What is the percent of decrease from 110 to 77?

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:

#(110-77)/110=33/110#

#color(white)((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.)

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: #" "110-77 = 33#

Multiplying by #100%# is the same as multiplying by #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%#