Section 7.1/7.2 Rational Expressions-Finding undefined values. YouTube Video

The following are rational expressions. What can x not equal?

2

5

x

x

12

3

xx

x

65

22 xx

x

x

25

7

132

41

xx

xx

92

422

x

xx

Rational Expressions – Reducing YouTube Video Monomials

zyx

yx22

5

2

6

zyyxx

yxxxxx

2

6

yz

xxx

1

3

yz

x33

Try this one:

c

dc

15

5 53

Trinomials

( )( )

( )2+

6+2+

x

xx

1

6+x 6+x

Try this one:

16-6

82 xx

x

+

+

𝑥2−4

2−𝑥

x

xx

2

22-

Try this one:

x

x

3

9-2

2+

12+8+2

x

XX

Section 7.3 LCM Least Common Multiple YouTube Video

LCM is the smallest multiple that two or more numbers share.

2 3 4 5 6

4 8 12 16 20 24

10 20 30 40 50 60

Find the LCM : each factor must be in the LCM and the largest exponent of each factor must be on that

factor..

1. Denominators: 3 zyx 32, 9 yzx5

2. Denominators: 216xy , xz4

LCM: LCM:

3. Denominators: yxx , 32 yxx 4. Denominators: 23 4 xx , 223 xx

LCM: LCM:

5. Denominators: 323 xx , 3253 xx

LCM:

6. Denominators: 24 2 xx , 226 xxxy

LCM:

6. Denominators: 94 2 x , 932 2 xx

LCM:

Find the LCM/LCD

1. 26ab , 318ab 2. 2410 yx ,

3315 yx

2. 37 xx , 27x 3. 1x , 1x

3. 452 xx , 2832 xx 4.

3

2

6 2

x

x

xx

5. 27

2;

7

3

yy 6.

2;

2

32 x

x

xx

x

7. 20

3;

4;

5

32 xxx

x

x

x

Section 7.4 Adding/Subtracting Rational Expressions YouTube Video

Rational Expressions: 32

2

9

3222

xx

x

x

x

1) Factor denominators

13

2

33

32

xx

x

xx

x

2) LCD____________________

3) Multiply top and bottom

13

2

33

32

xx

x

xx

x

4) Add or subtract

5) Reduce if possible

Rational Expressions: 3

52

3

152

yyyy

1) Factor denominators

2) LCD____________________

3) Multiply top and bottom

3

5

2

)3(

15

y

y

yy

4) Add or subtract

5) Reduce if possible

1) xyyx 6

11

12

52

2) xx

1

3

3

3) 65

72

65

1322

xx

x

xx

x

4) 2

1

2

3

tt

5) 1

4

1

2

1

42

xxx

6)

42

5

2

32

pp

7) 𝑡

𝑡+7+

9𝑡−35

𝑡2−49

Section 7.5 Complex Fractions YouTube Video

1)

5

57

x

x

x

2)

7

43

y

y

3)

11

11

a

a

4)

8

1

4

24

xx

5)

xy

xy

yx

35

925 22

6)

2

2

344

1252

xx

xx

7)

1

21

2

11

x

x

Section 7.6

Proportions/ratio warm up.

YouTube Video

1) What is the ratio of circles to triangles?_________

What is the ratio of triangles to circles?_________

2) What is the ratio of circles to triangles?_________

What is the ratio of triangles to circles?_________

Are the ratios of circles to triangles the same in 1 and 2? Why?

A proportion is two equal ratios

1) Using Cross Multiplication

14

6

7

3

2) Using Equivalent fractions: Picture form:

3) Using a unit rate:

14

21=

6

9

Solve for x:

14

6

7

3

YouTube Video

1) Cross multiplying: 86

3 x

2) Using Equivalent fractions:

8

24

x

3) Using a unit rate:

7250

125 x

4) Using a table:

x

10

3.3

15

Numerator Denominator Notes

15 3.3 Given

Solve for x:

1. 86

3 x 2.

8

24

x 3.

21

2

7

1

x

WORD PROBLEMS INVOLVING PROPORTIONS YouTube Video

My shadow is 4 feet long and I’m 6 feet tall. How tall is a tree with a shadow of 8

feet?

We set 𝒙 = 𝑻𝒉𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒕𝒓𝒆𝒆.

Set up two ratios. One involving one comparison, and the other involving the variable. Like Ian’s

shadow to Ian’s Height and The Trees shadow to the Trees Height. In this case the first sentence

can be made into the first ratio and the unknown will be in the second ratio.

tree me

HeightTrees

ShadowTrees

HeightsIan

ShadowsIan

'

' 4 8

6

feet feet

feet x

then solve 4 8

6 X to find the answer.

Set up a proportion and solve.

1. As part of a spring clearance, a men’s store put dress shirts on sale , 2 for $25.98. How much will a

business man pay if he buys five shirts?

2. A recipe for spaghetti sauce requires 4 bottles of ketchup to make 2 gallons of sauce. How many

bottles of ketchup are needed to make 10 gallons of sauce?

3. Jim can run 4 miles in 1.5 hours. How many miles can he run in 4 hours?

4. If three apples cost 45 cents, how much would five apples cost?

5. (special) $60 is to be divided between Brian and Kate in the ratio 2:3. How much does Kate get?

Section 7.7 Solving Rational Equations. YouTube Video

Rational Equations: 63

1

9

11

2

4

mm

1) Factor denominators

)2(3

1

9

11

2

4

mm

2) LCD___________________ m _________

3) Multiply both sides (all groupings) by the

LCD

)2(3

1

9

11

2

4

mm

4. Solve the resulting equation

Rational Equations: 2

1

4

2

2

32

kkk

1) Factor denominators

2) LCD____________________ k _________

3) Multiply both sides (all groupings) by the

LCD

4. Solve the resulting equation

63

1

9

11

2

4

mm

2),2(9 mmLCD

)2(3

1

9

11

2

4

mm

)2(9)2(9)2(9

)2(3

1

9

11

2

4

mmm

mm

3)2(1136 m

1m

Eliminate

8

1

4

24

xx

xxx

xx

x

88

18

4

82

84

xx

xx

88

1

4

82

4

12

1216

xx

x

xx

x

22

1632x

16

xLCD 8

Simplifying complex fractions

Rationals YouTube Video

Solving Rational Equations

Simplify rational (fraction) expression

)10(

)1)(10(

)1(

)1(

)1)(10(

1011

2

6

52

6

52

6

2

2

52

xy

x

xyxx

xxyx

xy

xx

xx

yx

xy

xx

xx

yx

Add/Subtracting Rational Expressions

)6(

)4(

)6)(1(

)4)(1(

)6)(1(

43

)6)(1(

25

)6)(1(

25

)6)(1()6(

)6)(1(

6

)1(

1

)6)(1(

)6)(1(

25

)6()1(

1

65

25

61

1

2

2

2

x

x

xx

xx

xx

xx

xx

x

xx

x

xx

xx

x

x

xx

x

x

xxLCD

xx

x

x

x

x

xx

x

x

x

x

15

16

Section 7.8

Work Problems YouTube Video

Rate= the speed at which a person/thing can perform, travel, or do something= it complete toTime

completedWork .

Example: If Jimbo can mow one lawn in 25 minutes. Then his rate would be:

minutes 25

lawn 1 = minute /lawns

25

1

Find the rate:

1. Johnny can wash 6 dogs in 2 hours.

2. Tommy can write 40 words in 2 minutes.

3. A clerk can stock a shelf in 20 minutes.

4. A clerk can stock a shelf in 30 minutes.

5. Sally can fill 4 bottles every t hours.

6. Jimmy can squish 1 ant every t minutes.

7. Working together Jimmy and Sally can mow 1 lawn in t minutes.

Ex1/ One grocery clerk can stock a shelf in 20 min. A second clerk requires 30 min to stock the same shelf.

How long would it take to stock the shelf if the two clerks worked together?

a) Clerk 1's rate: Clerk 2's rate:

b) Rate together = Clerk 1's rate + Clerk 2's rate

= +

17

1) Jimmy can mow a lawn in 75 minutes. Sally can mow a lawn in 50 minutes. How long would it take

them to mow the lawn together?

a) Jimmy's rate: Sally's rate:

b) Rate together = +

2. A small air conditioner can cool a room in 60 minutes. A larger air conditioner can cool the room in 40

minutes. How long would it take to cool the room with both air conditioners working together?

3. Jimmy can stock three times as many shelves in the same time it takes Tommy to stock one shelf. If they

work together, then it takes them two hours. How fast can Jimmy stock one shelf and how fast can Tommy

stock one shelf?

18

Section 7.9

American Units of Measurement YouTube Video

Perform the conversions

1) 4 feet to inches

1

4 feet________________inches

2) 3

22 feet to inches

3

8 feet________________inches

3) 21 feet to yards

4) 8 pounds to ounces

5) 3

24 yards to feet

6) 2.5 tons to ounces

7) 2 quarts to fluid ounces

8) 3 gal to fluid ounces

9) 3 days to seconds

10) 240 minutes to days

11) 3

2day to minutes

13) 2 miles to yards

19

Metric Units of Measurement

YouTube Video

g - grams, unit measure of weight

m - meters, unit measure of length

l - liters, unit measure of volume

1 m, or 1 meter, is approximately 3 feet.

1L, or 1 liter, of soda. The amount of liquid the bottle holds has a volume of 1 liter.

1g, or 1 gram, is about the weight of a paperclip.

Questions:

1) What is the approximate weight of five paperclips?

2) What is the volume of a barrel that can hold the contents of seven of the above soda bottles?

3) A person who is 6 feet tall is about how many meters tall?

4) What unit of measure would you use to determine the weight of an object?

5) What unit of measure would you use to determine the length of an object?

6) What unit of measure would you use to determine the amount of volume an object displaces?

A mnemonic device to remember the metric prefixes is:

Kilo Hecto Deka Base Deci Centi Mili

“King Henry Died By Drinking Chocolate Milk.”

1 kg is said “1 kilogram.” 1 kilogram = 1000 grams 1000

2 hm is said “2 hectometers.” 2 hectometers =2(100)meters= 200 meters 100

1 dl is said “1 deciliter.” 1 deciliters = 1/10 liters 1/10

20

Metric Units of Measurement

YouTube Video

Change 300 dm to km Change 0.4 hl to cl Change 7g to cg

300 0.4 7

Convert the following to centi. Ex: 4.5 dm = 45 cm

1) 0.3 m 2) 1.3 kl

3) 65.78 dag 4) 3 mm

Convert the following to the base unit grams, meters or liters

1) 4.5 cm 2) 6.45 mm

3) 7hm 4) 4000kg

Convert the following to kilo.

1) 456 m 2) 73 hg

3) 54.444 ml 4) 500mg

21

US to Metric and visa-versa YouTube Video

1. Convert 100 yds to meters.

2. Convert 40 grams to ounces.

3. Convert 5 qts to liters.

4. Convert 7 miles to Km.

5. Convert 60 mph to kph.

6. Convert 100 Kph to mph.