If the cost of a cell phone has decreased 400% during the past 10 years, does that correspond to a cost decrease of four times? Explain your answer as though you were talking to someone who has never taken algebra.
To understand whether a 400% decrease corresponds to a cost decrease of four times, we need to break down what a 400% decrease means.
When we say "400% decrease," we are referring to a decrease of 400% of the original value. In mathematical terms, a 400% decrease is equivalent to subtracting 400% of the original value from the original value.
To calculate a 400% decrease, we first need to determine what 400% of the original value is. In other words, we multiply the original value by 400%. Mathematically, this can be represented as:
400% × original value
To multiply a value by a percentage, we convert the percentage to a decimal by dividing it by 100. So, 400% becomes 4 as a decimal (400 ÷ 100 = 4). Therefore, the calculation becomes:
4 × original value
Now that we have determined what 400% of the original value is, we need to subtract this amount from the original value to understand the effect of the decrease. Mathematically, this can be represented as:
original value - (4 × original value)
Simplifying this expression, we distribute the 4 to each term inside the parentheses:
original value - 4 × original value
Now, let's use a simple example to illustrate this. Suppose the original cost of a cell phone was $100. To calculate the decrease, we substitute the original value with $100:
$100 - 4 × $100 = $100 - $400 = -$300
As you can see, the result of a 400% decrease is -$300, which means the cost went below zero. This suggests that a 400% decrease does not correspond to a cost decrease of four times.
In conclusion, a 400% decrease results in a negative value and does not correspond to a cost decrease of four times. It is important to recognize that a 400% decrease is a dramatic reduction that cannot be simply interpreted as a fourfold decrease in cost.