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2-4 Multiplying Rational Numbers
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
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
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
2-4 Multiplying Rational Numbers
Learn to multiply fractions, mixed numbers, and decimals.
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
2-4 Multiplying Rational Numbers
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
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
2-4 Multiplying Rational Numbers
–3 5 8
Multiply. Write the answer in simplest form.
Multiply.
Simplify.
–15 8
–1 7 8
–3 • 5 8
Check It Out: Example 1A
2-4 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
Check It Out: Example 1B
Multiply. Write the answer in simplest form.
2-4 Multiplying Rational Numbers
A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors.
Caution!
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
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.
2-4 Multiplying Rational Numbers
3(5) 5(8)
Multiply. Write the answer in simplest form.
5 8
Simplify.3 8
3 5
3(5) 5(8)
Multiply numerators.Multiply denominators.
Look for common factors: 5.1
1
Check It Out: Example 2A
2-4 Multiplying Rational Numbers
–7(4) 8(7)
–7(4) 8(7)
1
2
Simplify.
Multiply numerators.Multiply denominators.
Look for common factors: 4, 7.
4 7
7 8
–
1
–1
1 2 –
Multiply. Write the answer in simplest form.
Check It Out: Example 2B
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
2-4 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
Check It Out: Example 3
A.
B.
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
2-4 Multiplying Rational Numbers
Mark runs mile each day. What is the total
distance Mark runs in a 5-day week?
Write as an improper fraction.
1 7
Check It Out: Example 4
=
(5) = 1 7
Multiply.
1 7
51
1 • 5 I7 • 1
= 5 7
Mark runs mile in a 7-day week. 5 7
2-4 Multiplying Rational Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
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
2-4 Multiplying Rational Numbers
1. Multiply.
8
A. 1 C. 2
B. 1 D. 8
Lesson Quiz for Student Response Systems
2 5
3 5
4 5
1 5
1 5
2-4 Multiplying Rational Numbers
2. Multiply.
–
A. – C. –
B. – D. –
Lesson Quiz for Student Response Systems
7 12
5 12
7 18
5 18
7 9
3 4
2-4 Multiplying Rational Numbers
3. Multiply.
–0.39(3.2)
A. –1.238
B. –1.248
C. –1.428
D. –1.842
Lesson Quiz for Student Response Systems
2-4 Multiplying Rational Numbers
4. Sam cycles mile each day. What is the
total distance that Sam cycles in 5 days?
A. 7 miles C. 6 miles
B. 6 miles D. 4 miles
Lesson Quiz for Student Response Systems
7 8
3 8
3 8
7 8
