Transcript Document

Page 133 #14-26 ANSWERS
Student Learning Goal Chart
Lesson Reflections
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)
3-3 Multiplying Rational Numbers
Today’s Learning Goal Assignment
Learn to multiply
fractions,
decimals, and
mixed numbers.
Pre-Algebra
3-3 Multiplying Rational Numbers
Pre-Algebra HW
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#33-64 all
Pre-Algebra
3-3
3-3 Multiplying
MultiplyingRational
RationalNumbers
Numbers
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
3-3 Multiplying Rational Numbers
Warm Up
Write each number as an improper fraction.
1. 2 1
3
7
3
2. 1 7
8
15
8
4. 6 2
3
20
3
5. 5 3
8
43
8
Pre-Algebra
3. 3 2 17
5 5
3-3 Multiplying Rational Numbers
Problem of the Day
The sum of three consecutive integers is
168. What are the three integers?
55, 56, and 57
Pre-Algebra
3-3 Multiplying Rational Numbers
Today’s Learning Goal Assignment
Learn to multiply
fractions,
decimals, and
mixed numbers.
Pre-Algebra
3-3 Multiplying Rational Numbers
Kendall invited 36 people to a party. She
needs to triple the recipe for a dip, or multiply
the amount of each ingredient by 3.
Remember that multiplication by a whole
number can be written as repeated addition.
Repeated addition
1
1
1
3
=
+
+
4
4
4
4
Multiplication
1 =3•1 = 3
3
4
4
4
Notice that multiplying a fraction by a whole
number is the same as multiplying the whole
number by just the numerator of the fraction
and keeping the same denominator.
Pre-Algebra
3-3 Multiplying Rational Numbers
RULES FOR MULTIPLYING TWO
RATIONAL NUMBERS
If the signs of the factors are the same,
the product is positive.
(+) • (+) = (+) or (–) • (–) = (+)
If the signs of the factors are different, the
product is negative.
(+) • (–) = (–) or (–) • (+) = (–)
Pre-Algebra
3-3 Multiplying Rational Numbers
Additional Example 1A: Multiplying a Fraction and an
Integer
Multiply. Write the answer in simplest form.
A. –8 6
7
Helpful Hint
–8 • 6
7
–48
=
Multiply
7
6
= –6
Simplify
7
number, divide:
=
Pre-Algebra
To write
12
5
12
5
as a mixed
= 2 R2
2
=2 5
3-3 Multiplying Rational Numbers
Additional Example 1B: Multiplying a Fraction and an
Integer
Multiply. Write the answer in simplest form.
B. 2 5 13
=2
=
16
3
32
3
= 10
Pre-Algebra
1
53
5(3) + 1
= 3
Multiply
2
3
Simplify
=
16
3
3-3 Multiplying Rational Numbers
Try This: Example 1A
Multiply. Write the answer in simplest form.
A. –3
5
8
–3 • 5
=
8
–15
=
8
7
= –1
8
Pre-Algebra
Multiply
Simplify
3-3 Multiplying Rational Numbers
Try This: Example 1B
Multiply. Write the answer in simplest form.
B. 4 9
2
5
47
=4
5
2
9(5) + 2 47
9
=
=
5
5
5
188
=
5
Multiply
= 37 3
5
Simplify
Pre-Algebra
3-3 Multiplying Rational Numbers
3
5
•
2
3
A model of
is shown. Notice that to
multiply fractions, you multiply the
numerators and multiply the denominators.
3
5
•
•
2
3
=
6
15
=
If you place the first rectangle on top of the
second, the number of green squares
represents the numerator, and the number of
total squares represents the denominator.
Pre-Algebra
3-3 Multiplying Rational Numbers
To simplify the product, rearrange the six green
squares into the first two columns. You can see
that this is 25 .
=
6
15
=
2
5
Helpful Hint
A fraction is in lowest terms, or simplest form,
when the numerator and denominator have
no common factors.
Pre-Algebra
3-3 Multiplying Rational Numbers
Additional Example 2A: Multiplying Fractions
Multiply. Write the answer in simplest form.
A. 1 6
8 7
1(6)
=
8(7)
Multiply numerators.
Multiply denominators.
3
1(6)
=
8(7)
Look for common factors: 2.
4
=
Pre-Algebra
3
28
Simplest form
3-3 Multiplying Rational Numbers
Additional Example 2B: Multiplying Fractions
Multiply. Write the answer in simplest form.
B.
2 9
–
3 2
–2(9)
=
3(2)
–1
3
–2(9)
=
3(2)
Multiply numerators.
= –3
Simplest form
1
Pre-Algebra
Multiply denominators.
Look for common factors: 2, 3.
1
3-3 Multiplying Rational Numbers
Additional Example 2C: Multiplying Fractions
Multiply. Write the answer in simplest form.
C.
3
4
7
1
2
43
1
2
7
= 31 1
7
2
Write as an improper
fraction.
31(1)
=
7(2)
Multiply numerators.
Multiply denominators.
31
3
=
or 2
14
14
31 ÷ 14 = 2 R3
Pre-Algebra
3-3 Multiplying Rational Numbers
Try This: Example 2A
Multiply. Write the answer in simplest form.
A.
3 5
5 8
3(5)
=
5(8)
Multiply numerators.
Multiply denominators.
1
3(5)
=
5(8)
Look for common factors: 5.
3
=
8
Simplest form
1
Pre-Algebra
3-3 Multiplying Rational Numbers
Try This: Example 2B
Multiply. Write the answer in simplest form.
B. – 7 4
8 7
–7(4)
=
8(7)
–1
1
–7(4)
=
8(7)
2
1
=–
2
Pre-Algebra
Multiply numerators.
Multiply denominators.
Look for common factors: 4, 7.
1
Simplest form
3-3 Multiplying Rational Numbers
Try This: Example 2C
Multiply. Write the answer in simplest form.
C. 2 3 7
5 9
23
5
7
9
= 13 7
5
13(7)
=
5(9)
=
Pre-Algebra
91
1
or 2
45
45
9
Write as an improper
fraction.
Multiply numerators.
Multiply denominators.
91 ÷ 45 = 2 R 1
3-3 Multiplying Rational Numbers
Additional Example 3: Multiplying Decimals
Multiply.
A. 2(–0.51)
2 • (–0.51) = –1.02
Product is negative
with 2 decimal places.
B. (–0.4)(–3.75)
Product is
(–0.4) • (–3.75) = 1.500 positive with 3
decimal places.
= 1.500
You can drop the zeros after the decimal point.
Pre-Algebra
3-3 Multiplying Rational Numbers
Try This: Example 3
Multiply.
A. 3.1 (0.28)
3.1 • (0.28) = 0.868
Product is positive
with 3 decimal places.
B. (–0.4)(–2.53)
(–0.4) • (–2.53) = 1.012 Product is positive
with 3 decimal places.
Pre-Algebra
3-3 Multiplying Rational Numbers
Additional Example 4A: Evaluating Expressions with
Rational Numbers
Evaluate –3
A. x = 5
1
x for the value of x.
8
1
–3 8
x
1
= –3 8 (5)
Substitute 5 for x.
–25
=
(5)
8
Write as an improper
fraction.
–125
=
8
= –15 5
8
Pre-Algebra
–125 ÷ 8 = –15 R5
3-3 Multiplying Rational Numbers
Additional Example 4B: Evaluating Expressions with
Rational Numbers Continued
Evaluate –3
B. x = 2
7
1
x for the value of x.
8
1
–3 8
x
1
2
7
= –3 8
=
=
–25 • 2 1
4 8•7
=–
Pre-Algebra
2
7
–25
8
25
28
Substitute
2
7
for x.
Write as an
improper fraction.
Look for common
factors: 2.
3-3 Multiplying Rational Numbers
Try This: Example 4A
3
Evaluate –5 y for the value of y.
5
A. y =
6
7
–5
3
5
y
= –5
=
3
5
6
7
–4–28 • 6
=
5•71
Pre-Algebra
24
5
6
7
for x.
Write as an
improper fraction.
–28 6
7
5
=–
Substitute
Look for common
factors: 7.
, or – 4 45
3-3 Multiplying Rational Numbers
Try This: Example 4B
3
Evaluate –5 y for the value of y.
5
B. y = 3
3
–5 5
y
= –5 35 (3) Substitute 3 for y.
Write as an
(3)
= –28
5
improper fraction.
=
–84
5
= –16
Pre-Algebra
4
5
–84 ÷ 5 = –16 R4
3-3 Multiplying Rational Numbers
Lesson Quiz: Part 1
Multiply.
1
1. 9
7
2 5
2. – 8
3
2
17
5
–12
3. –0.47(2.2)
–1.034
1
4. Evaluate 2 2 (x) for x = 4.
5
2
Pre-Algebra
3-3 Multiplying Rational Numbers
Lesson Quiz: Part 2
5. Teri is shopping for new shoes. Her
mom has agreed to pay half the cost
(and all the sales tax). The shoes that
Teri likes are normally $30 a pair but
are on sale for 13 off. How much money
does Teri need to buy the shoes? $10
Pre-Algebra