Ratios

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Ratios Proportions
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Ratio (ray-she-yo)

• A ratio is the comparison of two numbers by
  division.
• A classroom has 16 boys and 12 girls.
• Also written as 16 boys, 1612 or 16 to 12
  12 girls
• Generally, ratios are in lowest terms
• 16 16/4 4
  12 12/4 3

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Ratio, continued

• Ratios can compare two unlike things
• Joe earned 40 in five hours
• The ratio is 40 dollars or 8 dollars
  5 hours 1 hour
• When the denominator is one, this is called a
  unit rate.

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Ratio, continued

• Lets look at a classroom
• Ratios can be part-to-part
• 16 boys15 girls
• Ratios can be part-to-whole
• 16 boys31 students

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Now, on to proportions!
What is a proportion?
A proportion is an equation that equates two
ratios
So we have a proportion
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Using Cross Products to Identify Proportions
Tell whether the ratios are proportional.
A.
60
Find cross products.
60
60 60
Since the cross products are equal, the ratios
are proportional.
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Using Cross Products to Identify Proportions
A mixture of fuel for a certain small engine
should be 4 parts gasoline to 1 part oil. If you
combine 5 quarts of oil with 15 quarts of
gasoline, will the mixture be correct?
Set up ratios.
Find the cross products.
4 5 20
1 15 15
20 ? 15
The ratios are not equal. The mixture will not be
correct.
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Try This Example 1A
Tell whether the ratios are proportional.
A.
20
Find cross products.
20
20 20
Since the cross products are equal, the ratios
are proportional.
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Try This Example 1B
A mixture for a certain brand of tea should be 3
parts tea to 1 part sugar. If you combine 4
tablespoons of sugar with 12 tablespoons of tea,
will the mixture be correct?
Set up ratios.
Find the cross products.
3 4 12
1 12 12
12 12
The ratios are equal. The mixture will be correct.
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RATIOS PROPORTIONS
Are the following proportions?
FALSE Not a proportion
FALSE Not a proportion
TRUE this is a proportion
TRUE this is a proportion
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Solving Proportions

• When you do not know one of the four numbers in a
  proportion, set the cross products equal to each
  other and solve.

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Solve the proportion.
6p 12 5
Find the cross products.
Solve.
6p 60
p 10
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Solve the proportion.
14 3 2g
Find the cross products.
Solve.
42 2g
21 g
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RATIOS PROPORTIONS
Find the missing numbers to make the following
proportions.
10 10
9 9
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Proportions

• Proportion is a statement that says two ratios
  are equal.
• In an election, Damon got three votes for each
  two votes that Shannon got. Damon got 72 votes.
  How many votes did Shannon get?
• Damon 3 72
• Shannon 2 n
• n 48, so Shannon got 48 votes.

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Proportions, continued

• Tires cost two for 75. How much will four tires
  cost?
• of tires 2 4 cost 75 n
• n 150, so four tires cost 150

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Proportion, continued

• Three cans of soup costs 5. How much will 12
  cans cost?
• of cans 3 12 cost 5 n
• n 20, so 12 cans cost 20

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Now you know enough about properties, lets solve
the Mysterious problems!
If your car gets 30 miles/gallon, how many
gallons of gas do you need to commute to school
everyday?
5 miles to home
5 miles to school
Let x be the number gallons we need for a day
Can you solve it from here?
x Gal
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5 miles to home
5 miles to school
So you use up 1/3 gallon a day. How many gallons
would you use for a week?
Let t be the number of gallons we need for a week
What property is this?
Gal
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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
3.69(1.67) 1s
s 6.16 dollars
5 miles to home
5 miles to school
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So what do you think?
5 miles
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?
Think proportionally! . . . Its all about
proportions!
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Exit Ticket
Tell whether each pair of ratios is proportional.
yes
1.
2.
no
Solve each proportion.
3.
4.
n 30
n 16