ratios and proportions in mathematics grade 5.ppt

mathematics grade 5 ratio and proportion

1. Ratios and Proportions

2. Outline:
•Ratios!
What is a Ratio?
How to Use Ratios?
How to Simplify?
Proportions!
What is a proportion?
Properties of proportions?
How to use proportions?
•Mysterious Problems…

3. What is a Ratio?
•A ratio is a comparison of two numbers.
•Ratios can be written in three different ways:
a to b
a:b
Because a ratio is a fraction, b can not be zerob
a
Ratios are expressed in simplest form

4. How to Use Ratios?
•Theratioof boys and girls in the class is
12 to11.
4cm
1cm
This means, for every12 boys
you can find 11 girls to match.
•There could be just 12 boys, 11
girls.
•There could be 24 boys, 22
girls.
•There could be 120 boys, 110
girls…a huge class
What is the ratio if the
rectangle is 8cm long and
2cm wide?
Still 4 to 1, because for every
4cm, you can find 1cm to
match
•The ratioof length and width of this rectangle
is 4 to 1.
. •The ratioof cats and dogs at my home is 2 to 1
How many dogs and cats do I
have? We don’t know, all we
know is if they’d start a fight,
each dog has to fight 2 cats.

5. How to simplify ratios?
•The ratios we saw on last
slide were all simplified.
How was it done?b
a
Ratios can be expressed
in fraction form…
This allows us to do math
on them.
The ratio of boys and girls in the
class is
The ratio of the rectangle is
The ratio of cats and dogs in my
house is11
12 b
a 1
4 1
2

6. How to simplify ratios?
•Now I tell you I have 12 cats and 6 dogs. Can you
simplify the ratio of cats and dogs to 2 to 1?6
12
=6/6
6/12 =1
2
Divide both numerator and
denominator by their
Greatest Common Factor6.

7. More examples…24
8 9
27 200
40
=
=
=5
1 3
1 50
12
=25
6 18
27
=2
3 1
3

8. Now, on to proportions!d
c
b
a

What is a proportion?
A proportion is an equation
that equates two ratios
The ratio of dogs and cats was 3/2
The ratio of dogs and cats now is 6/4=3/2
So we have a proportion :4
6
2
3


9. Properties of a proportion?4
6
2
3

2x6=12
3x4= 12
3x4 = 2x6
Cross Product Property

10. Properties of a proportion?d
c
b
a

•Cross Product Property
ad = bc
means
extremes

11. Properties of a proportion?d
c
b
a
 d
d
c
d
b
a
 cd
b
a

Let’s make sense of theCross Product Property…cbbd
b
a
 bcad
For any numbers a, b, c, d:

12. Properties of a proportion?4
6
2
3

If
Then6
4
3
2

•ReciprocalProperty
Can you see it?
If yes, can you think
of why it works?

13. How about an example?62
7x

Solvefor x:
7(6) = 2x
42 = 2x
21 = x
Cross ProductProperty

14. How about another example?x
12
2
7

Solve for x:
7x = 2(12)
7x = 24
x =7
24
Cross ProductProperty
Can you solve it
using Reciprocal
Property? If yes,
would it be easier?

15. Now you know enough about properties,
let’s solve the Mysterious problems!galx
miles
gal
miles
_
)55(
1
30 
 x
10
1
30

If your car gets 30 miles/gallon, how many gallons
of gas do you need to commute to school
everyday?
5 miles to school
5 miles to home
Let x be the number gallons we need for a day:
Can you solve it
from here?
x = Gal3
1

16. So you use up 1/3 gallona day. How many gallons would
you use for a week?
5 miles to school
5 miles to home
Let t be the number of gallons we need for a week:days
galt
day
gal
5
_
1
3/1
 51
3/1 t
 53
1t
 t3)5(1 3
5
t
Gal
What property
is this?

17. So you use up 5/3 gallonsa week (which is about 1.67
gallons). Consider if the price of gas is 3.69 dollars/gal,
how much would it cost for a week?
Let s be the sum of cost for a week:
5 miles to school
5 miles to homegallons
dollarss
gallon
dollars
67.1
_
1
69.3
 67.11
69.3 s

3.69(1.67) = 1s s = 6.16 dollars

18. So what do you think?
10 miles
You pay about 6 bucks a weekjust to get to school!
What about weekends?
If you travel twice as much on weekends, say drive
10 miles to the Mall and 10 miles back, how many
gallons do you need now? How much would it cost
totally? How much would it cost for a month?
5 miles
Think proportionally! . . . It’s all about proportions!