# What is the percent of decrease from 110 to 77?

Aug 28, 2017

The decrease is 30%.

#### Explanation:

Let's start by asking ourselves a similar, yet simpler, question: what is the percent decrease from $10.00 to$9.00? In other words, if a $10 item is sold for$9, what percent did the buyer save?

This seems a bit more intuitive. The answer is 10%. But how did we get that? Well, we figured out the difference between the two prices ($10 -$9, which is $1), and then compared this difference to the original price of $10, and found that $1 was 10% of $10.

This is the math we did in our head:

("original value "-" new value")/"original value"

We measured how big the difference between the two numbers is, when compared to the original number. This formula works all the time, to find percentage increases/decreases. Just plug and chug!

In this question, the original value is 110, and the new value is 77:

$\frac{110 - 77}{110} = \frac{33}{110}$

$\textcolor{w h i t e}{\frac{110 - 77}{110}} = 0.3$
color(white)((110-77)/110)=30%

(To turn a decimal number into a percentage, multiply the number by 100, then add the % sign.)

Aug 28, 2017

30%

#### Explanation:

Any percent increase or decrease can be determined by using the process:

color(red)("change"/"original" xx 100%)

The change is the amount of increase or decrease, simply subtract:
Bigger value - smaller value.

In this case: $\text{ } 110 - 77 = 33$

Multiplying by 100% is the same as multiplying by $\frac{100}{100}$, which is equal to $1$. This does not change the value of a number, simply what it looks like. The % sign is used in the answer.

(110-77)/110 xx 100%

=33/110 xx 100%

=30%