course 3 2-5 dividing rational numbers warm up multiply. 1. 5656 –3 1212 –2 2. 2323 –15 – 3....
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Course 3
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
Course 3
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
Course 3
2-5 Dividing Rational Numbers
Learn to divide fractions and decimals.
TB P. 80-84
Course 3
2-5 Dividing Rational Numbers
reciprocal
Vocabulary
Course 3
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.
Course 3
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
Course 3
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
=
Course 3
2-5 Dividing Rational Numbers
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=
Course 3
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
Course 3
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
=
Course 3
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
Course 3
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
Course 3
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
Course 3
2-5 Dividing Rational Numbers
Course 3
3-4 Dividing Rational Numbers
Additional Example 4 Continued
Set up an equation.
22 Make a Plan
Course 3
2-5 Dividing Rational Numbers
Course 3
3-4 Dividing Rational Numbers
Let n = number of batches.
Solve33
12
34 = n÷
34
21
= n•
64 , or 1 batches of the cookies.1
2
Additional Example 4 Continued
Course 3
2-5 Dividing Rational Numbers
Course 3
3-4 Dividing Rational Numbers
Look Back44
One cup of oats would make two batches so 1 is a reasonable answer.
12
Additional Example 4 Continued
Course 3
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.
about 181