Post on 01-Jan-2016
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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
Adding and Subtracting Decimals Practice:
Practice Problems: Find the sum or difference for each.
31.73 – 12.07 =
9 – 8.185 =
23.5 – 17.097 =
19.66
0.815
8.593
Adding and Subtracting Decimals Practice:
Practice Problems: Find the sum or difference for each.
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
Multiplying Decimals Practice:
Practice Problems: Find the product of each.
4.7 x 1000 =
3 x 0.567 =
0.27 • 15 =
4,700
1.701
4.05
Multiplying Decimals Practice:
Practice Problems: Find the product of each.
(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
Division Practice:Practice Problems: Find the quotient for each.
428.6 ÷ 2 =
2.436 ÷ 0.12 =
4.563 ÷ 0.003 =
21.35 ÷ 0.7 =
214.3
20.3
1,521
30.5
Division Practice:Practice Problems: Find the quotient for each.
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
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
Solving Proportions Practice Problems:
Practice: Solve each.
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
Solving Proportions Practice Problems:
Practice: Solve each.
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
Solving Proportions Practice Problems:
Practice: Solve each.
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)
Applications Using Percents:
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)
Applications Using Percents:
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)
Applications Using Percents:
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)
Applications Using Percents:
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.
Applications Using Percents:
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
Applications Using Percents:
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
Applications Using Percents:
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
Applications Using Percents:
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