ratios and proportions. what is a ratio? a ratio is a comparison of two numbers. ratios can be...
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![Page 1: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/1.jpg)
Ratios and Proportions
![Page 2: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/2.jpg)
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
![Page 3: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/3.jpg)
How to Use Ratios?
• The ratio of boys and girls in the class is 12 to11.
4cm
1cm
This means, for every 12 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 classWhat 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 ratio of length and width of this rectangle
is 4 to 1.
. • The ratio of 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.
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Now, on to proportions!
d
c
b
a
What is a proportion?
A proportion is an equation showing two ratios are equivalent
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
![Page 5: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/5.jpg)
Properties of a proportion?
4
6
2
3
2x6=12 3x4 = 12
3x4 = 2x6
Cross Product Property
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Properties of a proportion?
4
6
2
3If
Then
6
4
3
2
• Reciprocal Property
Can you see it?If yes, can you think
of why it works?
![Page 7: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/7.jpg)
How about an example?
62
7 x Solve for x:
7(6) = 2x
42 = 2x
21 = x
Cross Product Property
![Page 8: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/8.jpg)
How about another example?
x
12
2
7 Solve for x:
7x = 2(12)
7x = 24
x =7
24
Cross Product Property
Can you solve it using Reciprocal Property? If yes,
would it be easier?
![Page 9: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/9.jpg)
Can you solve this one?
xx
3
1
7
Solve for x:
7x = (x-1)3
7x = 3x – 3
4x = -3
x =
Cross Product Property
4
3
Again, Reciprocal Property?
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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
![Page 11: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/11.jpg)
So you use up 1/3 gallon a 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
1 t t3)5(1 3
5t Gal
What property is this?
![Page 12: Ratios and Proportions. 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](https://reader030.vdocuments.site/reader030/viewer/2022032607/56649ec55503460f94bcfa22/html5/thumbnails/12.jpg)
So you use up 5/3 gallons a 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 home
gallons
dollarss
gallon
dollars
67.1
_
1
69.3
67.11
69.3 s
3.69(1.67) = 1s s = 6.16 dollars
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So what do you think?
10 miles
You pay about 6 bucks a week just 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!
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