Transcript 3-4

Page 124 #33-64 ANSWERS
Student Learning Goal Chart
Lesson Reflection
Pre-Algebra Learning Goal
Students will
understand rational
and real numbers.
Students will understand rational and real numbers
by being able to do the following:
• Learn to write rational numbers in equivalent forms (3.1)
• Learn to add and subtract decimals and rational numbers with like
denominators (3.2)
• Learn to add and subtract fractions with unlike denominators (3.5)
• Learn to multiply fractions, decimals, and mixed numbers (3.3)
• Learn to divide fractions and decimals (3.4)
3-4 Dividing Rational Numbers
Today’s Learning Goal Assignment
Learn to divide
fractions and
decimals.
Pre-Algebra
3-4 Dividing Rational Numbers
Pre-Algebra HW
Page 129
#24-57 all
Pre-Algebra
Rational
Numbers
3-4
Dividing
Rational
Numbers
3-4 Dividing
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
3-4 Dividing Rational Numbers
Warm Up
Multiply.
1. –3
5
6
2. –15 –
1
–2 2
2
3
10
3. 0.05(2.8)
0.14
4. –0.9(16.1)
–14.49
Pre-Algebra
3-4 Dividing Rational Numbers
Problem of the Day
Katie made a bookshelf that is 5 feet long.
The first 6 books she put on it took up 8
inches of shelf space. About how many
books should fit on the shelf?
45 books
Pre-Algebra
3-4 Dividing Rational Numbers
Today’s Learning Goal Assignment
Learn to divide
fractions and
decimals.
Pre-Algebra
3-4 Dividing Rational Numbers
Vocabulary
reciprocal
Pre-Algebra
3-4 Dividing Rational Numbers
A number and its reciprocal have a product of 1.
To find the reciprocal of a fraction, exchange the
numerator and the denominator. Remember that
an integer can be written as a fraction with a
denominator of 1.
Pre-Algebra
3-4 Dividing Rational Numbers
Multiplication and division are inverse operations.
They undo each other.
1
2 ÷ 2
=
15
5
3
Notice that multiplying by the reciprocal gives the
same result as dividing.
1
2 5
2•5
=
=
15 2
15 • 2
3
1 2 = 2
15
3 5
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 1A: Dividing Fractions
Divide. Write the answer in simplest form.
A.
1
5
÷
2
11
1 = 5
2
5
÷
Multiply by the reciprocal.
•
2
11
11 1
=
2
5
No common factors.
•
11 1
10
=
11
Pre-Algebra
Simplest form
3-4 Dividing Rational Numbers
Additional Example 1B: Dividing Fractions
Divide. Write the answer in simplest form.
B. 2 3 ÷ 2
8
÷
2 38 ÷ 2 = 19
8
2
1
19 1
8 2
19 • 1
=
8•2
=
Write as an improper fraction.
Multiply by the reciprocal.
No common factors
19
3 19 ÷ 16 = 1 R 3
= 16 = 1 16
Pre-Algebra
3-4 Dividing Rational Numbers
Try This: Example1A
Divide. Write the answer in simplest form.
A.
3
7
÷
4
15
3
4
7
7
÷
Multiply by the reciprocal.
=
•
4
15
15 3
7 • 4 No common factors.
=
15 • 3
28
=
45
Pre-Algebra
Simplest form
3-4 Dividing Rational Numbers
Try This: Example1B
Divide. Write the answer in simplest form.
B.
2
45÷3
22
3
÷
5
1
Write as an
improper fraction.
= 5
22 1
3
Multiply by the reciprocal.
22 • 1
=
5•3
No common factors.
22
7
1
= 15 or 15
22 ÷ 15 = 1 R 7
4 25 ÷ 3 =
Pre-Algebra
3-4 Dividing Rational Numbers
When dividing a decimal by a decimal,
multiply both numbers by a power of 10 so
you can divide by a whole number. To decide
which power of 10 to multiply by, look at the
denominator. The number of decimal places
is the number of zeros to write after 1.
1.32
1.32 10
13.2
=
=
4
0.4
0.4 10
1 decimal place
Pre-Algebra
1 zero
3-4 Dividing Rational Numbers
Additional Example 2: Dividing Decimals
Divide.
0.384 ÷ 0.24
0.384 ÷ 0.24 = 0.384 100 = 38.4
100
0.24
24
= 38.4
24
= 1.6
Pre-Algebra
Divide.
3-4 Dividing Rational Numbers
Try This: Example 2
Divide.
0.585 ÷ 0.25
0.585 ÷ 0.25 = 0.585 100 = 58.5
100
0.25
25
= 58.5 Divide.
25
= 2.34
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 3A: Evaluating Expressions with
Fractions and Decimals
Evaluate the expression for the given value of
the variable.
A.
5.25 for n = 0.15
n
5.25 100
5.25
=
0.15
0.15 100
=
525
15
= 35
Pre-Algebra
0.15 has 2 decimal
places, so use 100 .
100
Divide.
3-4 Dividing Rational Numbers
Additional Example 3B: Evaluating Expressions with
Fractions and Decimals
Evaluate the expression for the given value of
the variable.
B.
4
k÷
for k = 5
5
4 = 5 • 5
5÷
1
4
5
5•5
1
25
=6
=
=
4
4
1•4
Pre-Algebra
3-4 Dividing Rational Numbers
Try This: Example 3A
Evaluate the expression for the given value of
the variable.
2.55
A.
for b = 0.75
b
2.55 100
2.55
=
0.75 100
0.75
= 255
75
= 3.4
Pre-Algebra
0.75 has 2 decimal
places, so use 100 .
100
Divide.
3-4 Dividing Rational Numbers
Try This: Example 3B
Evaluate the expression for the given value of
the variable.
4
B. u ÷ , for u = 9
7
9 7
Write as in improper fraction
4
9÷ 7 = 1 4
and multiply by the reciprocal.
Pre-Algebra
9•7
=
1•4
No common factors.
3
= 15 4
63 ÷ 4 = 15 R 3
3-4 Dividing Rational Numbers
Additional Example 4: Problem Solving Application
1
A cookie recipe calls for 2 cup of oats. You
have 3 cup of oats. How many batches of
4
1
cookies can you bake using all of the oats
you have?
Understand the Problem
The number of batches of cookies you can
bake is the number of batches using the
oats that you have. List the important
information:
3
The amount of oats is cup.
4
1
One batch of cookies calls for cup
2
of oats.
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 4 Continued
2
Make a Plan
Set up an equation.
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 4 Continued
3
Solve
Let n = number of batches.
3
1
÷2 =n
4
2
3
• =n
1
4
6
1
, or 1 2 batches of the cookies.
4
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 4 Continued
4
Look Back
1
One cup of oats would make two batches so 1
2
is a reasonable answer.
Pre-Algebra
3-4 Dividing Rational Numbers
Try This: Example 4
A ship will use 1 of its total fuel load for a typical
6
round trip. If there is 7 of a total fuel load on
8
board now, how many complete trips can be
made?
Pre-Algebra
3-4 Dividing Rational Numbers
Try This: Example 4 Continued
1
Understand the Problem
The number of complete trips the ship can
make is the number of trips that the ship
can make with the fuel on board. List the
important information:
1
It takes 6 of the total fuel load for a complete
trip. You have 7 of a total fuel load on board
8
right now.
Pre-Algebra
3-4 Dividing Rational Numbers
Try This: Example 4 Continued
2
Make a Plan
Set up an equation.
Amount of
fuel on board
Pre-Algebra
÷
Amount of fuel
for one trip
=
Number of
trips
3-4 Dividing Rational Numbers
Try This: Example 4 Continued
3
Solve
Let t = number of trips.
5
1
÷ =t
8
6
6
5
• 1 =t
8
30
3
, or 3 4 round trips, or 3 complete
8
round trips.
Pre-Algebra
3-4 Dividing Rational Numbers
Try This: Example 4 Continued
4
Look Back
A full tank will make the round trip 6
times, and 5 is a little more than 1 , so
8
2
half of 6, or 3, is a reasonable answer.
Pre-Algebra
3-4 Dividing Rational Numbers
Lesson Quiz: Part 1
Divide.
5
1. 2 6
1
÷ –1
2
8
–1 9
2. –14 ÷ 1.25
–11.2
3. 3.9 ÷ 0.65
6
112
4. Evaluate x for x = 6.3.
17.7
Pre-Algebra
3-4 Dividing Rational Numbers
Lesson Quiz: Part 2
5. A penny weighs 2.51 grams. How
many pennies would it take to equal
one pound (453.6 grams)?
181
Pre-Algebra