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Course 3 2-4 Multiplying Rational Numbers Warm Up Write each number as an improper fraction. 1. 1 3...
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Course 3 2-4 Multiplying Rational Numbers Warm Up Write each number as an improper fraction. 1. 1 3 2 7 3 2. 7 8 1 15 8 3. 2 5 3 17 5 4. 2 3 6 20 3 5. 3 8 5 43 8
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Transcript of Course 3 2-4 Multiplying Rational Numbers Warm Up Write each number as an improper fraction. 1. 1 3...
Course 3
2-4 Multiplying Rational Numbers
Warm UpWrite each number as an improper fraction.
1. 13
2 73
2. 78
1 15 8
3. 25
3 17 5
4. 23
6 203
5. 38
5 438
Course 3
2-4 Multiplying Rational Numbers
Problem of the Day
The sum of three consecutive integers is 168. What are the three integers?
55, 56, and 57
Course 3
2-4 Multiplying Rational Numbers
Learn to multiply fractions, mixed numbers, and decimals.
TB P. 76-79
Course 3
2-4 Multiplying Rational Numbers
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 addition
1 4 3 3
4= =
Multiplication3 • 1
414
Course 3
2-4 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 (–) • (+) = (–)
Course 3
2-4 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
–48 7
–487 = –6 R6
6 7= –6
Additional Example 1A: Multiplying a Fraction and an Integer
Course 3
2-4 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
Course 3
2-4 Multiplying Rational Numbers
A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors.
Caution!
Course 3
2-4 Multiplying Rational Numbers
1(6) 8(7)=
Multiply. Write the answer in simplest form.
6 7
Simplify.3 28
=
1 8
=1(6) 8(7)
Multiply numerators.
Multiply denominators.
Look for common factors: 2.3
4
Additional Example 2A: Multiplying Fractions
Course 3
2-4 Multiplying Rational Numbers
–2(9) 3(2)=
=–2(9) 3(2)
3
1
Simplify.–3=
Multiply numerators.
Multiply denominators.
Look for common factors: 2, 3.
9 2
2 3
–
1
–1
Additional Example 2B: Multiplying Fractions
Multiply. Write the answer in simplest form.
Course 3
2-4 Multiplying Rational Numbers
Multiply.
Product is negative with 2 decimal places.
2 • (–0.51) = –1.02
B. (–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. 2(–0.51)
00
Course 3
2-4 Multiplying Rational Numbers
Joy completes of her painting each day.
How much of her painting does she complete in a 7 day week?
Write as an improper fraction.
1 20
Additional Example 4: Application
=
(7) = 1 20
Multiply.
1 20
71
1 • 7 20 • 1
= 7 20
Joy completes of her painting in a 7-day week. 7 20
Course 3
2-4 Multiplying Rational Numbers
4. Evaluate 2 (x) for x = .
1.
Lesson QuizMultiply.
–1.034
2. 5 8
2 3
–
1 7
9
3. –0.47(2.2)
1 2 2
45
– 5 12
1 2 7
Edgar runs mile each day. What is the total distance that Edgar runs in a 7-day week?
5.8 9
6 miles2 9
