$
y = \frac{164}{16}
$
Step 3: Perform the Division
Calculating 164 ÷ 16 requires basic arithmetic. Breaking it down:
- 16 × 10 = 160
- 164 − 160 = 4
This leaves a remainder of 4, which can be expressed as a fraction:
$ \frac{4}{16} = \frac{1}{4} = 0.25 $
Adding this to the 10 gives:
$ y = 10 + 0.25 = 10.25 $
Alternatively, *164
