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)
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
Pre-Algebra HW
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Pre-Algebra
3-3 Multiplying Rational Numbers3-3 Multiplying Rational Numbers
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
3-3 Multiplying Rational Numbers
Warm UpWrite each number as an improper fraction.
Pre-Algebra
3-3 Multiplying Rational Numbers
1. 13
2 73
2. 78
1 15 8
3. 25
3 17 5
4. 23
6 203
5. 38
5 438
Pre-Algebra
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.
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.
1 4
3 4
1 4
+ + =
Repeated
addition1 4 3 3
4= =
Multiplication3 • 1
414
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.
If the signs of the factors are different, the product is negative.
(+) • (+) = (+) or (–) • (–) = (+)
(+) • (–) = (–) or (–) • (+) = (–)
Pre-Algebra
3-3 Multiplying Rational Numbers
–8 6 7
Multiply. Write the answer in simplest form.
Multiply
Simplify
–48 7
=
–6 6 7
=
–8 • 6 7
=
To write as a mixed
number, divide:
Helpful Hint
12 5
125 = 2 R2
2 5= 2
Additional Example 1A: Multiplying a Fraction and an Integer
A.
Pre-Algebra
3-3 Multiplying Rational Numbers
2 1 3
Multiply
Simplify 10 2 3=
16 3=2
32 3=
5
5(3) + 1 3= =1 35 16
3
Multiply. Write the answer in simplest form.
Additional Example 1B: Multiplying a Fraction and an Integer
B.
Pre-Algebra
3-3 Multiplying Rational Numbers
–3 5 8
Multiply. Write the answer in simplest form.
Multiply
Simplify
–15 8
=
–1 7 8
=
–3 • 5 8
=
Try This: Example 1A
A.
Pre-Algebra
3-3 Multiplying Rational Numbers
4 2 5
Multiply
Simplify 37 3 5
=
47 5
= 4
188 5
=
9
9(5) + 2 5
= =2 5
9 47 5
Try This: Example 1B
B.
Multiply. Write the answer in simplest form.
Pre-Algebra
3-3 Multiplying Rational Numbers
A model of is shown. Notice that to multiply fractions, you multiply the numerators and multiply the denominators.
3 5 • 2
3
35
•
•
=
= 6 15
23
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 .2
5
=
= 2 5
6 15
A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors.
Helpful Hint
Pre-Algebra
3-3 Multiplying Rational Numbers
1(6) 8(7)=
Multiply. Write the answer in simplest form.
6 7
Simplest form3 28
=
1 8
=1(6) 8(7)
Multiply numerators.
Multiply denominators.
Look for common factors: 2.3
4
Additional Example 2A: Multiplying Fractions
A.
Pre-Algebra
3-3 Multiplying Rational Numbers
–2(9) 3(2)=
=–2(9) 3(2)
3
1
Simplest form–3=
Multiply numerators.
Multiply denominators.
Look for common factors: 2, 3.
9 2
2 3
–
1
–1
Additional Example 2B: Multiplying Fractions
B.
Multiply. Write the answer in simplest form.
Pre-Algebra
3-3 Multiplying Rational Numbers
Multiply numerators. Multiply denominators.
1 2
3 7
4
Write as an improper fraction.
= 31(1) 7(2)
31 ÷ 14 = 2 R3 = or 231 14
3 14
Additional Example 2C: Multiplying Fractions
C.
Multiply. Write the answer in simplest form.
1 2
3 7
4 = 31 17 2
Pre-Algebra
3-3 Multiplying Rational Numbers
3(5) 5(8)=
Multiply. Write the answer in simplest form.
5 8
Simplest form3 8
=
3 5
=3(5) 5(8)
Multiply numerators.Multiply denominators.
Look for common factors: 5.1
1
Try This: Example 2A
A.
Pre-Algebra
3-3 Multiplying Rational Numbers
–7(4) 8(7)=
=–7(4) 8(7)
1
2
Simplest form
Multiply numerators.Multiply denominators.
Look for common factors: 4, 7.
4 7
7 8
–
1
–1
1 2= –
B.
Multiply. Write the answer in simplest form.
Try This: Example 2B
Pre-Algebra
3-3 Multiplying Rational Numbers
7 9
3 5
2C.
Multiply. Write the answer in simplest form.
Try This: Example 2C
Multiply numerators. Multiply denominators.
Write as an improper fraction.
= 13(7) 5(9)
91 ÷ 45 = 2 R 1 = or 291 45
1 45
7 9
3 5
2 = 13 75 9
Pre-Algebra
3-3 Multiplying Rational Numbers
2(–0.51)
Multiply.
Product is negative with 2 decimal places.
2 • (–0.51) = –1.02
(–0.4)(–3.75)Product is positive with 3 decimal places.
(–0.4) • (–3.75) = 1.500
You can drop the zeros after the decimal point.
= 1.5
Additional Example 3: Multiplying Decimals
A.
B.
00
Pre-Algebra
3-3 Multiplying Rational Numbers
3.1 (0.28)
Multiply.
Product is positive with 3 decimal places.
3.1 • (0.28) = 0.868
(–0.4)(–2.53)Product is positive with 3 decimal places.
(–0.4) • (–2.53) = 1.012
Try This: Example 3
A.
B.
Pre-Algebra
3-3 Multiplying Rational Numbers
A. x = 5
Evaluate –3 x for the value of x.1 8
Substitute 5 for x.
–3 x 18
–125 8
=
= –15 5 8
–125 ÷ 8 = –15 R5
Additional Example 4A: Evaluating Expressions with Rational Numbers
–25 8
= (5)
–3 (5) 18=
Write as an improper fraction.
Pre-Algebra
3-3 Multiplying Rational Numbers
–25 • 2 8 • 7
=
= – 25 28
27
Write as an improper fraction.
Substitute for x.2 7
1
4
27
Additional Example 4B: Evaluating Expressions with Rational Numbers Continued
B. x = –3 x 18
27
–25 8=
–3= 18
Look for common factors: 2.
Evaluate –3 x for the value of x.1 8
Pre-Algebra
3-3 Multiplying Rational Numbers
A. y =
–28 • 6 5 • 7=
67
Write as an improper fraction.
1
–4
–28 5
= 67
35–5= 6
7
–5 y 35
Try This: Example 4A
Look for common factors: 7.
= – 24 5 , or – 4 4
5
Evaluate –5 y for the value of y.3 5
Substitute for x.6 7
Pre-Algebra
3-3 Multiplying Rational Numbers
B. y = 3
Substitute 3 for y.
–5 y 35
–84 5=
= –16 4 5
–84 ÷ 5 = –16 R4
–28 5= (3)
Try This: Example 4B
Evaluate –5 y for the value of y.3 5
Write as an improper fraction.
35–5 (3)=
Pre-Algebra
3-3 Multiplying Rational Numbers
4. Evaluate 2 (x) for x = .
1.
Lesson Quiz: Part 1
Multiply.
–1.034
2. 5 8
2 3
–
1 7
9
3. –0.47(2.2)
1 2 24
5
– 5 12
1 2 7
Pre-Algebra
3-3 Multiplying Rational Numbers
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 off. How much money does Teri need to buy the shoes?
Lesson Quiz: Part 2
5.
$10
1 3