Evaluating Algebraic Expressions

2-5 Dividing Rational Numbers

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.

California Standards

Evaluating Algebraic Expressions

2-5 Dividing Rational Numbers

Two numbers whose product is 1 are multiplicative inverses, or reciprocals.

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.

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

=

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=

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

=

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

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. 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.

13.24

=1.320.4

= 1.320.4

1 decimal place 1 zero

1010

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

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

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

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

Evaluating Algebraic Expressions

2-5 Dividing Rational NumbersAdditional Example 4: Problem Solving Application

A muffin recipe calls for cup of oats.

You have cup of oats. How many batches of muffins can you bake using all of the oats you have?

1 2

11 Understand the ProblemThe number of batches of muffins 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 muffins calls for cup of oats.

12

34

3 4

Evaluating Algebraic Expressions

2-5 Dividing Rational NumbersAdditional Example 4 Continued

Set up an equation.

22 Make a Plan

Evaluating Algebraic Expressions

2-5 Dividing Rational Numbers

Let n = number of batches.

Solve33

12

34 = n÷

34

21

= n•

64 , or 1 = n1

2

Additional Example 4 Continued

You can bake 1 batches of the muffins.

12

Evaluating Algebraic Expressions

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