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CONTENTS

RATIOS

the ratio of the number of

teaching assistants to the number

of students in any course …

the ratio of the number of defective

chips to the total number of chips …

What is the ratio of the surface

area of a cube to the surface area

of a rectangular solid

SETTING UP A RATIO

The ratio of x to y

: orx

x yy

The ratio of 24 apples

to 12 oranges is

24 2

12 1

apples

oranges

EQUIVALENT RATIOS

The ratio of 24 apples to 12 oranges is

24 2 4 6

12 1 2 3

apples

oranges

Apples Oranges Total

2 1 3

4 2 6

6 3 9

8 4 12

24 12 36

EQUIVALENT RATIOS

SOLVING A PROPORTION

Cross multiply

3

5 4

x

3.75 3

5 4

4 3 5

15

4

3.75

x

x

x

PART TO PART RATIOS

In a classroom, the ratio of

males to females is 1 to 2, then:

1

2

males

females

3

1 : 2

:

students

m f f

2

1

females

males

PART TO WHOLE RATIOS

In a classroom, the ratio of males

to females is 1 to 2, then:

1

3

males

students

2

3

females

students

3

1 : 2

:

students

m f f

In a classroom, the ratio of

males to females is 1 to 2, then:

3

1 : 2

:

students

m f f

The total number of students in the

classroom must be a multiple of 3.

Females Males Total

2 1 3

4 2 6 Times 2

6 3 9 Times 3

8 4 12 Times 4

10 5 15 Times 5

EQUIVALENT RATIOS

RATIOS WITH MORE THAN TWO TERMS

The sum of the parts

does equal the whole

: :a b c 2:3:5

10

2:3:5

The ratio of is .

a b c Total

2 3 5 10

4 6 10 20 Times 2

6 9 15 30 Times 3

8 12 20 40 Times 4

10 15 25 50 Times 5

EQUIVALENT RATIOS

2 3 2,

3 5 5

a b aIf and then

b c c

COMBINED RATIO

The ratio of a:b is 2:3 and the ratio of

b:c is 3:5. What is the ratio of a:c?

: : c

2 :3:5

a b

COMBINED RATIO

The ratio of a:b is 7:3 and the ratio of

b:c is 2:5. What is the ratio of a:c?

7 2, , ?

3 5

a b a

b c c

2 3 6

5 3 15

b

c

7 2, , ?

3 5

a b a

b c c

14

15

athen

c

7 2 14

3 2 6

a

b

RATIO/FRACTION PROBLEMS

A fraction is a ratio

between two numbers.

2 4 6 1 30

3 6 9 1.5 45

2

3

x

x

RATIOS

RATES

Rate

is a fraction that compares two

quantities that are measured in different

units.

Last year the rate of inflation was 1.2

percent, but for the current year …

A train travels at the

rate of 10 miles/hr …

The rate of boys to girls in a

classroom is ….

RATE

Keep the units straight.

20 students 40 students

1 class 2 classes=

Don’t just average the rates.

Total Aaverage A per B

Total B

AVERAGE RATE

Edwin Lapuerta, Feb 2014

distance

speed time

AVERAGE SPEED

Total Distanceaverage speed

Total Time

Total Distanceaverage speed

Total Time

AVERAGE SPEED

distance

0.010.020:030:040:050:06 sec

= 18m

time

18m m3sec6sec

MOTION PROBLEMS

Jane traveled for 2 hours at a rate of 70 kilometers per hour and

for 5 hours at a rate of 60 kilometers per hour. What was her

average speed for the 7-hour period?

Time = 2 h

Speed = 70 km/h

Time = 5 h

Speed = 60 km/h

Jane traveled for 2 hours at a rate of 70 kilometers per

hour and for 5 hours at a rate of 60 kilometers per hour.

What was her average speed for the 7-hour period?

Distance = Rate . Time

A 70 2

B 60 5

Total 7

140

300

440 440 / 7

= 62.8

RATES

PROPORTIONS

DIRECT PROPORTION

Both quantities

increase simultaneously or

decrease simultaneously.

DIRECT PROPORTION

If Biff can shape 3 surfboards in 50 minutes, how many

surfboards can he shape in 5 hours?

Surfboard Time Rate

3 50

6 100

9 150

12 200

3

50

6 3

100 50

9 3

150 50

12 3

200 50

Constant rate

3

50 300

3 300

50

18

x

x

x

INVERSE PROPORTION

The first quantity

increases while the

second quantity

decreases or viceversa.

INVERSE PROPORTION

If 7 workers can assemble a car in 8 hours, how long

would it take 12 workers to assemble the same car?

Workers Time Product

7 8

14 4

28 2

56 1

56

56

56

56

Constant product

7 8 12

7 8

12

4.66

h

h

h

PROPORTIONS

UNITS OF MEASUREMENT

UNITS OF TIME

1 minute = 60 seconds

1 hour = 60 minutes

1 day = 24 hours

1 week = 7 days

1 year = 52 week

1 year = 365 days

1 leap year = 366 days

UNITS OF MASS

1 pound = 16 ounces

UNITS OF CAPACITY

1 pint = 2 cups

1 quart = 2 pints

1 gallon = 4 quarts

UNITS OF LENGHT

1 foot = 12 inches

1 yard = 3 feet

1 yard = 36 inches

1 ft = 12 in 1 ft2 = 144 in2

1 yd = 3 ft 1 yd2 = 9 ft2

UNITS OF AREA

UNITS OF VOLUME

1 ft = 12 in 1 ft3 = 1,728 in3

1 yd = 3 ft 1 yd3 = 27 ft3

UNITS OF

MEASUREMENT

SUMMARY

edwinxav@hotmail.com

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