If you know the original amount and the new amount, you can find what percent the new amount is of the original by computing $\frac{\text{new}}{\text{original}}$ and then multiplying by 100.

When you compute $\frac{28}{32}$, try to simplify the fraction first to make the multiplication by 100 easier.

In the expression line, type (28/32)*100 and look at the numerical result that Desmos gives. That value is $q$, the percent that the morning charge is of the previous night’s charge.

The phone’s charge went from 32% at night to 28% in the morning. The question says the morning charge was $q\%$ of the charge the night before.

This means:

Here, $\frac{q}{100}$ is the decimal form of $q\%$, and multiplying it by 32 (the original charge) should give 28 (the new charge).

Instead of solving the equation step by step, you can think:

new amount = (some percent of) original amount.

So the percent (as a decimal) is:

Then convert this decimal to a percent by multiplying by 100:

Now simplify $\frac{28}{32}$ before multiplying.

First simplify the fraction $\frac{28}{32}$:

• Both 28 and 32 are divisible by 4.

So

Now find $\frac{7}{8}$ as a decimal:

• $\frac{1}{8} = 0.125$, so $\frac{7}{8} = 7 \times 0.125 = 0.875$.

Convert this to a percent:

So $q = 87.5$, meaning the morning charge was 87.5% of the charge the night before.