Name
Place Value
R 1-1
The 8 in 577,800,000,000,000 is in the hundred-billions place, and
its value is 800 billion.
5
7
7,
8
es
Ones
on
Thousands
h
th und
ou re
sa d
n
te ds
th n
ou
sa
nd
th
s
ou
sa
nd
s
hu
nd
re
ds
te
ns
Millions
h
m und
illi r e
on d
s
te
m n
illi
on
s
m
illi
on
s
Billions
h
bi und
llio r e
ns d
te
bi n
llio
ns
bi
llio
ns
h
tri und
llio r e
ns d
te
tr i n
llio
ns
tr i
llio
ns
Trillions
0
0,
0
0
0,
0
0
0,
0
0
0
9
2,
2
8
2,
0
0
0,
0
0
0
The number 577,800,000,000,000 can be written in different ways.
Standard form: 577,800,000,000,000
Word form: five hundred seventy-seven trillion, eight hundred billion
Short-word form: 577 trillion, 800 billion
Expanded form: 500,000,000,000,000 70,000,000,000,000 7,000,000,000,000 800,000,000,000
1. Write the place and value for the underlined digit.
7,656,871,228
2. Write 32,600,009,000 in short-word form.
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3. Write the number in word form and in standard form.
9,000,000,000,000 8,000,000,000 6,000,000 5,000 1
4. Writing in Math What is the value of the 7 in 568,971,433,009?
Explain how you know.
Use with Lesson 1-1.
1
Name
Exponents
base
R 1-2
How to write a power as a product
and then evaluate:
exponent
35
The number 3 is the base.
It is the factor that is multiplied.
24
The number 5 is the exponent.
It tells how many times the base is used as a factor.
The base (2) is used as a factor
the number of times as shown by
the exponent (4):
35 is read “three to the fifth power.”
35 3 3 3 3 3
24 2 2 2 2 16
Five factors of 3
are multiplied.
How to write a product in
exponential form:
How to use exponents to write a number in
expanded form:
555
4,512 (4 1,000) (5 100) (1 10) (2 1)
Step 1: Write the base.
5
Step 2: Count the number of
times the base is used
as a factor. This is the
exponent.
53
(4 103) (5 102) (1 101) (2 100)
Write each power as a product and then evaluate.
1. 53
2. 25
3. 73
4. 8 8 8
5. 20 20 · 20 · 20
Write the number in expanded form using exponents.
6. 1,324 (1 103) + ( 3 102) + (
)+(
7. Number Sense Are 24 and 42 equal? Explain why or why not.
2
Use with Lesson 1-2.
)
© Pearson Education, Inc. 6
Write each product in exponential form.
Name
Comparing and Ordering
Whole Numbers
R 1-3
Here is one way to compare two numbers:
Which is greater: 452,198 or 452,189?
First, align the numbers. Then, start at the
left and compare digits in each place.
452,1 9 8
452,1 8 9
The numbers in the tens
place are different. Since
9 is greater than 8, the
top number is larger.
So 452,198 452,189.
Order 46,525; 44,434; 44,737; and 46,895 from greatest to least.
Order ten
thousands.
Order
thousands.
Order
hundreds.
4
4
4
4
46 ,
46 ,
44 ,
44 ,
46,895
46,525
44,737
44,434
,
,
,
,
From greatest to least, the numbers are 46,895; 46,525; 44,737; and 44,434.
Use or to compare.
1. 445
4. 71,297
472
71,279
2. 354,123
5. 5,280
345,129
5,379
3. 8,367
6. 22,420
8,381
22,421
For 7 and 8, order the numbers from greatest to least.
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7. 6,731 67,331 671 6,713
8. 18,910 18,901 18,909 18,919
9. Number Sense Which place-value position helps you decide if
312,879 is less than 321,978?
Use with Lesson 1-3.
3
Name
Rounding Whole Numbers
R 1-4
You round numbers when an exact amount is not needed.
Here is how to round numbers.
Step 1
Find and
underline the
place you must
round to.
Round 3,281
to the nearest
hundred.
Round 58,241
to the nearest
thousand.
Step 2
Look at the digit
to the right of
this place.
3,281
3,2 8 1
This is the
hundreds
place.
8 is to the right
of the hundreds
place.
58,241
58, 2 41
This is the
thousands
place.
2 is to the right
of the thousands
place.
Step 3
If this digit is 5 or more,
add 1 to the rounding digit.
If it is less than 5, leave the
rounding digit alone.
3,281 rounded to the
nearest hundred is 3,300.
It was “rounded up.”
58,241 rounded to the
nearest thousand is 58,000.
It was “rounded down.”
1. 3,459
2. 45,248
3. 292,420
4. 22,654
5. 153,744
6. 102,291
7. 964,499
8. 908,748
9. 1,898,234
10. 2,409,158
11. 6,365,054
12. 8,935,102
13. Number Sense James has been asked to round 453,215 to the
nearest thousand. Which digit and what place will he look at to
decide if he should round up or down?
4
Use with Lesson 1-4.
© Pearson Education, Inc. 6
Round each number to the underlined place.
Name
Estimating Sums and Differences
R 1-5
Estimate 2,675 189.
Determine the greatest place
value of the lesser number.
Round both numbers to this place.
2,675 → 2,700
Subtract the rounded numbers.
hundreds
189 → 200
2,700 200 2,500
You can also estimate by using front-end estimation with and without adjusting.
Estimate 8,243 4,686 129.
Front-end Estimation
8 ,243
4 ,686
129
12 ,000
Front-end Estimation with Adjusting
Add only the first digits
that have the same
place value to get a
rough estimate.
8 , 2 43
4 , 6 86
1 29
12 , 0 00
9 00
12 , 9 00
Add thousands.
Add hundreds.
Adjusted estimate
Clustering can be used when the numbers are close to each other.
Estimate 252 297 305 327.
↓
↓
↓
↓
300 300 300 300 1,200
Estimate each answer. Tell which method you used.
1. 196 29
2. 3,769 4,109
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3. 4,312 1,162
4. 369 409 430 378
5. Reasonableness Is 5,500 a reasonable estimate for
5,128 921? Why or why not?
Use with Lesson 1-5.
5
Name
Estimating Products and Quotients
R 1-6
Here are two different methods to estimate products and quotients.
Use Rounding Round each factor to its greatest place. Multiply or
divide mentally. When both numbers are rounded up, you have an
overestimate. When both numbers are rounded down, you have an
underestimate.
Estimate 4,698 165.
4,698
165
→
→
5,000
200
1,000,000
Since both numbers were
rounded up, this is an
overestimate.
Use Compatible Numbers Think of numbers that are close to the
actual ones, but are easier to use. Multiply or divide mentally.
Estimate 718 89.
718 89
↓
↓
720 90 8
72 and 9 are
compatible
numbers.
So, 718 89 8.
Estimate each answer. Tell which method you used.
1. 4 19
2. 17 59
3. 6,192 11
4. 781 7
5. 289 29
7. 7,248 82
8. Number Sense Dean estimated 39 28 by rounding.
He got 1,200 as his estimated product. Is this an overestimate
or underestimate? How do you know?
6
Use with Lesson 1-6.
© Pearson Education, Inc. 6
6. 425 94
Name
Order of Operations
R 1-8
Order of operations is a set of rules that mathematicians use when
computing numbers. Here is how order of operations is used to solve
the following problem: 7 (5 4 ) 3.
Order of Operations
First, compute all numbers
inside parentheses.
7 (5 4) 3
7 20 3
Next, simplify exponents. If there are
no exponents, go to the next step.
7 20 3
Then, multiply and divide the
numbers from left to right.
7 60
Finally, add and subtract the
numbers from left to right.
67
How to use parentheses to make a
number sentence true:
6 2 9 72
Using order of operations,
6 2 9 24, not 72.
Place parentheses around 6 2
so that this operation is done first:
(6 2) 9 72
8 9 72
1. 8 7 5 2. 18 3 2 3. 3 7 3 5 4. 40 (2 4) 5. 6 3 6 2 6. 9 23 7. 7 12 3 2 8. 4 (5 5) 20 6 9. 42 (3 5) 10. (3 2) 32 11. Reasoning Which operation should be performed last in this
problem: 32 7 4? Why?
Use parentheses to make each sentence true.
12. 0 6 9 9
13. 32 2 2 13
8
Use with Lesson 1-8.
© Pearson Education, Inc. 6
Evaluate each expression.
Name
Properties of Operations
R 1-9
Commutative Properties
You can add or multiply numbers in any order
and the sum or product will be the same.
Associative Properties
You can group numbers differently. It will not
affect the sum or product.
Examples:
Examples:
10 5 3 5 3 10 18
7 5 5 7 35
2 (7 6) (2 7) 6 15
(4 5) 8 4 (5 8) 160
Identity Properties
You can add zero to a number or multiply it
by 1 and not change the value of the number.
Multiplication Property of Zero
If you multiply a number by zero, the product
will always be zero.
Examples: 17
0 17
45 1 45
Example: 12
00
Find each missing number. Tell what property or properties are shown.
1. 9 5 5 2.
89 89
3. (3 4) 19 3 (
4. 128 © Pearson Education, Inc. 6
5.
19)
128
18 18 12
6. Reasoning What is the product of 1 multiplied by zero? Explain
how you know.
Use with Lesson 1-9.
9
Name
Mental Math: Using the
Distributive Property
R 1-10
You can use the Distributive Property to multiply mentally.
Problem A: 6 (50 4)
If you followed the order of operations, you would add the
numbers in the parentheses first, then multiply 6 54.
Since 6 54 is difficult to multiply mentally, use the Distributive Property.
Multiply each number in
the parentheses by 6.
Add the products.
6 (50 4)
(6 50) (6 4)
↓
↓
300 24
324
Problem B: 8(15) Remember, 8(15) means 8 15.
Use the Distributive Property to make it easier to multiply mentally.
Break apart 15 into 10 5.
Then use the Distributive
Property to find the products,
and add them together.
8(15)
8(10 5)
(8 10) (8 5)
80 40
120
Find each missing number.
1. 6(5 4) 6(5) (4)
2. 2(12 ) 2(12) 2(7)
3. 9(15) 9(8) 9(
8)
4. 8(7 3) 8(7) (3)
Use the Distributive Property to multiply mentally.
6. 4(21) 7. 7(10 8) 8. 5(5 4) 9. (10 12)3 10. 8 36 10
Use with Lesson 1-10.
11. 7(89) © Pearson Education, Inc. 6
5. Number Sense What are two other ways to write 6(24)?