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2-5 Dividing Rational Numbers
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
2-5 Dividing Rational Numbers
Warm UpMultiply.
1. 5 6–3 1
2–2
2. 23–15 –
3. 0.05(2.8)
4. –0.9(16.1)
10
0.14
–14.49
2-5 Dividing Rational Numbers
Problem of the Day
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
2-5 Dividing Rational Numbers
MA.8.A.6.4 Perform operations on real numbers (including…rational numbers…)…using real-world problems…
Sunshine State Standards
2-5 Dividing Rational Numbers
reciprocal
Vocabulary
2-5 Dividing Rational Numbers
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.
2-5 Dividing Rational Numbers
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
10 30=
2-5 Dividing Rational Numbers
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
=
2-5 Dividing Rational Numbers
Additional Example 1B: Dividing Fractions
Divide. Write the answer in simplest form.
B. 5 8
÷ 32
5 8
÷ 32 = 21 8
3 1÷ Write as an improper fraction.
Multiply by the reciprocal.
Divide out common factors.
= 21 8
1 3
21 • 18 • 3
=
Simplest form.7 8=
7
1
2-5 Dividing Rational Numbers
9 5
÷ 3 10
Check It Out: Example1A
Divide. Write each answer in simplest form.
–
– 3 • 2=
–9 5
÷ 3 10
9 5
• 10 3
–
9 5
• 10 3
–23
– 6=
2-5 Dividing Rational Numbers
2 5 ÷ 34
Divide. Write each answer in simplest form.
2 5
÷ 34
22 5
1 3
•
7 15
, or 122 5
Check It Out: Example1B
2-5 Dividing Rational Numbers
When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places is the number of zeros to write after the 1.
13.24
=1.320.4
= 1.320.4
1 decimal place 1 zero
1010
2-5 Dividing Rational Numbers
= 1.6
38.424
=
Find 0.384 ÷ 0.24.
Additional Example 2: Dividing Decimals
0.3840.24
0.384 ÷ 0.24 = 100100
Divide.38.424
=
0.24 has 2 decimal places, so use .100
100
2-5 Dividing Rational Numbers
0.585 ÷ 0.25
Check It Out: Example 2A
Find each quotient.
= 2.34
585250
=
0.585 ÷ 0.2510001000
0.585 0.25
2-5 Dividing Rational Numbers
1.76 ÷ 0.8
Check It Out: Example 2B
Find each quotient.
= 2.2
17680
=
1.76 ÷ 0.8100
1001.76 0.8
2-5 Dividing Rational Numbers
5.25 for n = 0.15n
Divide.
= 35
Additional Example 3A: Evaluating Expressions with Fractions and Decimals
Evaluate the expression for the given value of the variable.
5.250.15
5.250.15
=100100 100
100
0.15 has 2 decimal
places, so use .
52515=
When n = 0.15, = 35.5.25
n
2-5 Dividing Rational Numbers
k ÷ for k = 54 5
5 ÷ 5 4
= 5 1
•4 5
1 46
5 • 51 • 4
= == 254
Additional Example 3B: Evaluating Expressions with Fractions and Decimals
Evaluate the expression for the given value of the variable.
Divide.
Multiply by the reciprocal.
When k = 5, k ÷ = .4 5
1 46
2-5 Dividing Rational Numbers
2.55 , for b = 0.75b
Check It Out: Example 3A
Evaluate each expression for the given value of the variable.
= 3.4
2.550.75
2.550.75
= 100100
25575
=
2-5 Dividing Rational Numbers
x ÷ , for x =1 3
Check It Out: Example 3B
Evaluate each expression for the given value of the variable.
3 4
–2
•3 4
= 3 1
÷ 1 3
–2 11 4
–
334
= , or 1 4
8– –
2-5 Dividing Rational Numbers
Additional Example 4: Problem Solving Application
A cookie recipe calls for cup of oats. You have cup of oats. How many batches of cookies can you bake using all of the oats you have?
1 2
11 Understand the Problem
The number of batches of cookies you can bake is the number of batches using the oats that you have. List the important information:
The amount of oats is cup.
One batch of cookies calls for cup of oats.
12
34
3 4
2-5 Dividing Rational Numbers
Additional Example 4 Continued
Set up an equation.
22 Make a Plan
2-5 Dividing Rational Numbers
Let n = number of batches.
Solve33
12
34 = n÷
34
21
= n•
64 , or 1 batches of cookies.1
2
Additional Example 4 Continued
2-5 Dividing Rational Numbers
Look Back44
One cup of oats would make two batches so 1 is a reasonable answer.
12
Additional Example 4 Continued
2-5 Dividing Rational Numbers
Check It Out: Example 4
A ship will use of its total fuel load for
a typical round trip. If there is of a total
fuel load on board now, how many
complete trips can be made?
1 6 5
8
16
58 = c÷
58
61
= c•
154 , or 3 3
4308
=
So, 3 complete round trips can be made.
2-5 Dividing Rational Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
2-5 Dividing Rational Numbers
Lesson QuizDivide.
1.
2. –14 ÷ 1.25
4. Evaluate for x = 6.3.112 x
3. 3.9 ÷ 0.65 6
–11.2
–1 89
÷5 6
2 1 2
–1
17.7
A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)?
5.
182
2-5 Dividing Rational Numbers
1. Divide.
3 ÷ –1
A. –1 C. –2
B. –2 D. –3
Lesson Quiz for Student Response Systems
7 9
1 2
5 8
1 6
1 5
4 5
2-5 Dividing Rational Numbers
2. Divide.
–12 ÷ 2.5
A. –4.8
B. –4.3
C. 5.0
D. 5.2
Lesson Quiz for Student Response Systems
2-5 Dividing Rational Numbers
3. Divide.
18 ÷ 2.4
A. 3
B. 5.5
C. 7.5
D. 10
Lesson Quiz for Student Response Systems
2-5 Dividing Rational Numbers
4. Evaluate for p = 7.2.
A. 19.7
B. 19.72
C. 20.3
D. 20.72
Lesson Quiz for Student Response Systems
142 p
2-5 Dividing Rational Numbers
5. A piece of cake weighs 46 grams. How many pieces of cake would it take to equal 1 kg (1000 grams)?
A. 20 pieces
B. 21 pieces
C. 22 pieces
D. 23 pieces
Lesson Quiz for Student Response Systems
