Download Lesson 2-3 Multiplying Rational Numbers

Lesson 2-3 Multiplying Rational Numbers
Write in simplest form:
3 8
1. Find  .
7 9
Multiplying Fractions – Multiply
numerator times numerator and
denominator times denominator.
2 4 8
 
3 5 15
3 7
2. Find   .
4 12
1 3
3. Find 3  1 .
5 4
4. Evaluate prq if
4
2
7
p = , r =  , and q = .
5
3
8
a c ac
 
b d bd
where b  0, d  0.
Cross-Cancel – Divide a numerator and
denominator by the same number.
5 31 5
  
6 2 8 16
Multiplying Mixed Numbers:
1. Backwards C (multiply, then add).
2. Cross cancel.
3. Multiply.
1
2 9 3 8 4 12
4 2   
 12
2
3 21 31
1
1
gallons
2
of water per minute. If family members
1
shower a total of 2 hours per week,
3
about how much water does the family
use for showers each week?
5. Low-flow showerheads use 2
Glencoe Math App & Con (2006) – Course 3
Lesson 2-4 Dividing Rational Numbers
Find the multiplicative inverse:
5
1
1.  2
2. 
8
3
3. 7
4.  2
4
7
Write in simplest form:
3 2
5.
 .
10 5
Inverse Property of Multiplication – Any
number times it’s reciprocal (multiplicative
inverse) equals 1.
2 3
 1
3 2
a b
 1
b a
Divide Fractions – Multiply by the
multiplicative inverse.
Why does this work?
4 2 42 2
 

9 3 93 3
6.
7.
6
 12 .
7
4 2 4 3 12  6 2
   

9 3 9 2 18  6 3
2  8
  .
7  9
1  1
8. 3    2  .
4  8
9. One summer day, a cinema shows a
1
hit action movie repeatedly for 12
2
hours. It takes about 150 minutes to run
the movie and prepare for the next
showing. How many times does the
cinema show the movie that day?
Glencoe Math App & Con (2006) – Course 3
Lesson 2-5 Adding and Subtracting Like Fractions
Write in simplest form:
5 7
1.  .
9 9
2. 
5 1
 .
6 6
1  5
3.      .
6  6
Add Like Fractions – Add the numerators
and write the sum over the denominator.
1 1 11 2
 

3 3
3
3
a b ab
, where c  0
 
c c
c
5  7  5  (7)
2
1
   
 
8  8
8
8
4
Add mixed numbers:
4.
3  15 
  .
16  16 
5. 
7
9
 .
10 10
4 7
6.
 .
15 15
7.
1  4
  .
9  9
8. In the U.S., the average 9-year-old girl
4
is 53 inches tall. The average height of
5
1
a 16-year-old girls is 64 inches. How
5
much does an average girl grow from
age 9 to age 16?
7
4
74
11
2
5  8  (5  8) 
 13   14
9
9
9
9
9
Subtract fractions – Instead of subtract,
add the opposite.
3  11  3  (11) 3  11 14
1
   

 1
13  13 
13
13
13 13
Subtract mixed numbers:
1
3 241  235 6
2 1
60  58 
 1 1
4
4
4
4 4 2
Glencoe Math App & Con (2006) – Course 3
Lesson 2-6 Adding and Subtracting Unlike Fractions
Write in simplest form:
1  2
1.     .
5  7
Add/Subtract Unlike Fractions:
1. Identify the least common (multiple)
denominator.
2. Rename the fractions so they have
common denominators.
3. Add or subtract the numerators.
4. Simplify.
1  3
2.      .
3  4

3. 
1 7
 .
2 8
2  3
2 8  3  3  16  (9)
          
3  8
3 8  8 3
24

 16  9
7

24
24
1
1
4.  3  8 .
2
3
3
1
5. 2  6 .
4
3
6. During January, Nikki watched
1
television 2 hours the first week,
4
1
3
2 hours the second week, 1 hours the
8
4
1
third week, and 1 hours the fourth
2
week. How much time did she watch
television during the 4-week period?
5
5
A. 4 hours
B. 7 hours
8
8
C. 10
5
hours
8
C. 12
5
hours
8
Glencoe Math App & Con (2006) – Course 3
Lesson 2-7 Solving Equations with Rational Numbers
Solve and check each solution.
1. r – 7.81 = 4.32
Opposite operation solves all equations.
3
1
1
23
=
=
= 
4
4
2
4
3
3


4
4
t
2. 7.2v = –36
3. s 
4. 
4
2
=
5
3
4
1
z
5
10
5.
2
3
 n
3
5
6.
 21 
7
c
11
7. 9.7t = -67.9
8. You can determine the rate an object
is traveling by dividing the distance it
travels by the time it takes to cover that
d

distance  r   . If an object travels at a
t

rate of 14.3 meters per second for 17
seconds, how far does it travel?
Glencoe Math App & Con (2006) – Course 3
Lesson 2-8 Powers and Exponents
1. Write p  p  p  q  p  q  q using
exponents.
The base is the
number that is
multiplied.
{
24
The exponent tells
how many times
the base is used as
a factor.
Evaluate:
2. 33
3. 26
4. 25  52
5. 42  34
6. 3-7
7. 8-2
8. 2-3
The number that is
expressed using an
exponent is called a power.
24 = 2  2  2  2 = 16
Zero Exponents equal 1 so long as x doesn’t
equal zero.
50 = 1
x0 = 1, x  0
Negative Exponents is 1 divided by the
number to the nth power so long as x
doesn’t equal zero.
1
1
=
7  7  7 147
1
x-n = n , x  0
x
7-3 =
9. x3  y5 if x = 4 and y = 2.
Glencoe Math App & Con (2006) – Course 3
Lesson 2-9 Scientific Notation
Convert to standard notation:
1. 9.62 x 105
2. 3.6 x 106
3. 2.85 x 10-6
Scientific Notation is a number that is
written as the product of a factor and a
power of 10.
7.325 x 103
3.12 x 10-4
The exponent
tells how many
times to move the
decimal right or
left.
The number before the
decimal must be between
1 and 10.
4. 6.1 x 10-3
Positive Exponent – decimal moves right.
Write in scientific notation.
5. 931,500,000
6. 72,100
5.34 x 104 = 53,400
Negative Exponent – decimal moves left.
5.34 x 10-4 = 0.000534
7. 0.00443
8. 0.0000231
Standard Form – regular number form.
9. The following 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.
Planet
Radius (km)
Earth
6.38 x 103
Jupiter
7.14 x 104
Mars
3.40 x 103
Mercury
2.44 x 103
Neptune
2.43 x 104
Pluto
1.5 x 103
Saturn
6.0 x 104
Uranus
2.54 x 104
Venus
6.05 x 103
Glencoe Math App & Con (2006) – Course 3
Lesson 2-1 Fractions and Decimals
Write each fraction as a decimal.
1.
3
16
2. 3
2
11
3. Agriculture – A Florida 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.
Rational Number – any number that
can be written as a fraction.
Terminal decimal - when the division
ends.
Repeating Decimal – when the digits
repeat in a pattern.
Bar Notation – putting a bar over the
part that repeats.
0.353535…≈ 0. 35
We use the “≈” because it isn’t exactly,
but approximately.
To Change a Fraction to a Decimal:
Divide by the denominator to get a
decimal.
3.125 = 3 125  25 = 3 5  5 = 3 1
1,000  25
4. Write 0.32 as a fraction.
5. Write 2.7 as a mixed number in
simplest form.
40  5
8
To Change a repeating decimal to a
fraction:
1. Make the decimal = N.
2. Multiply the decimal by a
multiple of 10 so the repeating
part is now before the decimal.
3. Subtract and solve as an
algebraic problem.
10N = 1. 1
- N = - 0. 1
9N = 1
9
9
N=
1
9
100N = 335. 35
- N = - 3. 35
99N = 332
99
99
N=3
35
99
Glencoe Math App & Con (2006) – Course 3
Lesson 2-2 Comparing and Ordering Rational Numbers
Compare each of the following:
1.
3
7
8
13
2.
5
6
7
9
3. – 6.7
3
–6
4
Comparing Fractions – just multiply.
5
8
5 4
20
3
4
83
24
Since 24 is greater than 20,
greater than
4. –
5
7
3
is
4
5
.
8
– 0.7
To compare a fraction and a decimal,
change on form into the other, then
compare.
5. Chemistry – The values for
approximate densities of various
substances are shown in the table
below. Order the densities from
least to greatest.
Substances
Density (g/cm3)
aluminum
2.7
beryllium
1.87
brick
4
1
5
crown glass
1
2
4
fused silica
2. 2
marble
3
2
5
nylon
1.1
pyrex glass
2.32
rubber neoprene 1. 3
– 5.2
– 5.2
1
4
– 5.25
–5
Glencoe Math App & Con (2006) – Course 3