A laptop has 41.6 percent of its battery left. Express, in its simplest form, the fraction of the battery that has been used.
We need to take this percentage, 41.6, and convert it to a fraction. After that, we need to reduce that fraction to its simplest form. We know that a percentage is a number out of 100. We start with 41.6 out of 100, but we really need to get rid of this decimal.
I can move the decimal one place to the right by multiplying the numerator and the denominator by 10. 41.6 out of 100 is the same thing as 416 out of 1000. This is our fraction. Our fraction step is complete. Now we need to reduce this value to its simplest form.
We need to find out if there is a value we can multiply both the numerator and the denominator by. 416 and 1000 are both divisible by four. We divide 416 by four and it gives us 104. 1000 divided by four equals 250. However, I can already tell that this is not simplest form.
Both the numerator and the denominator are even numbers, and that means both the numerator and the denominator are divisible by two. 104 divided by two equals 52. 250 divided by two equals 125. The fraction of the battery that has been used is 52 out of 125. Knowing this information, we can also find the fraction of the battery that has not been used.
To find the portion in the battery that has not been used, we take the whole battery, one, and subtract the part that is been used, 52 over 125. Before we do this, we rewrite the whole number one as the fraction 125 over 125, and then we subtract the numerators. 125 minus 52 equals 73. The denominator doesn’t change.
The fraction of the not-used portion of the battery is 73 out of 125. In this question, we’re looking for the fraction that has been used. That means the answer is 52 out of 125.