Chapter 1 Lesson 1
Properties of Operations
NOTES
Date __________________________
PROPERTIES OF ADDITION
Commutative Property of Addition – Changing the order of addends does not change the sum.
Example: 9 + 5 = 5 + 9
Practice:
a.) 4 + 2 = 2 + _________
b.) 1 + 6 = _______ + ________
Associative Property of Addition – Changing the groping of addends does not change the sum.
Example:
Practice:
(9 + 5) + 4 = 9 + (5 + 4)
a.) (2 + 6) + 3 = 2 + (____________ + _____________)
b.) (1 + 8) + 5 = 1 + (__________ + _______________)
Identity Property of Addition – The sum of 0 and any number is that number.
Example:
Practice:
9+0=9
a.) 12 + 0 = __________
b.) 6 + __________ = 6
Circle the correct property shown.
1.) (3 + 4) + 9 = 3 + (4 + 9)
a.) Commutative Property of Addition
b.) Associative Property of Addition
c.) Identity Property of Addition
2.) 6 + 8 = 8 + 6
a.) Commutative Property of Addition
b.) Associative Property of Addition
c.) Identity Property of Addition
1
PROPERTIES OF MULTIPLICATION
Commutative Property of Multiplication – Changing the order of factors does not change
the product.
Example: 4 × 2 = 2 × 4
Practice:
a.) 6 × 4 = 4 × ____________
b.) 12 × 2 = _________ × ___________
Associative Property of Multiplication – Changing the grouping of factors does not change
the product.
Example: (4 × 6) × 2 = 4 × (6 × 2)
Practice:
a.) (3 × 5) × 4 = 3 × (__________ × __________)
b.) (5 × 2) × 6 = 5 × (___________ × __________)
Identity Property of Multiplication – The product of 1 and any number is that number.
Example: 4 × 1 = 4
Practice:
a.) 6 × 1 = ______________
b.) ___________ × 1 = 2
Part II: Find each sum or product.
1.) 63 + 12 + 14
2.) 4 × 2 × 5
2
3.) 18 + 6 + 22
Chapter 1 Lesson 1
REVIEW
Date __________________________
PART I: Name each property of addition or multiplication used below.
1.) (6 + 3) + 21 = 6 + (3 + 21)
2.) 13 × 1 = 13
a.) Commutative Property of Addition
b.) Associative Property of Addition
c.) Identity Property of Addition
a.) Commutative Property of Multiplication
b.) Associative Property of Multiplication
c.) Identity Property of Multiplication
3.) 8 + 20 + 12 = 8 + 12 + 20
4.) 5 × 2 × 11 = 2 × 11 × 5
a.) Commutative Property of Addition
b.) Associative Property of Addition
c.) Identity Property of Addition
a.) Commutative Property of Multiplication
b.) Associative Property of Multiplication
c.) Identity Property of Multiplication
Part II: Find each sum or product.
5.) 53 + 12 + 7
6.) 2 × 5 × 3
7.) 8 + 0 + 6
8.) (19 + 22) + 8
3
9.) 5 × (13 × 1)
10.) 25 + (13 + 5)
11.) 6 × 1 × 20
12.) 7 + 14 + (23 + 6)
13.) Rachel’s garden produced 25 carrots, 127 blackberries, and 5 pumpkins. What was the
total number of fruits and vegetables produced by Rachel’s garden?
14.) Michael washes the Taylor family’s cars once a month. They pay him $25 every 3 months.
At this rate, how much money will Michael earn in one year?
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Chapter 1 Lesson 2
Order of Operations
NOTES
Date __________________________
VOCABULARY
 Order of Operations – the correct order to complete a math problem
1. Do all operations within parentheses first.
2. Multiply and divide in order from left to right.
3. Add and subtract in order from left to right.
 Expression – a mathematical phrase that contains numbers and operation symbols.
ORDER OF OPERATIONS AND EXPRESSIONS
When solving math problems you’re looking for one correct answer. Using Order of
Operations makes sure your answer is correct.
1. Do all operations within parentheses first.
2. Multiply and divide in order from left to right.
3. Add and subtract in order from left to right.
Practice:
a.) 6 + 6 ÷ 3
b.) 30 − (6 + 2) × 3
5
More Practice:
c.) 34 + 5 × 2 − 17
d.) (6 + 8) ÷ 2 × 3
e.) You are paid $7.00 per hour to rake leaves. Your brother is paid $5.00 per hour. You
worked 4 hours and your brother worked 3 hours. How much did the two of you earn
together?
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Chapter 1 Lesson 2
REVIEW
Date _________________________
Part I: Circle the operation would you perform first in each expression.
1.) 4 + 6 × 9
2.) (7 – 5) × 3
3.) 14 ÷ 2 × 3
Part II: Find the value of each expression.
4.) 8 − 3 × 1 + 5
5.) 7 × (8 + 6)
7.) 8 − 3 × 2 + 7
8.) 4 + (20 ÷ 4) − 2
6.) 15 − (5 + 7)
9.) 7 × (10 − 2) ÷ 4
Part III: Insert parentheses to make each statement true.
10.) 14 − 5 ÷ 3 = 3
11.) 27 ÷ 4 + 5 − 1 = 2
Part IV: Write a mathematical expression and solve.
12.) Haircuts for boys cost $7. Haircuts for men cost $10. If 20 boys and 20 men went
to the barber yesterday, how much did the barber earn?
7
Chapter 1 Lessons 1 & 2
REVIEW
Date __________________________
Part I: Identify each property.
-Commutative Property of Addition
-Associative Property of Addition
-Identity Property of Addition
-Commutative Property of Multiplication
-Associative Property of Multiplication
-Identity Property of Multiplication
1.) 6 x 1 = 6
_________________________________________
2.) (3 x 5) x 7 = 3 x (5 x 7)
_________________________________________
3.) 9 + 2 = 2 + 9
_________________________________________
4.) 0 + 5 = 5
_________________________________________
5.) 9 + (3 + 8) = (9 + 3) + 8
_________________________________________
6.) 6 x 1 x 3 = 1 x 3 x 6
_________________________________________
Part II: Find the value of each expression.
7.) 30 − 6 × 5
8.) (12 + 23) × 2
9.) 3 × ( 18 ÷ 6) + 2
10.) (17 + 3) ÷ 2 − 1
8
Part III: Word Problems
11.) List the operations in the order you will perform them to simplify the expression below.
12 + (60 – 2) ÷ 7
12.) You are paid $5 per hour to shovel the snow. Your sister is paid $8 per hour. You worked
3 hours and your sister worked 4 hours. How much did the two of you earn together?
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Chapter 1 Lessons 1 & 2
REVIEW FOR QUIZ
Date _________________________
PART I: Name each property of addition or multiplication used below.
1.) (8 + 5) + 21 = 8 + (5 + 21)
2.) 13 × 6 = 6 × 13
a.) Commutative Property of Addition
b.) Associative Property of Addition
c.) Identity Property of Addition
3.)
a.) Commutative Property of Multiplication
b.) Associative Property of Multiplication
c.) Identity Property of Multiplication
8+0=8
4.) 5 × 2 × 11 = 2 × 11 × 5
a.) Commutative Property of Addition
b.) Associative Property of Addition
c.) Identity Property of Addition
a.) Commutative Property of Multiplication
b.) Associative Property of Multiplication
c.) Identity Property of Multiplication
Part II: Find each sum or product.
5.)
6 + (4 + 2)
6.) 5 × 2 × 0
10
7.) 5 × 1 × 13 × 2
Find the value of each expression.
8.) 18 − 13 × 1 + 5
9.) (40 − 20) × 5
10.) (12 − 9) × (3 + 2)
11.) 29 − 4 × 6
12.) 7 × (10 − 2) ÷ 4
13.) 1 × 2 + 8 ÷ 4 × 5
14.) Steve is going to buy 3 pencils. Each pencil will cost him $2. Steve also wants to buy 5 pens.
Each pen will cost him $3. How much money did Steve spend to get his pencils and pens?
11
Chapter 1 Lesson 3
Understanding Decimals
NOTES
Date __________________________
VOCABULARY
 Standard form – It is the way of writing numbers using digits.
Examples:
47
2.5
.75
 Expanded form – It is a sum that shows the place and value of each digit.
Example:
.75
=
0.7
+ .05
seventy-five hundredths = seven tenths + five hundredths
Writing a Decimal in Words
Practice:
a.) 3.25
three and twenty-five hundredths
b.) 67.3
c.)
6.734
d.)
0.67
12
Standard Form and Expanded Form
At a gymnastics meet, the best score on the pommel horse was nine and forty-two
thousandths. Write in standard form and in expanded form.
Standard form
Expanded form
The winning car in a race won by fifteen hundredths of a second. Write the decimal in
standard and expanded forms.
Standard form
Expanded form
Rounding Numbers
Round 0.426 to the nearest hundredth.
0.426
*Look at the digit to the right of the hundredths place.
*If the value to the right of the hundredths place is < 5,
round down. If the value to the right of the hundredths is
equal or greater than 5, round up.
Tip: 5 and above, give it a shove. 4 and below, let it go.
So 0.426 rounded to the nearest hundredth is 0.43.
Practice: Round each decimal to the underlined place.
a.) 2.342
b.) 0.175
13
c.)
9.053
Chapter 1 Lesson 3
REVIEW
Date __________________________
Part I: Write each decimal in words.
1.) 213.23
2.) 7,430.25
Part II: Write each decimal in standard form.
3.) three tenths
4.) eight tenths
5.) two hundredths
6.) forty hundredths
Part III: What is the value of the digit 7 in each number?
7.) 0.7
8.) 4.00712
9.) 2.179
10.) 1.8887
11.) 27.002
12.) 174
14
Part IV: Round each decimal to the underlined place.
13.) 28,467.089
14.) 348.92971
15.) 72.14
16.) 22.98553
Part V: Word Problems
17.) The word thousandths represents how many decimal places to the right of the decimal
point?
18.) When you are rounding a number, how do you determine if the number rounds up or
rounds down?
15
Chapter 1 Lesson 4
Adding and Subtracting Decimals
NOTES
Date __________________________
Finding Decimal Sums
*Estimate before you add to tell whether your answer is reasonable. Estimate by rounding to
the nearest whole number.
Steps to add decimals:
1. Line up the decimal points.
2. Annex zeroes as placeholders.
3. Add and bring down the decimal point.
Practice:
a.) 𝟐. 𝟓𝟔 + 𝟑. 𝟏
b.) 𝟑. 𝟎𝟐𝟔 + 𝟏𝟒. 𝟕 + 𝟏. 𝟑𝟖
Estimate: ___________________
Estimate: ________________________
Find the sum:
Find the sum:
+
+
c.) 𝟎. 𝟖𝟒 + 𝟐. 𝟎 + 𝟑. 𝟑𝟐
Estimate: __________________________
Find the sum:
+
16
Finding a Difference
*Estimate before you subtract to tell whether your answer is reasonable. Estimate by
rounding to the nearest whole number.
Steps to subtract decimals:
1. Line up the decimal points.
2. Annex zeroes as placeholders.
3. Subtract and bring down the decimal point.
Practice:
d.) 𝟏𝟗. 𝟖 − 𝟓. 𝟐
e.) 𝟒𝟔 − 𝟐𝟒. 𝟐𝟖
Estimate: ___________________
Estimate: ________________________
Find the
difference:
Find the difference:
-
f.) 𝟏𝟔. 𝟑 − 𝟗. 𝟒𝟕
Estimate: __________________________
Find the
difference:
-
17
Chapter 1 Lesson 4
Adding and Subtracting Decimals
REVIEW
Date __________________________
Find each sum or difference.
1.)
4.6 + 8.79
3.)
2.) 107.5 + 6
0.6 + 5.8
4.) 5.98 − 2.71
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5.) 4.7 − 1.9
6.) 14.3 + 6
7.) 3.086 + 6.15
8.) 17.1 + 23.4 + 10.6
10.) You and your friend calculate
your grade for a class. You have an
83.5 and your friend has an 81.65.
Who has the higher grade? How
much higher is it?
9.) An orange costs $0.39. You have $1.
How much money do you have left if you
buy an orange?
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Chapter 1 Lessons 3 & 4
REVIEW
Date ___________________________
Write each decimal in words.
1.) 0.09
2.)
5.376
Write each decimal in standard form.
3.) eight and seven tenths
4.)
thirty six and five thousandths
Write each decimal in expanded form.
5.) 42.93
6.)
5.302
Round each decimal to the underlined place.
7.) 65.73
8.)
20
451.347
First estimate and then find each sum or difference.
Estimate
Find the sum.
9.) 0.8 + 5.6
10.)
25.67 + 13.42
11.)
6.5 − 2.4
12.)
37.8 − 15.16
13.)
At one store a bike costs $156.75. At another store, the same bike costs
$203.74. What is the difference in prices?
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Chapter 1 Lesson 5
Multiplying Decimals
NOTES
Date __________________________
There are several ways to show multiplication.
3 × 5
3 • 5
3 (5)
(3) (5)
Steps to Multiplying Decimals
1. Line up the numbers on the right. Do not align the decimal point.
2. Multiply as if the factors are whole numbers.
(Don’t worry about the decimal point right now.)
3. Count the number of decimal places in both factors.
4. Place the decimal point in your answer the same amount of places you counted in
your factors.
Practice Multiplying Decimals
a.) 𝟑. 𝟕 × 𝟗
c.)
b.) 𝟎. 𝟒𝟕
𝟏. 𝟑𝟏 • 𝟐. 𝟒
d.)
22
• 𝟖
𝟓. 𝟑𝟐 (𝟏. 𝟗)
Problem Solving
a.) A eucalyptus tree grows 5.45 meters in one year. At that rate, how much does the tree
grow in 3.5 years?
b.) At your part-time job, you earn $7.30 per hour. You work for four hours. How much
money do you earn?
c.) One pound of tomatoes costs $1.29. To the nearest cent, how much do 2.75 pounds of
tomatoes cost?
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Chapter 1 Lesson 5
REVIEW
Date __________________________
1.) 3.7 × 4
2.) 1.07 ● 9
3.) 0.06 × 4.2
4.) 3.2 ●0.7
24
5.) 0.5 × 9.6
6.) 4.2 ● 2.3
7.) 4.23 × 1.2
8.) 2.6 ● 9.8
9.) 5.2 × 4.5
10.) 9.65 ● 3.7
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Chapter 1 Lesson 6
Dividing Decimals
NOTES
Date __________________________
Vocabulary
- dividend: the number being divided
- divisor: the number you are dividing by
- quotient: the answer to a division problem
- terminating decimal: the decimal ends or stops
There are three ways to write a division problem.
12 ÷ 3
4
3 12
12
3 12
3
quotient
dividend
divisor
Review Dividing Whole Numbers
a)
3,348 ÷ 9
b)
26
27 8 3 7
Dividing a Decimal by a Whole Number
c.)
8 3 85 .6
d.)
9.12 ÷ 6
f.)
9.674 ÷ 0.7
Dividing a Decimal by a Decimal
e.)
0 .5 2 .2 5
27
Problem Solving
d.) A roller coaster at the amusement park has 8 cars. Each car holds 4 riders. How many
times will the ride have to run so that 384 people can ride?
e.) You have $2.75. You want to buy trading cards that cost $0.25 each. How many can you
buy?
28
Chapter 1 Lesson 6
REVIEW
Date __________________________
1.) 3.5 ÷ 0.1
2.) 0.7 ÷ 0.5
3.) 15.8 ÷ 2
4.) 22 ÷ 0.4
29
5.) 12.15 ÷ 2.7
6.) 14 ÷ 0.28
7.) 5.4 ÷ 7.2
8.) 37 ÷ 0.2
9.) 1.414 ÷ 1.4
10.) 98 ÷ 3.5
30
Chapter 1
Review for Test #1
Date __________________________
Part I: Write each number in words.
1.) 0.26 ____________________________________________________________________
2.) 72.05 ____________________________________________________________________
3.) 691.4 ____________________________________________________________________
Part II: Write each number in standard form.
4.) two and seventeen hundredths ______________________________________________
5.) fifteen and three thousandths ________________________________________________
Part III: Find each sum. Estimate when you are finished to see if your answer is
reasonable.
6.) 1.14 + 9.3
7.) 8 + 3.51
8.) 0.02 + 5.6
31
Part IV: Find each difference. Estimate when you are finished to see if your
answer is reasonable.
9.) 4.93 – 1.3
10.) 18.01 – 4.5
11.) 34 – 1.94
Part V: Find each product. Estimate when you are finished to see if your answer
is reasonable.
12.) 1.8 × 4.1
13.) 5.1(3)
14.) 16.4 ∙ 3.2
Part VI: Find each difference. Estimate when you are finished to see if your
answer is reasonable.
15. 6.72 ÷ 3
16.) 1.23 ÷ 0.3
32
Chapter 1
Review for Test #2
Date __________________________
Part I: Write each number in words.
1.) 175.29 __________________________________________________________________
2.) 6.008 ____________________________________________________________________
Part II: Write each number in standard form.
3.) thirty eight and fourteen thousandths _________________________________________
4.) sixteen and nine hundredths ________________________________________________
Part III: Find each sum or difference. Estimate when you are finished to see if
your answer is reasonable.
5.) 3.48 + 12.3
6.) 6 + 4.72
7.) 3.6 − 1.07
33
Part IV: Find each product or quotient.
8.) 0.12 × 0.96
9.) 0.475 ÷ 0.05
10.) 10.54 ÷ 0.17
Part VI: Find the value of each expression.
11.) 6 − 2 + 4 × 2
12.) 4 × 3 + 20 ÷ 5
13.) 30 – (6 – 2) × 3
14.) Cameron can read 196 words in a minute. Robert reads 1.6 times as fast. How many
words can Robert read in a minute?
15.) A class of 27 students held a picnic. They purchased food and drinks for the picnic for a
total cost of $93.15. What was the price for each student’s meal?
34
35