chapter 2 study guides

Mixed Number A mixed number has a part that is a whole

number and a part that is a fraction.

= 1 34

#1

An improper fraction is when the numerator is greater than the denominator.

Improper Fraction

1/4 1/4

1/4 1/4

1/4 1/4

1/4 1/484=

numeratordenominator

How To Change An Improper Fraction To A Mixed Number

=52

2 ) 5 numeratordenominator 2

1

Divide the numerator by the denominator.Put your remainder over the denominator.

2

#2

How To Change A Mixed Number To An Improper

Fraction1) Multiply the whole number

times the denominator.

2) Add your answer to the numerator.

3) Put your new number

over the denominator.

4 12x

+=

92

#3

DecimalsTerminating Decimal Is a decimal that stops. The decimal terminates if you reach a remainder of zero when you divide.

Repeating DecimalIs a decimal that shows a pattern of repeating digits.

#4

10.5

2

40.36

11

Decimal Place Value

___ , ___ ___ ___ ___ ___ ___ ___

Th

ou

san

ds

Hu

nd

red

s Ten

s On

es

Ten

ths

Hu

nd

red

ths

Th

ou

san

dth

sTen

Th

ou

san

dth

s

2 4 3 1 6

Read as 243 and 16 hundredths

#5

Decimals are read as “and”

To A Fraction: Read the decimal using the correct place value. How you say it determines the fraction.

0.2 2

10

#6

Two tenths

To a Decimal: Divide the numerator by the denominator.

#7

34

34 0.7

2 82

0

0

5

200

30.75

4

means 3 4

#8 Writing Repeating Decimals as Fractions

one tenth0.1

19

0.1

110

less than one trepea

enthting

22 hundredths0.22 22100

2299

0.22 less than 22 hundrepe

redthsating

three tenths0.3

39

0.3

310

less than 3 terepea

nthsting

123 thousandths0.123 123

1000

123999

0.123 less than 123 thourep

sanea

dthsting3

3 13

Equivalent Fractions

Equivalent fractions name the same amount or the same part of a whole. You use the giant one to show equivalent fractions.

Example:

#9

1

2 2

4

A fraction shows:

35

610

35

915

22 3

3

Parts ShadedTotal Parts

NumeratorDenominator

Least Common Denominator

TO FIND THE LCM OF 4 and 12:

2) Find the least multiple that both numbers have in common.

1) List the multiples of both numbers

4 = 4, 8, 12, 16, 20…12 = 12, 24, 36…

LCM is 12

#10

Least Common Multiple is also known as LCD.

< Less than> Greater than

Less than or equal to Greater than or equal to

Read these symbols from left to right.

****************************************************************

Comparing Fractions #11

To compare fractions you must show your work!

810

91260

60

48 45> 66 5

5

Steps for RoundingFind the number. Circle it.

Look next door.4 or less just ignore.5 or more add one more.

Example: Round 5.328 to nearest hundredth. Circle the 2 in the hundredths place.

Look next door at the 8. It is 5 or more so add 1 more to the hundredths place.

5.328 rounds to 5.33

# 12

Add DecimalsAdd 3.41 + 2.5

1

Step 1: Line up the decimals 3.41+ 2.5 Step 2: If needed, put zeros in

as place holders

Step 3: Add decimals

Step 4: Bring decimal down

. 0

#13

9 5

Subtract DecimalsSubtract 3.58 – 1.6

8

Step 1: Line up the decimals 3.58- 1.6

Step 2: If needed, put zeros in as place holders

Step 3: Subtract decimals

Step 4: Bring decimal down

.

0

#14

2 1

91

2 3ADD

6 6

-2

6

3

6

1

+You ADD numerators

The denominator STAYS THE SAME!

Add Fractions With The Same Denominator#15

6

2 3

Giant One/ Simplest Form

The Giant One is used to reduce or simplify fractions.

#16

4 2 2

10 2 5

16 4 4

20 4 5

To find the simplest form divide the numerator and denominator by the greatest common factor.

12 6 2

18 6 3

Draw one-third (horizontal)

Draw negative one-half (vertical)

1

3-1 2

What is of ? Draw a picture (overlay them).

#17

1 1

3 2

One-Third of a Negative One-Half Piece

1

3

1

2

1

6

1 3

1

2

1

6

+ • – = –

Multiply

43

72 = 28

6

6)284

244

= 234

You do NOT need common denominators Multiply the numerators and denominators straight across.

#18

Change the improper fraction to a mixed number4

6÷

÷22

Reduce!

4 46

7 4

2 3

Multiplying Decimals

Steps for Multiplying Decimals

Step 1: Write the problem vertically.

Step 2: Ignore the decimal point(s) and multiply.

Step 3: Determine where the decimal point goes in the product.

Place the decimal point in the answer by counting how many places the decimal point has moved.

#19

Divide 3 1) Draw a picture to show 3 wholes.

2) How many ’s fit into 3 wholes?

There are 12 one-fourths that fit into 3.

1 2 3 4 5 6 7 8 9 10 11 12

1

4

1

4

#20

To find the reciprocal just flip the fraction over.

#21Two numbers are reciprocals if their product is one.

Change your mixed number to an improper fraction to find the reciprocal.

5 23x

+=

173

317

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

#22

NO decimal point in the divisor.

Divide 0.27 3

3 0. 27. 0

0 02 7

9

27 0

#23 Divisor Dividend

Step 2: Move the decimal point in the dividend straight up into the quotient

Step 3: Divide as usual

Step 1: Write the problem in the long division format

TRICK: Dead Monkeys Smell Bad!

Divide Decimals

Step 2: Move the decimal point in the divisor to the far right of the divisor

Step 5: Divide as usual

Step 1: Write the problem in the traditional long division

Divide 0.42 0.6

0 6 0 4 2. 0

0 042

7

42 0

Step 3: Move the decimal point the SAME NUMBER of places in the dividendStep 4: Move the decimal point in the dividend straight up into the quotient

. .. .

#24Dividend Divisor

Yes, decimal point in the divisor.

EQUIVALENT FRACTIONS OF #25

2

3

4

6

6

9

8

12

2

3

23

22

2

333

2

344

One-Third Plus Two-Fourths#26

horizontal

vertical

1

3

2

4

• 4

• 4

Giant One

• 3

• 3

4

12

6

12

10

12

+

5

6

=

=

Add Fractions

45-23+

15

15x 5 =

x 3 =x 5 =

x 3 =

-10

12

215

1) Find a common denominator.

2) Add the numerators.

3) Keep the common denominator the same.

#27

4) Simplify or reduce. Change improper fractions to mixed #s.

Subtract Fractions5618-

24

24x 3 =

x 4 =x 3 =

x 4 =

3

20

1724

Always SHOWYOUR WORK! This includes theGiant One.

#28

Giant O

ne

Add Mixed Numbers

5658+

24

24x 3 =

x 4 =x 3 =

x 4 =

15

20

3524

24

3 24)351

11

1124

24

1

28 1124

#29

IMPROPER

Subtract Mixed Numbers

2767-

7

7 13

30

177

41

= 1st: Change your mixed numbers to improper fractions.

= 2nd: Subtract numerators.

3rd : The denominator stays the same.

4th : Change your answer to a mixed number.

7)172

14

37

3

#30

Multiply Mixed Numbers

14

=47x

35

35+4

5+ 39

73928

28)391

1128

#31

IMPROPER

FRACTION REVIEWAdd Fractions: Find a common denominator. Add the numerators, and keep the denominator the same.Subtract Fractions: Find a common denominator. Subtract the numerators, and keep the denominator the same.Multiply Fractions: Multiply the numerators and denominators straight across.Divide Fractions: Multiply the first fraction by the reciprocal of the second fraction.Mixed Numbers: Change it to an improper fraction first.

#32