**CKY Mathematics**

**by Barnabas Lai**

**Ratios and Rates**

**Ratio**

**Rates**

relationship of 2 or more quantities

specific type of ratios with

different units

measure

change

**A**

:

B

:

B

**A**

to

B

to

B

INGREDIENTS

•1 cup sugar

•1 cup water (for the simple syrup)

•1 cup lemon juice

•4 cups cold water (to dilute)

lemon juice

to

water

water

to

lemon juice

usually

no unit needed

lemon juice

to

water

to

sugar

yield 6

when it is the same for all

**=**

**A**

**B**

when units are different

2 cm : 5 m

convert to the same

6

24

1 : 5

juice : water

2 cm : 500 cm

1 : 250

1 : n

Equivalent Ratios

4 : 20

=

simplify

multiply

5:20

13:104

16:25

2:4

256:64

1:3

3:5

4:3

comparing ratios

or

m : 1

2 : 3

3 : 4

boys : girls

1.

2.

3.

4.

A : B : C : D : E : ...

clear

breaking

combining

A : B : C

A : B

B : C

A : C

2 : 7 : 7

T : B : G

more than 2

A : B B : C

A : B : C

3 : 5

A : B

B : C

5 : 7

3 : 5

10 : 2

A : B

B : C

2 : 3

5 : 3

A : B

B : C

Find A : B : C

2 : 3

2 : 7

B : A

B : C

consistency

2 : 6

3 : 4

A : B

B : C

2 : 3

4 : 7

B : A

B : C

A : B : C

special method

(cross product)

Given A:B is 4:3 and B:C is 7:5, find A:B:C

4 : 3

7 : 5

line up the

common value

28 : 21 : 15

multiply as follow

rearrange and

simplify as needed

ratios with the same meaning

Class 1

Class 2

Class 3

1 : 5

order

Unit Ratios

change to unit ratios

ratios with 1 as one of its values

A : B

modeling using ratios

Find the appropriate ratios

Relate it to the unknown

Given that that you have 250 mL of lemon juice, how much water do you need to make the perfect lemonade?

juice : water

= 250mL : W

= 1 : 5

=

5

1

water

juice

W

250

=

solve for the unknown

modeling ratios with total

Given that that you have 250 mL of lemon juice, how much lemonade can you make?

5

1

W

250

=

1

5

250

W

=

cross products property

b

a

d

c

=

a

c

d

=

b

250 : 1250

1 : 5

250 + 1250 = 1500mL

1 : 6

juice : lemonade

250 : L

L = 1500

If you want to make 7.2L of lemonade,

how much water and juice do you need?

7.2L = 7200mL

7200

6

= 1200

(1 part)

1 : 5

= 1200(1 : 5) = 1200 : 6000

speed

heartrate

interest rate

354 km/h

55-65 beat/min

0.0010%/month

at least 2 different units

**Unit Rate**

rate per 1 unit

used for comparison

comparing rates

park n' shop 17 Sep 2012

$3.27/L

$3.87/L

$3.32/L

0.31L/$

0.26L/$

0.30L/$

convert to unit rates

B

A

=

A

B

=

3 : 4

which one to buy?

A

B

=

A

B

1.

2.

per

=

m

/

1 or n

/

1

3.

changing denominator to numerator

higher boys to girls ratios?

higher girls to boys ratios?