Math 6 High ( Period 3)

Solving Percent Problems 7.4

You can use a proportion to find what percent one number is of another number.
The statement:

“ a is p percent of b” is expressed by the proportion shown below where

a is the  part of the base      b is the base… and    p is the percent

a/b = p/100

Part of the base / base = percent/100

What percent of 40 is 15?

First think which is the base? 40

Which number is the part?  15

Now write the proportion

a/b = p/100

15/40 =  p/100

Use cross products to multiply… simplify first if you can…

15(100) = 40p

Divide both sides by 40

15(100)/40 = 40p/40

37.5 = p

Note: there are a number of ways to simplify first! You should still arrive at p = 37.5 which means 37.5%

Finding a Percent

Your team won 19 of its 25 softball games. What percent did it win?

Games won/games played = percent/100

It really is still      a/b = p/100

19/25 = p/100

19(100) = 25p

Divide both sides by 25

19(100)/25 = 25p/25

76= p

Again there are a variety of ways to simply BEFORE you multiply! You could even utilize the equivalent fraction method to determine the p percent.

Therefore your team won 76% of its games!

You can use the proportion to find a base or a part of the base.

Finding a part of the base

You buy a pair of pants on sale. The price is 80% of the regular price of $24.50, WOW! That’s a bargain! What is this incredible sales price?

Sale price / regular price = Percent/100

a/24.50 = 80/100

Multiply and divide carefully

100a = 24.50(80)

divide both sides by 100

100a/100 = (24.50)(80)/100

a = 19.6

The sale price is $19.60

Now, you could use the writing an equation method

80% of 24.50 = sale price  or

(.80) (24.50) = p

Multiply carefully

19.60 = p

$19.60 is the sale price.

Finding a Base

8 is 32% of what number?

Method 1: Write and solve a proportion

a/b = p/100

8/b = 32/100
Using cross products
(8)(100) = 32b
Divide both sides by 32

(8)(100)/32 = 32b/32

25 = b

Method 2: Write and solve an equation

8 is 32% of what number?
8 = .32(x)

8/.32 = .32x/.32
Divide carefully

25= b

8 is 32% of 25

Solving Percent Problems

a/b = p/100   means a is p percent of b

Out of 80 students taking Algebra, 95% passed the final exam. About 80% of those who passed the exam got a grade better than a C. How many students got an A or a B?

First find out how many passed the final exam

Using the proportion method for this:

a/80 = 95/100

100a = 80(95)

100a/100 = (80)(95)/100

a = 76

76 students passed the final exam

About 80% of 76 got a grade better than a C

Using the writing an equation method

(.80)(76)  =60.8

Since you can’t have a part of a student your answer would be about 61 students got an A or a B in Algebra

Math 6High ( Period 3)

Large & Small  Percent 7.3

The methods you learned from Lesson 7.2 can be used to find large and small percents.

Rewrite Numbers

Rewrite 1.4 as a percent
1.4 = 1  4/10 = 14/10 = 140/100 = 140%

Rewrite   ½%  as a decimal
½ %= 0.5% = 0.5/100 = 5/1000 = 0.005

Finding a Large Percent of a Number

You can use either of two methods to find 130% of 250

Method 1: Set up a proportion      percent/100 = is/of

130/100 = x/250

Cross multiply carefully

(130)(250) = 100x  Then divide by 100 on both sides

(130)(250)/100 = 100x/100

325 = x

There were a number of different ways to simplify BEFORE you multiply but do them carefully . You still need to get x = 325

Method 2: Rewrite 130% as a decimal and set up a written equation

Find 130% of 250.   Think “ Find”  means “What is…” so you have

What is 130% of 250
x = (1.3 )(250)
x = 325

Find a Small Percent of a Number

You can use the same two methods to find 0.5% of 40

Method 1: Set up a proportion.

.5/100 = x/40  or

5/1000 = x/40

Cross multiply and divide carefully
(5)(40)/1000 = 1000x/1000

0.2 = x

There were a number of different ways to simplify BEFORE you multiply but do them carefully . You still need to get x = 0.2

Method 2: Rewrite 0.5% as a decimal and use the writing an equation method

Find 0.5% of 40   Think “ Find”  means “What is…” so you have
What is 0.5% of 40.
x = (0.005)(40)
x = 0.2

Estimating:

In many real-life situations—such as figuring the amount for a tip, it is helpful to use mental math to estimate the percent of a number.

Use mental math to estimate 123% of 84. You know it will be MORE than 84… because the percent is over 100% and we know 123%  is about 125%   100% + 25% so all we need to figure is 25% o 84… and that is just ¼ so 21.. 84 + 21 = 105. So 123% is just a little under 105.  

Use mental math to find ½ % of 140

Wait… ½ % is just half of 1% so  figure 1% of 140. Just move the decimal over two places…1.4 would be 1% so half of that is 0.7

estimate 15% tip for a restaurant bill of $43.76

First round the restaurant bill up to $45.00. Then take 10% … that’s 4.50

5% is half of ten percent so half of 4.50  is 2.25

4.50 + 2.25 = 6.75  $6.75 is about 15% of43.76