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Ratios and Rates

PLKCKY Maths
by

Barnabas Lai

on 4 November 2014

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Transcript of Ratios and Rates

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

A
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?
Full transcript