divide rational numbers without models. how many groups of 0.3 are in 0.6? this problem is...

Divide Rational Numbers

Without models

How many groups of 0.3 are in 0.6?

This problem is equivalent to 0.6 ÷ 0.3. You canuse a grid to model this division by circling groupsof 0.3 and counting the number of groups.

There are 2 groups of 0.3 in 0.6, so 0.6 ÷ 0.3 = 2.

Previously on Dividing Fractions

When you divide two numbers, you can multiply both numbers by the same power of ten withoutchanging the final answer.

Multiply both 0.6 and 0.3 by 10:

0.6 · 10 = 6 and 0.3 · 10 = 3

0.6 ÷ 0.3 = 2 and 6 ÷ 3 = 2

By multiplying both powers by the same power of ten, you can make the divisor an integer. Dividing by an integer is much easier than dividing by a decimal.

Divide.Insert Lesson Title Here

6.45 ÷ 0.5

) 64.5 51

5–14

–10

6.45 ÷ 0.5

2

4 5

.9

–4 50

Multiply both numbers by 10 to make the divisor an integer.

Divide as with whole numbers.

= 64.5 ÷ 5

Divide. Estimate to check whether each answer is reasonable.4 ÷ 1.25

4.00 ÷ 1.25 = 400 ÷ 125 Multiply both numbers by 100.

)125 400 .0 Use zero as a placeholder.3

–37525 0

–25 0

0

Divide as with whole numbers.

Estimate 4 ÷ 1 = 4

The answer is reasonable.

. 2

Lets take what we know of decimals and apply it to fractions

0.6 ÷ 0.3 = 2.

06/10 ÷ 3/10 = 2.

35

310÷ =

1

1/2How many halves are in one whole?

2

This process is very confusing so mathematicians came up with RECIPROCALS.

You could put all fractions into decimals, but not all fractions become nice decimals and the problem will be harder

Reciprocals can help you divide by fractions.

Two numbers are reciprocals if their product

is 1. The reciprocal of is because 1/3

13

· 3 = 13

· 31

= 33

= 1.

To divide by a fraction, find its reciprocal and thenmultiply.

2 ÷ 13

= 2 · 3 = 6

3

Divide. Write each answer in simplest form.

A. 37 ÷ 2

537

÷ 25

= 37 ·

52

= 37

· 5· 2

= 1514

or 1141

Multiply by the reciprocal of . 25

B. 38

÷ 12

38

÷ 12 =38

· 112

= 38

· 112

1

4=

Multiply by the reciprocal of 12.

132

Simplify.

Divide. Write each answer in simplest form.

A. 35 ÷ 1

235

÷ 12

= 35 ·

21

= 35

· 2· 1

= 65

or 1 51

Multiply by the reciprocal of . 12

B. 34

÷ 3

34

÷ 3 =34

· 13

= 34

· 13

1

1=

Multiply by the reciprocal of 3.

14

Simplify.

Divide. Write each answer in simplest form.

Insert Lesson Title Here

A. 5 23

÷ 1 14

5 23

÷ 1 14

= 17 3

÷ 54

= 17 3

· 45

= 6815

or 4 815

Write mixed numbers as improperfractions.

Multiply by the reciprocal of 54

B. 34

÷ 212

34

÷ 2 12

= 34

÷ 52

= 34

· 25

=3 · 24 · 5

1

2= 3

10

Write 2 as an improper fraction.12

Multiply by the reciprocal of . 52

Simplify.

.

Divide. Write the answer in simplest form.

C. 8 23

÷ 1327

8 23

÷ 1327

= 26 3

÷ 1327

= 26 3

· 2713

9

1

2

1

= 18 1

or 18

Write 8 as an improper fraction.23

Multiply by the reciprocal of . 1327

=26 3

· 2713·

Lesson Quiz

Divide. Estimate to check whether each answer is reasonable.

1. 78.2 ÷ 0.04

2. –9.72 ÷ 2.7

3. 18.88 ÷ 1.6

4. 19.5 ÷ 3.25

5. Jordan used 32.46 gallons of gas to drive his

van 584.28 miles. How many miles did Jordan get

per gallon?

–3.6

1,995

Insert Lesson Title Here

11.8

6

18

Course 2

3-5 Dividing Decimals and Integers by Decimals

Notes start here

Divide Rational Numbers

Without models

Date __________

EX 1) Divide.Insert Lesson Title Here

6.45 ÷ 0.5 1. Multiply both numbers by __ to make the divisor an integer.

2. Divide as with _____ _______.

Divide. Estimate to check whether each answer is reasonable.

EX 2) 4 ÷ 1.25

Multiply both numbers by ___.

Use ____as a placeholder.

Divide as with whole numbers.

Estimate 4 ÷ 1 = 4

___________ can help you divide by fractions.

Two numbers are ___________if their product

is __. The reciprocal of is because 13

· 3 = 13

· 31

= 33

= 1.

To divide by a fraction, find its __________ and thenmultiply.

2 ÷ 13

= 2 =

Divide. Write each answer in simplest form.

EX 3). 37 ÷ 2

5

1. Multiply by the __________ of

EX 4)

2. Multiply by the __________ of 12.

3. _________

Divide. Write each answer in simplest form.

EX 5)

EX 6)

Divide. Write each answer in simplest form.

EX 6)

EX 7)

Divide. Write the answer in simplest form.

EX 8 ).