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11/18-19 Multiply Fractions & Decimals #42
LT: I will learn to multiply mixed numbers, fractions, and
decimals.
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
Today’s Plan:
-Warm up & correct homework
-Lesson
-Assignment
3. 3 2 17
5 5
Learning Target: I will learn to
multiply mixed numbers,
fractions, and decimals.
RULES FOR MULTIPLYING TWO
RATIONAL NUMBERS
If the signs of the factors are the same,
the product is positive.
(+) • (+) = (+)
(–) • (–) = (+)
If the signs of the factors are different, the
product is negative.
(+) • (–) = (–)
(–) • (+) = (–)
Multiply. Write the answer in simplest form.
A. –8 6
7
–8 • 6
7
–48
Multiply
7
6
–6
Simplify
7
Multiply. Write the answer in simplest form.
B. 2 5 13
2
16
3
32
3
10
1
53
5(3) + 1
= 3
Multiply
2
3
Simplify
=
16
3
Multiply. Write the answer in simplest form.
A. –3
5
8
–3 • 5
8
–15
8
7
–1
8
Multiply
Simplify
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
3
5
Simplify
37
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.
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.
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
=
3
28
Simplest form
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
Multiply denominators.
Look for common factors: 2, 3.
1
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
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
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
Multiply numerators.
Multiply denominators.
Look for common factors: 4, 7.
1
Simplest form
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)
=
91
1
or 2
45
45
9
Write as an improper
fraction.
Multiply numerators.
Multiply denominators.
91 ÷ 45 = 2 R 1
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.
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.
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
–125 ÷ 8 = –15 R5
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
2
7
=
–25
8
=
–25 • 2 1
4 8•7
=–
25
28
Substitute
2
7
for x.
Write as an
improper fraction.
Look for common
factors: 2.
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
24
5
6
7
for x.
Write as an
improper fraction.
–28 6
7
5
=–
Substitute
Look for common
factors: 7.
, or – 4 45
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
4
5
–84 ÷ 5 = –16 R4
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
Assignment
Pg 124
18-24 even and 36-56 even