evaluating algebraic expressions 2-5dividing rational numbers ns1.2 d ivide rational numbers...
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Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
NS1.2 Divide rational numbers (integers, fractions, and terminating decimals)
AF1.3 Simplify numerical expressions by applying properties of rational numbers (inverse)
California Standards
Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
Two numbers whose product is 1 are multiplicative inverses, or reciprocals.
Notes
Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
A division problem can always be rewritten as a multiplication problem by using the reciprocal of the divisor.
notes
Evaluating Algebraic Expressions
2-5 Dividing Rational NumbersAdditional 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= Simplest form
5 11
•2 1
=
Notes
Evaluating Algebraic Expressions
2-5 Dividing Rational NumbersAdditional Example 1B: Dividing Fractions
Divide. Write the answer in simplest form.
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
=119 16=
Notes
Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
7 15
÷ 3 4
7 15
• 4 3
=7 15
÷ 3 4
28 45
=
Check It Out! Example1A
Divide. Write the answer in simplest form.
Multiply by the reciprocal.
No common factors
Simplest form
7 • 415 • 3
=
Rally Coach A
Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
Write as an improper fraction.
2 5 ÷
Multiply by the reciprocal.
34
22 • 15 • 3
= No common factors
2 5 ÷ 34 = 22
53 1÷
Divide. Write the answer in simplest form.
= 22 5
1 3
7 15= or 122
15
Check It Out! Example1B
Rally Coach B
Evaluating Algebraic Expressions
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.
13.24
=1.320.4
= 1.320.4
1 decimal place 1 zero
1010
Notes
Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
Find 0.384 ÷ 0.24. Estimate the reasonableness of your answer.
Additional Example 2: Dividing Decimals
0.24 has two decimal places so multiple both numbers by 100 to make the divisor an integer.
0.24 )0.384
24 )38.4 Then divide as a whole number.1
24144
.6
0.384 ÷ 0.24 = 1.6Estimate: 40 ÷ 20 = 2
The answer is reasonable.– 144
0
Notes
Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
Find 0.65 ÷ 0.25. Estimate the reasonableness of your answer.
Check It Out! Example 2
0.25 has two decimal places so multiple both numbers by 100 to make the divisor an integer.
0.25 )0.65
25 )65.0 Then divide as a whole number.2
5015 0
.6
0.65 ÷ 0.25 = 2.6Estimate: 60 ÷ 20 = 3
The answer is reasonable.–150 n 0
Elbow Partners
Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
5.25 for n = 0.15n
Substitute 0.15 for n.
Additional Example 3: Evaluating Expressions with Rational Numbers
Evaluate the expression for the given value of the variable.
5.25n
5.250.15
=
When n = 0.15, = 35.5.25
n
0.15 )5.25 0.15 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.
5250
15 )52535
Notes
Evaluating Algebraic Expressions
2-5 Dividing Rational Numbers
3.60 for n = 0.12n
Substitute 0.12 for n.
Check It Out! Example 3
Evaluate the expression for the given value of the variable.
3.60n
3.600.12
=
When n = 0.12, = 30.3.60
n
0.12 )3.60 0.12 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.
3600
12 )36030
Face Partners
Evaluating Algebraic Expressions
2-5 Dividing Rational NumbersExample 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?
16 5
8
Numbers Understand the Problem
Make a Plan Solve Look Back
Notes