RATIO TABLES

1
Models You Can Count On

• RATIO TABLES
• A ratio table is a useful tool to organize and
  solve problems
• To set up a ratio table, label each row and set
  up the first column ratio
• Different operations (addition, subtraction,
  multiplication, division) may be used within the
  same ratio table
• Just remember, whatever you do to the top, you
  must also do to the bottom!
• For the example on the next page, one movie
  ticket costs 9, and we want to know the price
  for 3, 6, and 9 tickets.

2
Ratio Table
x3
x2
Movie Tickets 1 3 6 9
Price (Dollars) 9 27 54 81
x3
x2

• To get from the first column to the second
  column, we multiplied by three.
• Then to get from the second column to the third
  column, we multiplied by two. Notice that we did
  the same thing to both the top and bottom of the
  column.
• Lastly, to get the value of the last column, we
  add the second and third columns together
  (369), so we do the same for the bottom
  (2754 81).

3
Ratio Table

• There are other combinations that can be used to
  find the values of the last column.
• We could have multiplied the second column by
  three. 3 tickets x 3 9 tickets, so 27 x 3
  81.
• So, as you can see, there is more than one way to
  create a ratio table. How you do it will be up to
  you and it will depend on what the question is
  asking you.

4
Ratio Table - Recipes

• Most recipes need to be changed depending on the
  number of people you are cooking for.
• You will need more ingredients for a recipe for
  10 people, than you would if you were only
  cooking for two people.
• So how do know how many ingredients to use?
• A ratio table is always helpful for this type of
  problem.

5
Ratio Table - Recipe
X 5
Servings 2 10
Apples 6 cups Cups
Flour 3 cups 15 cups
Butter 1 tbsp 5 tbsp
Cinnamon 1 cup 5 cups
6
Ratio Table - Recipe

• As you can see in the recipe on the last page,
  the recipe calls for a certain amount of
  ingredients for two servings. However, you are
  cooking for 10 people (10 servings) but the
  recipe doesnt tell us how much we need.
• To do this, all we do is multiply 2 servings by
  five, to get 10 servings. Then we multiply all of
  the ingredients by five as well.
• This will give us the correct amount of
  ingredients for 10 servings.

7
Bar Model

• Fraction Bars
• Fraction bars can be used to represent how
  something is divided into pieces.
• For example, if four friends needed to share a
  plot of land to plant their favorite garden, we
  good create a fraction bar to represent each
  friends portion of the land.

Friend 1 Friend 2 Friend 3 Friend 4
8
Bar Model

• We can also include fractions to represent each
  friends portion of the land.

Friend 1 Friend 2 Friend 3 Friend 4
¼ ¼ ¼ ¼
9
Bar Model

• If the number of friends changes, so does the
  size of each portion of land. The more friends
  that share, the smaller each portion becomes.

Friend 1 Friend 2 Friend 3 Friend 4 Friend 5 Friend 6 Friend 7
1/7 1/7 1/7 1/7
1/7 1/7 1/7
1 2 3 4 5 6 7 8 9 10
1/10 1/10 1/10 1/10 1/10 1/10 1/10
1/10 1/10 1/10
10
Bar Model

• We can also add percents to a fraction bar.
• Of course if you use percents, you may want to
  change the name to a percent bar.
• Sometimes, you may want both percents and
  fractions.

Friend 1 Friend 2 Friend 3 Friend 4
¼ ¼ ¼ ¼
25 25 25 25
11
Bar Model

• Sometimes our fraction or percent bars will be
  horizontal (up and down) instead of vertical
  (left to right).

Friend 1
Friend 2
Friend 3
Friend 4
¼ or 25
¼ or 25
¼ or 25
¼ or 25
12
Bar Model

• Some bar models are not divided into fractions.
  They contain overall numbers, which you must use
  to determine the fraction or percent.
• For example, if a water tank holds a maximum of
  300 liters, but the water gauge is not filled to
  the top, how do you know how many liters of water
  are in the tank?
• With a little bit of thought and work, a correct
  answer can be determined.

13
Bar Model
300 L

• Here we have a water tank that holds 300 liters
  (L), but the gauge is not full to the top, so
  there is less than 300 L in the tank.
• But how can we determine the amount of water?
• Knowing your fractions is the best tool to begin
  solving this problem.
• As you can see, there are five sections in the
  bar, therefore we can divide this into fifths.
• Our next step is to determine the amount of water
  that is in 1/5 of a tank that holds 300 L.
• 300 L divided by 5 60 L
• Therefore, each 1/5 section contains 60 L of
  water.

14
Bar Model
300 L
1/5 or 60 L
1/5 or 60 L
1/5 or 60 L
1/5 or 60 L
1/5 or 60 L

• Now we can see how each 1/5 section is 60 L.
• Here is the last step to solving this problem.
  We need to determine how many total L are in the
  tank.
• There are two 1/5 sections that are full of
  water, and each section has 60 L of water.
• To find our final answer, we multiply 60 L by two
  and we determine that there are 120 L of water in
  this tank.

15
300 L
If each section is 1/5 as a fraction, then it
must be 20 as a percent. Remember, this is one
of our benchmarks. If we want to find 20 of
the 300L, then we have to change 20 to a
decimal, then multiply it to 300L. 300 x .20
60, therefore, there are 60 L in each 20 section
of the bar graph. Since there are two sections,
multiply 60 L by two to get a total of 120L in
the tank the same as the answer we found using
the fractions.
1/5 or 60 L
1/5 or 60 L
1/5 or 60 L
1/5 or 60 L
1/5 or 60 L
16
Tips

• You just received your bill at a local
  restaurant.
• Your bill is 40.00
• How much of a tip do you live for your waitress?
• If the service was great, you leave 20, if it
  wasnt real good, maybe 10, and if the service
  was just good, 15 would do it.
• So how do we find out how much each tip is worth?

17
Tips

• To find a 10 tip, we can just move the decimal
  one place to the left of the bill. So, if we move
  the decimal in our 40.00 bill, our tip would be
  4.00
• Our other option is to simply change the tip
  percentage to a decimal then multiply to the
  bill. The answer will be the tip amount.
• Example - 40 x .10 4.00, so a 10 tip for this
  bill is 4.00

18
Tips

• For a 20 tip, we can find 10, then multiply by
  two.
• Our other choice is to change 20 to a decimal
  (.20) then multiply by the bill.
• 40 x .20 8.00, so your tip for the bill would
  be 8.00
• For the 15 bill, we can change the 15 to a
  decimal and multiply by the bill.
• 40 x .15 6.00, so 6.00 is the tip for the 40
  bill.

19
Tips
Bill 40.00
10 tip 4.00
15 tip 6.00
20 tip 8.00
20
Number Lines

• Number lines can be divided into sections using
  fractions or percents.

0
50
75
100
25
1/4
1/2
3/4
1 whole
0
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Number Lines

• Fractions with different denominators can be used
  on the same number line. The denominator tells
  you how many sections the number line should be
  divided into, even if you are not dividing the
  entire number line.
• For example, we can label 1/3, 1/4, and 1/5 on
  the same number line. But we only label these
  three fractions. We do not label 2/3, 3/4, 4/5,
  etc on the number line, so the line should be
  divided into all of the thirds, fourths, and
  fifths.
• See next picture

22
Number Lines

• Fractions with different denominators on the same
  number line

0
1/5
1/4
1/3
1
23
Number Lines

• Number lines can also be used to organize
  decimals.

1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
1
24
Double Number Lines

• Double number lines can be used to compare and
  label different numbers much like a ratio
  table.
• For example, if it takes 10 minutes to walk 1/2
  mile, we can label that on a double number line.
• We can then use that information to find out how
  long it takes to go, 1, 2, or even ten miles.
• We could also use it to find out how far we can
  go in 20, 30, or even 90 minutes.

25
Double Number Lines

• It takes 10 minutes to walk 1/2 mile. It would be
  labeled on a double number line like this

Minutes
0
10
Miles
0
1/2
26
Double Number Lines

• Weights and prices can also be labeled on double
  number lines.

Weight (lbs)
0
1/4
1/2
3/4
1
1 1/4
1 1/2
0
.50
1.00
1.50
2.00
2.50
3.00
Price ()