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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)
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
Pre-Algebra HW
Page 129#24-57 all
Pre-Algebra
3-4 Dividing Rational Numbers3-4 Dividing Rational Numbers
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
3-4 Dividing Rational Numbers
Warm UpMultiply.
Pre-Algebra
3-4 Dividing Rational Numbers
1. 5 6–3 1
2–2
2. 23–15 –
3. 0.05(2.8)
4. –0.9(16.1)
10
0.14
–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
reciprocal
Vocabulary
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.
Notice that multiplying by the reciprocal gives the same result as dividing.
1 3
2 5
2 15
= 2 5
=÷2 15
1 3
= 1 3=
2 • 5 15 • 2
5 2
2 15
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 1A: Dividing Fractions
Divide. Write the answer in simplest form.
Multiply by the reciprocal.
5 11
÷ 1 2
5 11
•2 1
=
No common factors.
5 11
÷ 1 2
10 11=
A.
Simplest form
5 11
•2 1
=
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 1B: Dividing Fractions
Divide. Write the answer in simplest form.
B. 3 8
÷ 22
3 8
÷ 22 = 19 8
2 1÷ Write as an improper fraction.
Multiply by the reciprocal.
No common factors
= 19 8
1 2
19 • 18 • 2
=
3 16
=1 19 ÷ 16 = 1 R 319 16=
Pre-Algebra
3-4 Dividing Rational Numbers
7 15
÷ 3 4
7 15
• 4 3
=7 15
÷ 3 4
28 45
=
Try This: Example1A
Divide. Write the answer in simplest form.
A.
Multiply by the reciprocal.
No common factors.
Simplest form
7 • 415 • 3
=
Pre-Algebra
3-4 Dividing Rational Numbers
Write as an improper fraction.
2 5 ÷
Multiply by the reciprocal.
34
22 • 15 • 3
= No common factors.
22 ÷ 15 = 1 R 7
2 5 ÷ 34 = 22
53 1÷
B.
Divide. Write the answer in simplest form.
= 22 5
1 3
7 15= or 122
15
Try This: Example1B
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.
13.24
=1.320.4
= 1.320.4
1 decimal place 1 zero
1010
Pre-Algebra
3-4 Dividing Rational Numbers
= 1.6
38.424
=
0.384 ÷ 0.24
Additional Example 2: Dividing Decimals
Divide.
0.3840.24
0.384 ÷ 0.24 = 100100
Divide.38.424
=
Pre-Algebra
3-4 Dividing Rational Numbers
= 2.34
58.525
=
0.585 ÷ 0.25
Try This: Example 2
0.5850.25
0.585 ÷ 0.25 = 100100
Divide.
Divide.58.525
=
Pre-Algebra
3-4 Dividing Rational Numbers
5.25 for n = 0.15n
Divide.
= 35
Additional Example 3A: Evaluating Expressions with Fractions and Decimals
Evaluate the expression for the given value of the variable.
5.250.15
5.250.15
=100100 100
100
0.15 has 2 decimal
places, so use .
52515=
A.
Pre-Algebra
3-4 Dividing Rational Numbers
k ÷ for k = 54 5
5 ÷ 5 4
= 5 1
•4 5
1 46
B.
5 • 51 • 4
= == 254
Additional Example 3B: Evaluating Expressions with Fractions and Decimals
Evaluate the expression for the given value of the variable.
Pre-Algebra
3-4 Dividing Rational Numbers
2.55for b = 0.75
b
Divide.
= 3.4
Try This: Example 3A
2.550.75
2.550.75
= 100100
25575
=
A.
Evaluate the expression for the given value of the variable.
100 100
0.75 has 2 decimal
places, so use .
Pre-Algebra
3-4 Dividing Rational Numbers
u ÷ , for u = 9
Write as in improper fraction and multiply by the reciprocal.
9 • 71 • 4
= No common factors.
4 7
63 ÷ 4 = 15 R 3
= 9 19 ÷ 4
7
= 3 415
7 4
B.
Try This: Example 3B
Evaluate the expression for the given value of the variable.
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 4: Problem Solving Application
A cookie recipe calls for cup of oats. You have cup of oats. How many batches of cookies can you bake using all of the oats you have?
34
1 2
11 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:
The amount of oats is cup.
One batch of cookies calls for cup of oats.
12
34
Pre-Algebra
3-4 Dividing Rational Numbers
Additional Example 4 Continued
Set up an equation.
22 Make a Plan
Pre-Algebra
3-4 Dividing Rational Numbers
Let n = number of batches.
Solve33
12
34 = n÷
34
21
= n•
64 , or 1 batches of the cookies.1
2
Additional Example 4 Continued
Pre-Algebra
3-4 Dividing Rational Numbers
Look Back44
One cup of oats would make two batches so 1 is a reasonable answer.
12
Additional Example 4 Continued
Pre-Algebra
3-4 Dividing Rational Numbers
Try This: Example 4
A ship will use of its total fuel load for a typical
round trip. If there is of a total fuel load on
board now, how many complete trips can be
made?
1 6 7
8
Pre-Algebra
3-4 Dividing Rational Numbers
It takes of the total fuel load for a complete
trip. You have of a total fuel load on board
right now.
78
1 6
11 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:
Try This: Example 4 Continued
Pre-Algebra
3-4 Dividing Rational Numbers
Set up an equation.
22 Make a Plan
Amount of fuel on board
Amount of fuel for one trip
Number of trips
÷ =
Try This: Example 4 Continued
Pre-Algebra
3-4 Dividing Rational Numbers
Let t = number of trips.
Solve33
58
16
= t÷
61
= t•58
, or 3 round trips, or 3 complete round trips.
308
34
Try This: Example 4 Continued
Pre-Algebra
3-4 Dividing Rational Numbers
Look Back44
Try This: Example 4 Continued
A full tank will make the round trip 6
times, and is a little more than , so
half of 6, or 3, is a reasonable answer.
58
12
Pre-Algebra
3-4 Dividing Rational Numbers
Lesson Quiz: Part 1
Divide.
1.
2. –14 ÷ 1.25
4. Evaluate for x = 6.3.112
x
3. 3.9 ÷ 0.65 6
–11.2
–1 89
÷5 62 1
2–1
17.7
Pre-Algebra
3-4 Dividing Rational Numbers
A penny weighs 2.51 grams. How many pennies would it take to equal one pound (453.6 grams)?
Lesson Quiz: Part 2
5.
181