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Lesson 2-1
Rational Numbers
Lesson 2-2
Comparing and Ordering Rational Numbers
Lesson 2-3
Multiplying Positive and Negative Fractions
Lesson 2-4
Dividing Positive and Negative Fractions
Lesson 2-5
Adding and Subtracting Like Fractions
Lesson 2-6
Adding and Subtracting Unlike Fractions
Lesson 2-7
Solving Equations with Rational Numbers
Lesson 2-8
Problem-Solving Investigation: Look for
a Pattern
Lesson 2-9
Powers and Exponents
Lesson 2-10 Scientific Notation
Five-Minute Check (over Chapter 1)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Rational Numbers
Example 1: Write a Fraction as a Decimal
Example 2: Write a Mixed Number as a Decimal
Example 3: Round a Repeating Decimal
Example 4: Write a Decimal as a Fraction
Example 5: Write a Decimal as a Fraction
• Express rational numbers as decimals and
decimals as fractions.
• Rational number
• Any number that can be expressed as a fraction
• terminating decimal
• fraction where division ends and remainder = 0
• repeating decimal
• Division NEVER ends, and digits repeat forever
• bar notation
• a line over the repeating digits
NOTES - Rational Numbers
• Rational Numbers contain ALL
•repeating decimals – 1/3 = .3
•terminating decimals – .25
•Fractions - 1/4
•positive and negative integers – 1, 2, -6, 28
•whole numbers – 1, 2, 3
NOTES - Rational Numbers – Cont.
 To convert FRACTIONSDECIMALS
1. TOP IN THE BOX!!
2. Do the Division.
Convert TERMINATING DECIMALS  FRACTIONS:
1. Put decimal over the place value
2. Reduce the fraction
 To convert MIXED NUMBERS  IMPROPER
1. Remember the BOWL method or the “Smiley Face”
method!
NOTES - Rational Numbers – Cont.
Convert REPEATING DECIMALS  FRACTIONS:
1. Figure out how many places repeat.
2. Put those numbers over that many 9’s.
3. Simplify the fraction
Write a Fraction as a Decimal
Write
as a decimal.
0 .18 75
–16
14 0
–128
12 0
–112
80
–80
0
Divide 3 by 16.
Write a Fraction as a Decimal
Answer: 0.1875
A. 0.0515
B. 0.0625
C. 0.0875
0%
0%
A
B
D. 0.16
A. A
B. 0% B
C. C
C
D. D
0%
D
Write a Repeating Decimal
You can divide as shown in Example 1 or use a
calculator.
–35 ÷ 11 ENTER –3.18181818
Answer:
A. 5.1111...
B. 5.1515...
C. 5.2222...
D. 5.9999...
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Round a Repeating Decimal
AGRICULTURE A Texas farmer lost the fruit on 8
of 15 orange trees because of unexpected freezing
temperatures. Find the fraction of the orange trees
that did not produce fruit. Express your answer as
a decimal rounded to the nearest thousandth.
To find the fraction of trees that did not produce fruit,
divide the number of lost trees, 8, by the total number
of trees, 15.
8 ÷ 15 ENTER 0.5333333333
Look at the digit to the right of the thousandths place.
Round down since 3 < 5.
Round a Repeating Decimal
Answer: The fraction of fruit trees that did not
produce fruit was 0.533.
SCHOOL In Mrs. Townley’s eighth grade science
class, 4 out of 22 students did not turn in their
homework. Find the fraction of the students who did
not turn in their homework. Express your answer as a
decimal rounded to the nearest thousandth.
A. 0.094
1.
2.
3.
4.
0%
B. 0.148
C. 0.182
D. 0.252
A
B
C
D
A
B
C
D
Write a Decimal as a Fraction
Write 0.32 as a fraction.
0.32 is 32 hundredths.
Simplify.
Answer:
Write 0.16 as a fraction.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Write a Decimal as a Fraction
ALGEBRA Write 2.7 as a mixed number.
Let N = 2.7 or 2.777... . Then 10N = 27.777... .
Multiply N by 10 because 1 digit repeats.
Subtract N = 2.777... to eliminate the repeating part,
0.777... .
Write a Decimal as a Fraction
10N = 27.777...
–1N = 2.777...
9N = 25
10N – 1N = 9N
Divide each side by 9.
Simplify.
Answer:
ALGEBRA Write 1.7 as a mixed number.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 2-1)
Main Idea
Targeted TEKS
Example 1: Compare Positive Rational Numbers
Example 2: Compare Using Decimals
Example 3: Order Rational Numbers
Example 4: Compare Negative Rational Numbers
Example 5: Compare Negative Rational Numbers
• Compare and order rational numbers.
Comparing and Ordering Rational Numbers
• I can only COMPARE things in math that ????
– LOOK ALIKE!
– I can only COMBINE things in math that ????
– LOOK ALIKE!
•In order to compare rational numbers, convert
them to the “SAME THING.”
– Fractions
– Decimals
– Percents
• When comparing NEGATIVE numbers
• LESS IS MORE AND MORE IS LESS.
Compare Positive Rational Numbers
Replace ■ with <, >, or = to make
sentence.
■
a true
Write as fractions with the same denominator.
Answer:
Replace ■ with <, >, or = to make
sentence.
■
a true
A. >
B. <
C. =
D. None of the above.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Compare Using Decimals
Replace ■ with <, >, or = to make 0.7 ■
sentence.
a true
■
■
Express
as a decimal.
In the tenths place, 7 > 6.
Answer:
Replace ■ with <, >, or = to make
sentence.
■ 0.5 a true
A. >
B. <
C. =
D. None of the above.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Order Rational Numbers
CHEMISTRY The values for the
approximate densities of various
substances are shown in the table.
Order the densities from least to
greatest.
Write each fraction as a decimal.
Order Rational Numbers
Answer: From the least to the greatest, the densities are
AMUSEMENT PARKS The ride times
for five amusement park attractions are
shown in the table. Order the lengths
from least to greatest.
A.
1.
2.
3.
4.
B.
0%
C.
D.
A
B
C
D
A
B
C
D
Compare Negative Rational Numbers
Replace ■ with <, >, or = to make –4.62 ■ –4.7 a true
sentence.
–4.62 ■ –4.7
Graph the decimals on a number line.
Answer: Since –4.62 is to the right of –4.7, –4.62 > –4.7.
Replace ■ with <, >, or = to make –2.67 ■ –2.7 a true
sentence.
A. <
B. >
C. =
D. None of the above.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Compare Negative Rational Numbers
Replace ■ with <, >, or = to make
sentence.
a true
Since the denominations are the same, compare the
numerators.
Answer:
Replace ■ with <, >, or = to make
sentence.
a true
A. >
B. <
C. =
D. None of the above.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 2-2)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Multiply Fractions
Example 1: Multiply Positive Fractions
Example 2: Multiply Negative Fractions
Example 3: Multiply Mixed Numbers
Example 4: Multiply Mixed Numbers
Example 5: Use Dimensional Analysis
• Multiply positive and negative fractions.
• dimensional analysis –
– including UNITS OF MEASURE in your multiplication and
division
– Example
• Distance = rate * time
• Distance = 25 miles
» -----------------»
hour
* 2 hours
Multiplying Fractions
•
See your “Fraction Rules” sheet
Couple of rules to ALWAYS remember:
1.
If you see a mixed number in a math problem
1.
CONVERT IT TO AN IMPROPER FRACTION TO
2.
DO THE MATH.
3.
CONVERT THE IMPROPER FRACTION BACK TO A
MIXED NUMBER WHEN YOU ARE DONE.
2.
Reduce the fractions FIRST if you can.
3.
To Multiply Fractions:
1.
Multiply STRAIGHT across the top and the bottom
4.
- * + = negative
5.
- * - = positive
6.
+ * + = positive
Animation:
Multiplying Fractions
Multiply Positive Fractions
Divide 3 and 9 by their GCF, 3.
Multiply the numerators.
Multiply the denominators.
Simplify.
Answer:
A.
B.
C.
0%
0%
A
B
D.
A. A
B. 0% B
C. C
C
D. D
0%
D
Multiply Negative Fractions
Divide –3 and 12 by their GCF, 3.
Multiply the numerators.
Multiply the denominators.
The numerator and denominator
have different signs, so the
product is negative.
Answer:
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Multiply Mixed Numbers
Divide 16 and 4 by their GCF, 4.
Multiply the numerators.
Multiply the denominators.
Multiply Mixed Numbers
Simplify. Compare to the estimate.
Answer:
A.
0%
B.
C.
1.
2.
3.
4.
A
D.
A
B
C
D
B
C
D
Multiply Mixed Numbers
VOLUNTEER WORK Last summer, the 7th graders
performed a total of 250 hours of community service.
If the 8th graders spent
this much time
volunteering, how many hours of community service
did the 8th graders perform?
The 8th graders spent
the amount of time as the
7th graders on community service.
Multiply Mixed Numbers
Answer: The 8th graders did 300 hours of community
service last summer.
VOLUNTEER WORK Last summer, the 5th graders
performed a total of 150 hours of community service.
If the 6th graders spent
this much time
volunteering, how many hours of community service
did the 6th graders perform?
0%
D
A
B
C0%
D
C
D. 225 hours
A.
B.
0%
C. 0%
D.
B
C. 200 hours
B. 190 hours
A
A. 175 hours
Use Dimensional Analysis
WATER USE Low–flow showerheads use
gallons
of water per minute. If family members shower a total
of
hours per week, how much water does the
family use for showers each week?
Words
Water used equals the time multiplied by the
water flow rate.
Variable
Let w represent the gallons of water used.
Equation
Use Dimensional Analysis
Divide by common
factors and units.
Use Dimensional Analysis
Answer: If the family showers
rate of
hours per week at a
gallons per minute, they will use
350 gallons of water.
0%
D
0%
A
0%
B
C
D
C
D. 897 gallons
A.
B.0%
C.
D.
B
C. 775 gallons
B. 38 gallons
A
A. 15 gallons
Five-Minute Check (over Lesson 2-3)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Inverse Property of Multiplication
Example 1: Find a Multiplicative Inverse
Key Concept: Divide Fractions
Example 2: Divide Fractions
Example 3: Divide Fractions
Example 4: Divide by a Whole Number
Example 5: Divide Mixed Numbers
Example 6: Real-World Example
• Divide positive and negative fractions.
• multiplicative inverses –
• AKA “reciprocal.”
• Multiplicative inverses are 2 numbers that
multiply to get 1.
– Example 4 * ¼ = 1
• Reciprocals –
• Turn the fraction upside down
Dividing Positive and Negative Fractions

To Divide a fraction, CONVERT PROBLEM IN A
MULTIPLICATION PROBLEM.

This is a 3 step process.
•
1.
KEEP the top (or FIRST) number the same.
2.
CHANGE the division to a multiplication.
3.
FLIP the bottom (or second) number to get
it’s reciprical.
Remember KEEP – CHANGE – FLIP.
BrainPop:
Multiplying and Dividing Fractions
BrainPop:
Multiplying and Dividing Fractions
Find a Multiplicative Inverse
Answer:
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Divide Fractions
Divide Fractions
Answer:
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Divide Fractions
Multiply by the multiplicative
The fractions have different signs,
so the quotient is negative.
Answer:
A.
0%
B.
C.
D.
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Divide by a Whole Number
Divide 6 and 12 by their
GCF, 6.
Divide by a Whole Number
Answer:
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Divide Mixed Numbers
The multiplicative
inverse of
Divide 4 and 8 by their
GCF, 4.
Divide Mixed Numbers
Simplify.
Check for Reasonableness
Answer:
Compare to the
estimate. The answer
seems reasonable
because –1.5 is close to
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Divide by common factors.
=5
Simplify.
Answer: The cinema shows the movie 5 times that day.
A. 4 times
B. 5 times
C. 6 times
D. 7 times
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 2-4)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Add and Subtract Like Fractions
Example 1: Add Like Fractions
Example 2: Subtract Like Fractions
Example 3: Add Mixed Numbers
Example 4: Subtract Mixed Numbers
• Add and subtract fractions with like denominations.
• like fractions
• Fractions with the same denominator
Adding and Subtracting LIKE Fractions
•
CHECK YOUR FRACTION RULES PAPER IF
YOU FORGET THE RULES!
•
I can only combine things in math that ??????
•
If I have a Mixed number, what do I do with it??
•
Can ONLY add/subtract if the denominator
(bottom number!) is the SAME!!
•
Once the denominator is the same:
•
1.
ADD or Subtract ACROSS THE TOP like normal.
2.
LEAVE the bottom number the SAME.
Rules for adding and subtracting fractions with
different signs are the same as the rules for
integers.
Add Like Fractions
Add the numerators.
The denominators
are the same.
Answer:
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Subtract Like Fractions
Subtract the numerators.
The denominators are the
same.
Answer:
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Add Mixed Numbers
Add the whole
numbers and fractions
separately.
Answer:
A.
0%
B.
C.
D.
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Subtract Mixed Numbers
Estimate
64 – 54 = 10
Subtract Mixed Numbers
Write the mixed numbers
as improper fractions.
Subtract the numerators.
The denominators are the
same.
Answer:
0%
D
A
B
0%
C
D
C
D.
A.
B.
0% C.0%
D.
B
C.
B.
A
A.
Five-Minute Check (over Lesson 2-5)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Add and Subtract Unlike Fractions
Example 2: Add and Subtract Unlike Fractions
Example 3: Add and Subtract Mixed Numbers
Example 4: Test Example
• Add and subtract fractions with unlike denominations.
• unlike fractions
• Fractions with DIFFERENT Denominators
Adding/Subtracting UNLIKE Fractions
•
I can only combine things in math that ??????
•
If I have a Mixed number, what do I do with it??
•
Can ONLY add/subtract if the denominator
(bottom number!) is the SAME!!
•
If the denominator’s aren’t alike, CONVERT
THEM TO A COMMON DENOMINATOR!!!
•
Once the denominator is the same:
1.
ADD or Subtract ACROSS THE TOP like normal.
2.
LEAVE the bottom number the SAME.
•
Rules for adding and subtracting fractions with
different signs are the same as the rules for
integers.
•
DEMO from NLVM
Add and Subtract Unlike Fractions
The LCD is 2 ● 2 ● 2 or 8.
Rename the fractions using
the LCD.
Add the numerators.
Add and Subtract Unlike Fractions
Simplify.
Answer:
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Add and Subtract Unlike Fractions
Rename each fraction
using the LCD.
Subtract
by
adding its inverse,
Add and Subtract Unlike Fractions
Answer:
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Add and Subtract Mixed Numbers
Write the mixed numbers
as fractions.
The LCD is 2 ● 2 ● 2 ● 3
or 24.
Add and Subtract Mixed Numbers
Add the numerators.
Simplify.
Answer:
A.
0%
B.
C.
1.
2.
3.
4.
A
D.
A
B
C
D
B
C
D
A
B
C
D
Read the Test Item
You need to find the sum of four mixed numbers.
Solve the Test Item
It would take some time to change each of the fractions
to ones with a common denominator. However, notice
that all four of the numbers are about 2. Since 2 x 4 = 8,
the answer will be about 8. Notice that only one of the
choices is close to 8.
Answer: B
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
Five-Minute Check (over Lesson 2-6)
Main Idea
Targeted TEKS
Example 1: Solve by Using Addition or Subtraction
Example 2: Solve by Using Addition or Subtraction
Example 3: Solve by Using Multiplication or Division
Example 4: Solve by Using Multiplication or Division
Example 5: Write an Equation to Solve a Problem
• Solve equations involving rational numbers.
Primary Goal of Solving Algebra Equations is:
GET THE VARIABLE BY ITSELF
REMEMBER:
1) Addition And Subtraction are OPPOSITES
2) Multiplication and Division are OPPOSITES
3) Dividing is the same thing as multiplying by the
reciprocal - KCF
4) If I do something to ONE SIDE of the equals sign,
I must do EXACTLY the same thing to the other
side!
Solve by Using Addition or Subtraction
Solve g + 2.84 = 3.62.
g + 2.84 = 3.62
Write the equation.
g + 2.84 – 2.84 = 3.62 – 2.84
Subtract 2.84 from
each side.
g = 0.78
Answer: 0.78
Simplify.
Solve h + 2.65 = 5.73.
A. 3.08
B. 3.26
C. 7.92
D. 8.38
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Solve by Using Addition or Subtraction
Solve by Using Addition or Subtraction
Rename each fraction using
the LCD, 15.
Answer:
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Solve by Using Multiplication or Division
Answer: –33
A. 22
0%
B. 9
C. –12
D. –45
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Solve by Using Multiplication or Division
Answer: –7
Solve 3.4t = –27.2.
A. –12
B. –8
C. –5
D. –2
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Write an Equation to Solve a
Problem
PHYSICS You can determine the rate an object is
traveling by dividing the distance it travels by the
time it takes to cover the distance
If an object
travels at a rate of 14.3 meters per second for 17
seconds, how far does it travel?
Words
Variable
Equation
Rate equals distance divided by time.
Write an Equation to Solve a
Problem
Answer: The object travels 243.1 meters.
PHYSICS You can determine the rate an object is
traveling by dividing the distance it travels by the
time it takes to cover the distance
If an object
travels at a rate of 73 miles per hour for 5.2 hours,
how far does it travel?
0%
D
D. 379.6 miles
A
B
C0%
D
C
C. 288.7 miles
A.
B.
0%C.0%
D.
B
B. 22.3 miles
A
A. 14.1 miles
Five-Minute Check (over Lesson 2-7)
Main Idea
Targeted TEKS
Example 1: Look for a Pattern
• Look for a pattern to solve problems.
8.14 The student applies Grade 8 mathematics to solve
problems connected to everyday experiences,
investigations in other disciplines, and activities in and
outside of school. (C) Select or develop an
appropriate problem-solving strategy from a variety
of different types, including...looking for a
pattern...to solve a problem.
Look for a Pattern
INTEREST The table shows the
amount of interest $3,000 would
earn after 7 years at various
interest rates. How much
interest would $3,000 earn at 6
percent interest?
Explore
You know the amount of interest earned at
interest rates of 1%, 2%, 3%, 4%, and 5%.
You want to know the amount of interest
earned at 6%.
Look for a Pattern
Plan
Look for a pattern in the amounts of
interest earned. Then continue the pattern
to find the amount of interest earned at a
rate of 6%.
Solve
For each increase in interest rate, the
amount of interest earned increases by
$210. So for an interest rate of 6%, the
amount of interest earned would be
$1,050 + $210 = $1,260.
Check
Check your pattern to make sure the
answer is correct.
Answer: $1,260
INTEREST The table below
shows the amount of interest
$5,000 would earn after 3 years
at various interest rates. How
much interest would $5,000
earn at 7 percent interest?
A. $800
B. $900
C. $1,000
D. $1,050
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Five-Minute Check (over Lesson 2-8)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Write Expressions Using Powers
Example 2: Write Expressions Using Powers
Key Concept: Zero and Negative Exponents
Example 3: Evaluate Powers
Example 4: Evaluate Powers
Example 5: Evaluate Powers
• Use powers and exponents in expressions.
• Power
– Repeated multiplication
• Base
– Factor that is repeatedly multiplied
• Exponent
– How many times the Base is multiplied
Exponents
:
Definition:
exponent/power
m
a =
base
.
.
.
.
a a a a a…
“m” number of times
Multiply the base times itself “m” times.
Exponent Rule
Power of 1
a=
or
1
1a
1
a
Any number raised to
the first power is
equal to the number.
=a
If no exponent or coefficient –
it is understood to be one.
Exponent Rule
Power of 0
0
a
=1
Any nonzero number raised to
the zero power is 1.
Exponent Rule
Negative Powers
a
m
1
 m
a
A negative exponent means
to take the reciprocal of that number, then
raise it to the indicated power.
REMEMBER: Negative exponent means FLIP
THE LINE AND CHANGE THE SIGN!
Write Expressions Using Powers
Write 3 ● 3 ● 3 ● 7 ● 7 using exponents.
3 ● 3 ● 3 ● 7 ● 7 = (3 ● 3 ● 3) ● (7 ● 7)
= 33 ● 72
Answer: 33 ● 72
Associative
Property
Definition of
exponents
Write 2 ● 2 ● 2 ● 2 ● 5 ● 5 ● 5 using exponents.
A. 23 ● 53
B. 24 ● 53
C. (2 ● 5)4
D. (2 ● 5)7
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Write Expressions Using Powers
Write p ● p ● p ● q ● p ● q ● q using exponents.
p●p●p●q●p●q●q=p●p●p●p●q●q●q
Commutative Property
= (p ● p ● p ● p) ● (q ● q ● q)
Associative Property
= p4 ● q3
Definition of exponents
Answer: p4 ● q3
Write x ● y ● x ● x ● y ● y ● y using exponents.
A. x3 ● y4
B. x4 ● y3
0%
C. x3 ● y7
D. (x ● y)7
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Evaluate Powers
Evaluate 95.
95 = 9 ● 9 ● 9 ● 9 ● 9
= 59,049
Simplify.
Check using a calculator.
9
5
Definition of exponents
ENTER 59049
Answer: 59,049
Evaluate 65.
A. 30
0%
B. 1,296
C. 6,842
D. 7,776
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Evaluate Powers
Evaluate 3–7.
Answer:
Evaluate 2–5.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Evaluate Powers
ALGEBRA Evaluate x3 ● y5 if x = 4 and y = 2.
x3 ● y5 = 43 ● 25
Replace x with 4 and y with 2.
= (4 ● 4 ● 4) ● (2 ● 2 ● 2 ● 2 ● 2)
Write the powers as products.
= 64 ● 32
Simplify.
= 2,048
Simplify.
Answer: 2,048
ALGEBRA Evaluate x2 ● y4 if x = 3 and y = 4.
A. 576
B. 1,846
C. 2,304
D. 3,112
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 2-9)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Scientific Notation to Standard Form
Example 1: Express Numbers in Standard Form
Example 2: Express Numbers in Standard Form
Key Concept: Standard Form to Scientific Notation
Example 3: Write Numbers in Scientific Notation
Example 4: Write Numbers in Scientific Notation
Example 5: Real-World Example
• Express numbers in scientific notation.
• Scientific Notation
– Compact way of expressing very LARGE or very SMALL
numbers
Rules of Scientific Notation
Example: 3.14 * 104
1) First number MUST be between 1
and 10!!
2) Second number will always be 10
raised to a power.
3) The power will be the number of
places the decimal point moves
•
POSITIVE means to the RIGHT
•
NEGATIVE means to the LEFT
Express Numbers in Standard Form
Write 9.62 × 105 in standard form.
9.62 × 105 = 962,000
Answer: 962,000
The decimal point moves
5 places to the right.
Write 5.32 × 104 in standard form.
A. 532
B. 5,320
C. 53,200
D. 532,000
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Express Numbers in Standard Form
Write 2.85 × 10–6 in standard form.
2.85 × 10–6 = 0.00000285
Answer: 0.00000285
The decimal point moves
6 places to the left.
Write 3.81 × 10–4 in standard form.
A. 0.000381
B. 0.00381
0%
C. 0.0381
D. 0.381
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Write Numbers in Scientific Notation
Write 931,500,000 in scientific notation.
931,500,000 = 9.315 × 100,000,000 The decimal point
moves 8 places.
= 9.315 × 108
Answer: 9.315 × 108
The exponent is
positive.
Write 35,600,000 in scientific notation.
A. 3.56 × 104
B. 3.56 × 105
C. 3.56 × 106
D. 3.56 × 107
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Write Numbers in Scientific Notation
Write 0.00443 in scientific notation.
0.00443 = 4.43 × 0.001
= 4.43 × 10–3
Answer: 4.43 × 10–3
The decimal point moves
3 places.
The exponent is negative.
Write 0.000653 in scientific notation.
A. 6.53 × 10–3
B. 6.53 × 10–4
C. 6.53 × 10–5
D. 6.53 × 10–6
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
PLANETS The table lists the
average radius at the equator for
each of the planets in our solar
system. Order the planets
according to radius from largest
to smallest.
First order the numbers according
to their exponents. Then order the
numbers with the same exponents
by comparing the factors.
Jupiter, Neptune,
Saturn, Uranus
Step 1
7.14
2.43
6.0
2.54
×
×
×
×
104
104
104
104
Earth, Mars, Mercury,
Pluto, Venus
>
6.38
3.40
2.44
1.5
6.05
×
×
×
×
×
103
103
103
103
103
Step 2
7.14 × 104 > 6.0 × 104 > 2.54 × 104 > 2.43 × 104
Jupiter
Saturn
Uranus
Neptune
6.38 × 103 > 6.05 × 103 > 3.40 × 103 > 2.44 × 103 > 1.5 × 103
Earth
Venus
Mars
Mercury
Pluto
Answer: The order from largest to smallest is Jupiter,
Saturn, Uranus, Neptune, Earth, Venus, Mars,
Mercury, and Pluto.
PLANETS The table lists the mass for
each of the planets in our solar system.
Order the planets according to mass from
largest to smallest.
A. Jupiter, Saturn, Neptune, Uranus,
Earth, Venus, Mars, Mercury, Pluto
B. Jupiter, Saturn, Uranus, Neptune,
Earth, Venus, Mercury, Mars, Pluto
0%
D
C
A
B
0% C0%
D
B
D. Pluto, Mercury, Mars, Earth, Venus,
Uranus, Saturn, Neptune, Jupiter
A
C. Saturn, Jupiter, Neptune, Uranus,
Venus, Earth, Mars, Mercury, Pluto
A.
B.
C.
0%
D.
Five-Minute Checks
Image Bank
Math Tools
Multiplying Fractions
Multiplying and Dividing Fractions
Lesson 2-1
(over Chapter 1)
Lesson 2-2
(over Lesson 2-1)
Lesson 2-3
(over Lesson 2-2)
Lesson 2-4
(over Lesson 2-3)
Lesson 2-5
(over Lesson 2-4)
Lesson 2-6
(over Lesson 2-5)
Lesson 2-7
(over Lesson 2-6)
Lesson 2-8
(over Lesson 2-7)
Lesson 2-9
(over Lesson 2-8)
Lesson 2-10
(over Lesson 2-9)
To use the images that are on the
following three slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
(over Chapter 1)
Evaluate 8 + (20 – 3)(2).
A. 22
B. 25
C. 42
D. 50
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Chapter 1)
Evaluate 16 + (–9).
A. 25
B. 7
C. –7
D. –25
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Chapter 1)
Evaluate –7 – 10.
A. 17
0%
B. 3
1.
2.
3.
4.
C. –3
A
B
C
D
D. –17
A
B
C
D
(over Chapter 1)
A. 90
B. 19
C. –19
D. –90
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Chapter 1)
Solve the equation
solution.
Then check your
A. 40
0%
B. 10
C. –10
D. –40
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Chapter 1)
Yasmine earns $0.25 for each cup of lemonade she
sells. She earned $86 last Thursday selling
lemonade. How many cups of lemonade did she sell
last Thursday?
0%
A. 344
1.
2.
3.
4.
B. 2,150
C. 340
A
D. 443
B
A
B
C
D
C
D
(over Lesson 2-1)
Write the fraction
as a decimal.
A. 1.143
B. 0.875
C. 0.78
D. 0.13
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-1)
Write the fraction
as a decimal.
A. –2.4
B. –0.4166
¯
C. 0.416
D. 2.4
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-1)
Write the
A. 2.15
0%
B. 2.3
1.
2.
3.
4.
C. 0.3
A
B
C
D
D. 0.15
A
B
C
D
(over Lesson 2-1)
Write the decimal 0.08 as a fraction in simplest form.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-1)
Write the decimal 1.375 as a mixed number in
simplest form.
A.
0%
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-1)
The largest moth is the Atlas moth. The Atlas moth is
11.8 inches long. Which of the following is the length
of an Atlas moth written as a mixed number?
A.
0%
1.
2.
3.
4.
B.
C.
A
D.
B
A
B
C
D
C
D
(over Lesson 2-2)
Use <, >, or = in
A. <
0%
B. >
C. =
1.
2.
3.
A
B
C
A
B
C
(over Lesson 2-2)
Use <, >, or = in
A. <
0%
B. >
C. =
1.
2.
3.
A
B
C
A
B
C
(over Lesson 2-2)
Use <, >, or = in
A. <
0%
B. >
C. =
1.
2.
3.
A
B
C
A
B
C
(over Lesson 2-2)
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-2)
A.
0%
B.
C.
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
(over Lesson 2-2)
Which number is least?
A.
0%
B. 0.83...
1.
2.
3.
4.
C.
D. 0.61
A
B
A
B
C
D
C
D
(over Lesson 2-3)
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-3)
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-3)
A.
0%
B.
1.
2.
3.
4.
C.
D.
A
B
A
B
C
D
C
D
(over Lesson 2-3)
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-3)
A.
0%
B.
C.
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
(over Lesson 2-3)
Which of the following is 0.032 written as a fraction
in simplest form?
A. 3.2
0%
1.
2.
3.
4.
B.
C.
A
D.
B
A
B
C
D
C
D
(over Lesson 2-4)
Write the multiplicative inverse of 9.
A.
B. 9
C. –9
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-4)
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-4)
A.
0%
B.
1.
2.
3.
4.
C.
D.
A
B
A
B
C
D
C
D
(over Lesson 2-4)
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-4)
A.
B. 1
C. –1
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-4)
A traditional salad dressing requires
and
cup of oil
cup of vinegar per serving. How much oil
is in a half serving?
0%
A.
B.
C.
D. 1 cup
1.
2.
3.
4.
A
B
A
B
C
D
C
D
(over Lesson 2-5)
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-5)
A. 9
B.
C.
D. 1
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-5)
A.
0%
B.
1.
2.
3.
4.
C.
D.
A
B
A
B
C
D
C
D
(over Lesson 2-5)
A.
B. 0
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-5)
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-5)
Julie and Carmen are both long jumpers on the
track team. Julie jumped
jumped
feet and Carmen
feet. How much farther did Julie jump
than Carmen?
A.
B. 1 ft
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-6)
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-6)
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-6)
A.
0%
B.
1.
2.
3.
4.
C.
D.
A
B
A
B
C
D
C
D
(over Lesson 2-6)
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-6)
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-6)
Two-eighths of a class wore green shirts and
of the
class wore white shirts. What fraction of the class
wore either a green or white shirt?
0%
A.
B.
C.
D.
1.
2.
3.
4.
A
B
A
B
C
D
C
D
(over Lesson 2-7)
Solve c + 2.16 = 5. Then check your solution.
A. 7.10
B. 2.84
C. –2.84
D. –16.6
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-7)
A.
B.
C. 12
D. 36
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-7)
Solve –49 – d = –71. Then check your solution.
A. 120
0%
B. 22
1.
2.
3.
4.
C. –22
A
B
C
D
D. –120
A
B
C
D
(over Lesson 2-7)
A. –112
B.
C.
D. 112
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-7)
Solve 9.16 = k – (–2.34). Then check your solution.
A. 3.91
B. 6.82
C. 11.5
D. 21.43
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-7)
A.
0%
1.
2.
3.
4.
B.
C.
A
D.
B
A
B
C
D
C
D
(over Lesson 2-8)
In a stadium there are 10 seats in the 1st row, 13
seats in the 2nd row, 16 seats in the 3rd row, and so
on. How many seats are in the 10th row?
A. 25
B. 31
C. 37
D. 43
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-8)
Find the next three numbers in the sequences 20,
24, 21, 25, 22, 26. . .
A. 28, 32, 29
0%
B. 23, 27, 24
C. 30, 27, 31
D. 24, 28, 25
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-8)
Sarah rents videos from a video rental store that
charges a monthly rate of $9.95 plus $0.75 per video
rental. If Sarah’s total monthly bill was $30.95, how
many videos did she rent?
A. 24
1.
2.
3.
4.
B. 28
0%
C. 30
D. 32
A
B
C
D
A
B
C
D
(over Lesson 2-8)
The Ito family is driving to Oklahoma City from
Houston. If they average 65 miles per hour, how far
will they drive in
hours?
A. 130 miles
B. 162.5 miles
C. 195 miles
D. 227.5 miles
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-9)
Write the expression c  c  c  c  c  c  c  c  c
using exponents.
A. 9c
B. 9c
C. c8
D. c9
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-9)
Write the expression 8  8  8  8  8 using
exponents.
A. 85
B. 84
C. 54
D. 58
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-9)
Write the expression x  y  x  x  y  x  x  x  y
using exponents.
A. (y2)(x6)
0%
B. (y3)(x5)
1.
2.
3.
4.
C. (x6)(y3)
D. (x7)(y2)
A
B
A
B
C
D
C
D
(over Lesson 2-9)
Evaluate 29.
A. 18
B. 81
C. 128
D. 512
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 2-9)
Evaluate 6(–3).
A.
B.
C. 36
D. 216
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 2-9)
Write the following using exponents m  n  m  p 
m  n  m  p  n  m  p.
A. (m3)(n5)(p3)
0%
B. (m3)(n3)(p3)
1.
2.
3.
4.
C. (m5)(n3)(p5)
5
3
3
D. (m )(n )(p )
A
B
A
B
C
D
C
D
This slide is intentionally blank.