**Finding percent decrease :**

Percents can be used to describe how an amount changes. The formula given below can be used to find how an amount changes in terms of percentage.

The change may be an increase or a decrease. Percent decrease describes how much a quantity decreases in comparison to the original amount.

**Example 1 : **

What is the percent decrease from $80 to $64 ?

**Solution :**

**Step 1 :**

Find the amount of change.

Amount of change = Greater value - Lesser value

= 80 - 64

= 16

**Step 2 : **

Percentage change is

= (Amount of change / Original amount) x 100 %

= (16 / 80) x 100%

= 0.2 x 100 %

= 20 %

Hence, the percent decrease from $80 to $64 is 20%.

**Example 2 : **

David moved from a house that is 89 miles away from his workplace to a house that is 51 miles away from his workplace. What is the percent decrease in the distance from his home to his workplace ?

**Solution :**

**Step 1 :**

Find the amount of change.

Amount of change = Greater value - Lesser value

= 89 - 51

= 38

**Step 2 : **

Find the percent decrease. Round to the nearest percent.

Percentage change is

= (Amount of change / Original amount) x 100 %

= (38 / 89) x 100%

= 0.427 x 100 %

= 42.7 %

**≃ **43 %

Hence, the percent decrease in the distance from his home to his workplace is 43%.

**Example 3 : **

The number of students in a chess club decreased from 18 to 12. Whatis the percent decrease ? Round to the nearest percent.

**Solution :**

**Step 1 :**

Find the amount of change.

Amount of change = Greater value - Lesser value

= 18 - 12

= 6

**Step 2 : **

Find the percent decrease. Round to the nearest percent.

Percentage change is

= (Amount of change / Original amount) x 100 %

= (6 / 18) x 100%

= 0.3333 x 100 %

= 33.33%

**≃ **33 %

Hence, the strength is decreased by 33%.

**Example 4 : **

Officer Brimberry wrote 16 tickets for traffic violations last week, but only 10 tickets this week. What is the percent decrease ?

**Solution :**

**Step 1 :**

Find the amount of change.

Amount of change = Greater value - Lesser value

= 16 - 10

= 6

**Step 2 : **

Find the percent decrease. Round to the nearest percent.

Percentage change is

= (Amount of change / Original amount) x 100 %

= (6 / 16) x 100%

= 0.375 x 100 %

= 37.5 %

**≃ **38 %

Hence, the percentage decrease is 38%.

**Example 5 : **

Over the summer, Jackie played video games 3 hours per day. When school began in the fall, she was only allowed to play video games for half an hour per day. What is the percent decrease? Round to the nearest percent

**Solution :**

**Step 1 :**

Find the amount of change.

Amount of change = Greater value - Lesser value

= 3 - 0.5

= 2.5

**Step 2 : **

Find the percent decrease. Round to the nearest percent.

Percentage change is

= (Amount of change / Original amount) x 100 %

= (2.5 / 3) x 100 %

= 0.8333 x 100%

= 83.33 %

**≃ **83 %

Hence, the percentage decrease is 83%.

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