DEV 085 Unit 3 Notes Decimals Percents Proportions

DEV 085 Unit 3 Notes

Decimals Percents

Proportions

Decimal Place Value:•Decimal points are read as the word “and”•Place values to the right of the decimal point represent part of a whole•Read the numbers in groups of three then read the place value name•Place values to the right of the decimal point end with “ths”•Place values to the right of the decimal point “mirror” place values to the left of the decimal point

Decimal Place Value:

___ , ___ ___ ___ ___ ___ ___

Th

ou

san

ds

Hu

nd

red

s Ten

sO

ne

s

Ten

ths

Hu

nd

red

ths

Th

ou

san

dth

s

Rounding Decimals:

• If the circled number is 0-4, the underlined number stays the same and all the digits to the right of the circled number fall off

• If the circled number is 5-9, the underlined number goes up one and all the digits to the right of the circled number fall off

Steps for Rounding:Step 1: Identify the place value you are

rounding to and underline itStep 2: Circle the number to the right

Step 3: Determine whether to “round up” or to “round down”

Rounding Practice Problems:

Nearest Tenth

Nearest Hundredt

h

4 . 5 7 6 4 . 5 7 6

1 3 . 8 0 4 1 3 . 8 0 4

1 7 9.8 5 6

1 7 9.8 5 6

4.6 4.58

13.8 13.80

179.9

179.86

Comparing Decimals:Steps for Comparing Decimals ValuesStep 1: List the numbers vertically

“Stack” the decimal pointsAdd zeros as place holders as

neededStep 2: Compare the whole number part then

compare the decimal parts moving to the right (as you would if you were alphabetizing words)Step 3: Put in the correct order (from least to

greatest or greatest to least)

Comparing Decimals Practice:

Practice Problems: Arrange each group of numbers in order from least to greatest.

0.342 0.304 0.324 0.340

2.37 2.7 2.3 2.73

0.304 0.324 0.340 0.342

2.3 2.37 2.7 2.73

Comparing Decimals Practice:

Practice Problems: Arrange each group of numbers in order from least to greatest.

5.23 5.023 5.203 5.032

1.010 1.101 1.011 1.110

5.023 5.032 5.203 5.23

1.010 1.011 1.101 1.110

Basic Operations with Decimals:

Addition and Subtraction

Step 1: Write the numbers vertically

“Stack” the decimal points

Add zeros as place holders

Step 2: Move the decimal point straight down into your answerStep 3: Add or subtract

Adding and Subtracting Decimals Practice:

Practice Problems: Find the sum or difference for each.

2.3 + 3.71 + 27 =

3.14 + 2.073 + 8.9 =

4.023 + 24.311 =

33.01

14.113

28.334



31.73 – 12.07 =

9 – 8.185 =

23.5 – 17.097 =

19.66

0.815

8.593



2.45 – 4.66 =

3 + 5.76 + 0.11 =

25 – 0.14 + 2.36 =

-2.21

8.87

27.22

Multiplying Decimals:Steps for MultiplicationStep 1: Write the problem vertically (just as you would a regular multiplication problem)Step 2: Ignore the decimal point(s) and

multiply as if you were multiplying whole numbersStep 3: Determine where the decimal point goes in the product

However many digits are to the right of the decimal point(s) in the problem… that’s how many digits are to be to the right of the decimal point in the product.

Multiplying Decimals Practice:

Practice Problems: Find the product of each.

2 x 3.14 =

8.097 x .05 =

1.042 • 2.3 =

6.28

0.40485

2.3966



4.7 x 1000 =

3 x 0.567 =

0.27 • 15 =

4,700

1.701

4.05



(2.5)(1.02) =

(1.003)(0.42) =

5.41 x 200 =

2.55

0.42126

1,082

Dividing with Decimals:

There are 2 types of division problems involving decimal points:

No decimal in the divisor

Decimal in the divisor

Division with Decimals:NO decimal point in the divisor…

Step 1: Write the problem in the traditional long division formatStep 2: Move the decimal point in the dividend straight up into the quotientStep 3: Divide as usual

Remember to divide out one more place than you are rounding to…

Division with Decimals:Yes…Decimal point in the divisor…Step 1: Write the problem in the traditional long division formatStep 2: Move the decimal point in the divisor to the far right of the divisorStep 3: Move the decimal point the SAME

number of places in the dividendStep 4: Move the decimal point in the dividend straight up into the quotientStep 5: Divide as usual

Remember to divide out one more place than you are rounding to…

Division Practice:Practice Problems: Find the quotient for each.

3.753 3 =

8.7 100 =

245.9 ÷ 1000 =

0.65 ÷ 5 =

1.251

0.087

0.2459

0.13


428.6 ÷ 2 =

2.436 ÷ 0.12 =

4.563 ÷ 0.003 =

21.35 ÷ 0.7 =

214.3

20.3

1,521

30.5


97.31 ÷ 5 =

0.8542 ÷ 0.2 =

67.337 ÷ 0.02 =

1500.4 ÷ 1000 =

19.462

4.271

3,369.5

1.5004

Problem Solving with Decimals:

Follow the correct Order of Operations only remember to apply the rules that go with decimals.

P.E.M.D.A.S.P – ParenthesisE – Exponents

M- MultiplicationD – Division

A – AdditionS – Subtraction

Do whichever one comes first

working from left to right

Order of Operations Practice:

Practice Problems: Solve each by following the correct order of operations.

2.3 x 4 2 + 4 =

3.5 7 + 2.15 x 0.13 =

2(7 – 2.49) + 0.3 =

14 0.2 + (3.1 – 2.56) x 2 =

8.6

0.7795

9.32

71.08

Order of Operations Practice:

Practice Problems: Solve each by following the correct order of operations.

5 + (7.8 – 5.5)2 – 14.3 =

(40 ÷ 0.5 • 7) + 5 – 14 =

-8 • 0.75 + 15.23 – 4 =

-4.01

551

5.23

Percents:Understanding Percent:•A percent is one way to represent a part of a whole. •“Percent” means per 100 •Sometimes a percent can have a decimal.•A percent can be more than 100.•A percent can be less than 1.•When you write a fraction as a percent: Change the fraction to a decimal value then change it to a percent.

Percents, Decimals, and Fractions:

To change between formats…

Fractions Decimals Percents

Divide the numerator by the

denominator

Move the decimal

point to the right 2

places and add a %

sign

Percents, Decimals, and Fractions:

To go the other direction…

Fractions Decimals Percents

Put the # (to the right of the

decimal) on top. The # on the bottom will

represent the appropriate place value. Reduce to

lowest terms

Move the decimal

point to the left 2

places and add drop

the % sign

Practice Problems:Fractions Decimals Percents

45

16

.52

3.25

32%

6%

.8 80%

.166 16.6%

52%

325%

.32

.06

1325

14

825

350

3

Proportions:

A proportion shows that two ratios are equal.

2 = 43 6

5 = 17.57 24.5

3 = 272 18

Ratio Equivalency:To check the equivalency of two ratios, you CROSS MULTIPLY. (If your products are equal, your ratios are equal).

3 = 12 5 20 (3)(20) = (12)(5) 60 = 60

EQUAL

Ratio Equivalency:To check the equivalency of two ratios, you CROSS MULTIPLY. (If your products are equal, your ratios are equal).

2.4 = 13 3 15(2.4)(15) = (13)(3) 36 = 39

NOT EQUAL

Proportion Practice:Check to see if the proportions are equal or not.

3 = 9 2 = 5 1 = 2

7 21 5 14 6 8

12

Equal Not Equal Equal

Proportion Practice:Check to see if the proportions are equal or not.

3 = 4 2.5 = 6.5 5¾

= 11½

8 9 5 13 9 20Not Equal Equal Not

Equal

Solving Proportions:

When you know three of the four parts of a proportion, you can

CROSS MULTIPLY then DIVIDE to find the missing value.

Solving Proportions:

Show what you are

multiplying in your first

line…in your second line show your products

4 = x5 20

(4)(20) = (x)(5)

80 = 5x

80 = 5x 5 5

16 = x

9 = 3x 8

(9)(8) = (3)(x)

72 = 3x

72 = 3x 3 3

24 = x

Cross Multiply

Divide (divide by

the number with the variable)

Solving Proportions Practice:

Solve for the missing value.

3 = X 2 = 5 X = 26 12 7 X 24 3

6 = X X = 17.5 X = 16

Solving Proportions Practice:

Solve for the missing value.

2.5 = X 10 = 5 4 = X5 18 11 X 10 33

9 = X X = 5.5 X = 13.2

Solving Proportions Practice Problems:

Practice: Solve each.

One person can move 120 barrels in one hour. How many barrels can that person move in 2.5 hours?

One person could move 300 barrels in 2.5

hours



A baseball player hits 55 times in 165 at bats. At this rate, how many at bats will he need to have to reach 70 hits?

The player would need 210 at bats to reach

70 hits



In her garden, Maggie plans to plant 8 blue petunias for every 12 red geraniums. If she buys a total of 70 plants, how many plants are petunias?

28 plants are petunias



The sun is shining on two buildings (short and tall) creating 30 ft and 45 ft shadows. The tall building is 60 ft tall. What is the height of the shorter building?

The shorter building was 40

feet tall

Solving Percent Problems:

A proportion setup can be used to solve percent problems. Set the problem up as a proportion and solve for the missing information.

When solving percent problems, think of the proportion set-up as:

Partial %

= “is”

100 % “of”

Solving Percent Problems using a Proportion Setup:

Step 1: Put your numbers in the correct places

Step 2: Solve the proportion by cross- multiplying then dividing

Solving Percent Problems Practice:

23 is 20% of what? Find 80% of 40

24 is what % of 72? 40 is 50% of what?

Find 6½ % of 24 5 is 5.5% of what?

115 32

33.3% 80

1.56 90.90

Solving Percent Problems Practice:

Find 8% of 150 108 is 72% of what?

3.75 is what % of 50

12 150

7.5%

Applications Using Percents:

TAXTax = (Purchase Price) x (Percent of Tax)

OR

% = Amount of Tax 100 Purchase Price

TOTAL COST = Purchase Price + Tax

Tax Application Example:

You buy a television set for $289. The local tax rate is 7.5%. Find 1) the amount of tax and 2) the total cost of your purchase.

$289x 0.075

1445 +20230

21.675

$21.675 becomes $21.68…must round because it is money

(Tax)

$289.00+ 21.68$310.68

(orig amt)(tax)(total cost)


DISCOUNTDiscount = (Original Cost) (Percent of Discount)

OR

% = Amount of Discount 100 Original Cost

Original Cost - Amount of Discount DISCOUNTED PRICE

Discount Application Example:

You buy a microwave oven for $135. You can save 25% if you shop at today’s sale. Find 1) the amount of discount and 2) the discounted price of your purchase.

$135x 0.20

$27.00(discount)

$135.00- 27.00

$108.00

(orig amt)(discount)(discounted price)


MARK-UPSMark-ups = (Original Cost) (Percent of Mark-up)

OR

% = Amount of Mark-up 100 Original Cost

Original Cost + Amount of Mark-up MARK-UP

Mark-Up Application Example:

I buy t-shirts for $3.00. I turn around and mark them up 75% and sell them. Find 1) the amount of mark-up and 2) the mark-up price.

$3.00x 0.751500

+ 21000$2.2500(mark-up)

$3.00+ 2.25$5.25

(orig amt)(mark-up)(mark-up price)


COMMISSIONCommission = (Total Sales) (Percent of Commission)

OR

% = Commission 100 Total Sales

Salary + Commission

TOTAL PAY

Commission Example:Tony has a base salary of $22,000 a year. He makes 5% commission on all of his sales. Over the course of a year, he has a total sales amount of $135,000. Find 1) the amount of his commission and 2) his total pay for the year. $135,000

x 0.05$6,750(commission)

$135,000+ 6,750

$141,750

(base salary)

(commission)(total pay)


In order to find Percent of Increase or Percent of Decrease you must first find the Amount of Increase or Amount of Decrease.

To find the amount of increase or the amount of decrease, find the difference between the original amount and the second amount.


PERCENT OF INCREASE

Percent of Increase = Amount of Increase Original Amount

OR

% = Amount of Increase 100 Original Amount

Percent of Increase Example:

I buy a box of pencils for $4.00 and sell it for $5.00. what is my percent of increase?

$5.00 - $4.00 $4.00

Find the difference between the two amounts… divide by the

original amount

$1.00$4.00

= .25 = 25% increase

Convert to a percent


PERCENT OF DECREASE

Percent of Decrease = Amount of Decrease Original Amount

OR

% = Amount of Decrease 100 Original Amount

Percent of Decrease Example:

I buy a box of books for $10.00 and sell it for $8.00. What is my percent of decrease?

$10.00 - $8.00 $10.00

Find the difference between the two amounts… divide by the

original amount

$2.00$10.00

= .20 = 20% decrease

Convert to a percent


SIMPLE INTEREST

I = P R T

I = InterestP = PrincipalR = Percentage

RateT = Time (in

years)

Total Amount = Principal + Interest

Simple Interest Application Example:

I had to borrow $15,000 to buy a new car. My interest rate was 5%. My loan was for 5 years. Find 1) how much interest will I pay for borrowing $15,000 and 2) the total amount of my loan.

I = P R T

I = ($15,000) (0.05) (5)

I = $3,750 $15,000+ 3,750$18,500

- Principal- Interest- Total amt of loan


MONTHLY PAYMENT OF A LOAN

principal + interestMonthly payment = Total # of payments

Monthly Payment of a Loan Example:

If my total loan for the purchase of a new car is $18,750 and I’m going to pay it over the course of 5 years, what is my monthly payment?

$18,75060 mo

Monthlypayment

(Loan amount)(Number of payments)

= $312.50/mo

Review the things that you need to review.

Study the things that you need to spend more time on.

Ask questions about things you don’t understand.

PRACTICE…PRACTICE…PRACTICE

Documents

DEV 085 Unit 3 Notes Decimals Percents Proportions