Transcript Ch 2-5 Dividing Rational Numbers

2-5 Dividing Rational Numbers
California
Standards
Evaluating
Algebraic Expressions
NS1.2 Add, subtract, multiply, and divide
rational numbers (integers, fractions, and
terminating decimals) and take positive rational
numbers to whole-number powers.
AF1.3 Simplify numerical expressions
by applying properties of rational numbers (e.g.
identity, inverse, distributive, associative,
commutative) and justify the process used.
2-5 Dividing Rational Numbers
TwoEvaluating
numbers whose
product is 1
are
Algebraic
Expressions
multiplicative inverses, or reciprocals.
2-5 Dividing Rational Numbers
A division
problem
can always be
rewritten as
Evaluating
Algebraic
Expressions
a multiplication problem by using the
reciprocal of the divisor.
2-5 Dividing Rational Numbers
Additional Example 1A: Dividing Fractions
Divide.
Write theAlgebraic
answer in simplest
form.
Evaluating
Expressions
1
5
÷
2
11
1 = 5
2
5
÷
Multiply by the reciprocal.
•
2
11
11 1
=
2
5
No common factors.
•
11 1
10
=
11
Simplest form
2-5 Dividing Rational Numbers
Additional Example 1B: Dividing Fractions
Divide.
Write theAlgebraic
answer in simplest
form.
Evaluating
Expressions
3
2 ÷2
8
3
28
÷
÷ 2 = 19
8
2
1
19 1
=
8 2
19 • 1
=
8•2
19
3
1
=
= 16
16
Write as an improper
fraction.
Multiply by the reciprocal.
No common factors
2-5 Dividing Rational Numbers
Check It Out! Example1A
Divide.
Write theAlgebraic
answer in simplest
form.
Evaluating
Expressions
3
7
÷
4
15
3
4
7
7
÷
Multiply by the reciprocal.
=
•
4
15
15 3
7 • 4 No common factors
=
15 • 3
28
=
45
Simplest form
2-5 Dividing Rational Numbers
Check It Out! Example1B
Divide.
Write theAlgebraic
answer in simplest
form.
Evaluating
Expressions
42
3
÷
5
2
45
÷
22
3
3= 5 ÷ 1
22 1
= 5 3
=
22 • 1
5•3
22
7
= 15 or 1 15
Write as an
improper fraction.
Multiply by the reciprocal.
No common factors
2-5 Dividing Rational Numbers
When dividing a decimal by a decimal,
multiply
both
numbers
by
a
power
of
10
so
Evaluating Algebraic Expressions
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
represents the number of zeros after the 1 in
the power of 10.
1.32
1.32 10
13.2
=
=
4
0.4
0.4 10
1 decimal place
1 zero
2-5 Dividing Rational Numbers
Additional Example 2: Dividing Decimals
Evaluating
Algebraic
Find
0.384 ÷ 0.24.
Estimate Expressions
the
reasonableness of your answer.
0.24 )0.384
1 .6
24 )38.4
- 24
144
– 144
0
0.24 has two decimal places so
multiple both numbers by 100
to make the divisor an integer.
Then divide as a whole number.
0.384 ÷ 0.24 = 1.6
Estimate: 40 ÷ 20 = 2
The answer is reasonable.
2-5 Dividing Rational Numbers
Check It Out! Example 2
Find 0.65 ÷ 0.25. Estimate the
Evaluating Algebraic Expressions
reasonableness of your answer.
0.25 has two decimal places so
0.25 )0.65
multiple both numbers by 100
to make the divisor an integer.
2 .6
25 )65.0
Then divide as a whole number.
- 50
15 0
–150
The answer is reasonable.
n 0
0.65 ÷ 0.25 = 2.6
Estimate: 60 ÷ 20 = 3
2-5 Dividing Rational Numbers
Additional Example 3: Evaluating Expressions with
Rational Numbers
Evaluate
the expression
for theExpressions
given value of
Evaluating
Algebraic
the variable.
5.25 for n = 0.15
n
5.25
5.25
=
Substitute 0.15 for n.
n
0.15
0.15 has two decimal places, so
0.15 )5.25
multiply both numbers by 100
to make the divisor an integer.
35
15 )525
5.25
- 525
When n = 0.15, n = 35.
0
2-5 Dividing Rational Numbers
Check It Out! Example 3
Evaluate the expression for the given value of
the Evaluating
variable.
Algebraic Expressions
3.60 for n = 0.12
n
3.60
3.60
=
Substitute 0.12 for n.
n
0.12
0.12 has two decimal places, so
0.12 )3.60
multiply both numbers by 100
to make the divisor an integer.
30
12 )360
3.60
- 360
When n = 0.12, n = 30.
0
2-5 Dividing Rational Numbers
Additional Example 4: Problem Solving Application
1
A muffin recipe calls for 2 cup of oats.
Evaluating3 Algebraic Expressions
You have 4 cup of oats. How many
batches of muffins can you bake using
all of the oats you have?
1
Understand the Problem
The number of batches of muffins you can
bake is the number of batches using the
oats that you have. List the important
information:
3
The amount of oats is cup.
4
1
One batch of muffins calls for cup
2
of oats.
2-5 Dividing Rational Numbers
Additional Example 4 Continued
2
Evaluating Algebraic Expressions
Make a Plan
Set up an equation.
2-5 Dividing Rational Numbers
Additional Example 4 Continued
3Evaluating
Solve
Algebraic Expressions
Let n = number of batches.
3
1
÷2 =n
4
2
3
• =n
1
4
6 , or 1 1 = n
4
2
1
You can bake 1 batches of the
2
muffins.
2-5 Dividing Rational Numbers
Additional Example 4 Continued
Evaluating Algebraic Expressions
4
Look Back
1
One cup of oats would make two batches so 1
2
is a reasonable answer.