11/30/09 Multiply & Divide Fractions #1
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Transcript of 11/30/09 Multiply & Divide Fractions #1
11/30/09 Multiply & Divide Fractions #1LT: I will learn to multiply and divide mixed numbers and fractions.
Today’s Plan:-Fraction, Decimal, Percent Wheel game-Lesson-Assignment
Learning Target: I will learn to multiply and divide mixed numbers and fractions.
Fraction, Decimal, Percent Wheels
1. Circle all fractions that are in lowest terms.2. Review the conversions & decorate your
wheel.
11/30/09 Multiply & Divide Fractions #1LT: I will learn to multiply and divide mixed numbers and fractions.
Today’s Plan:-Fraction, Decimal, Percent Wheel game-Lesson-Assignment
Learning Target: I will learn to multiply and divide mixed numbers and fractions.
Fraction, Decimal, Percent Wheels
11/30/09 Multiply & Divide Fractions #1LT: I will learn to multiply and divide mixed numbers and fractions.
Today’s Plan:-Fraction, Decimal, Percent Wheel game-Lesson-Assignment
Learning Target: I will learn to multiply and divide mixed numbers and fractions.
Warm-up
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
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.
(+) • (+) = (+) (–) • (–) = (+)
(+) • (–) = (–) (–) • (+) = (–)
–8 6 7
Multiply. Write the answer in simplest form.
Multiply
Simplify
–48 7
–6 6 7
–8 • 6 7
A.
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.
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.
–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.
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.
–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
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
13 75 9
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.
–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
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
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)=
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.
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
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
=
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=
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
=
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
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.
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.
Assignment
Pg 124 5-12