1. Ratios: a comparison of two numbers using division
To see if a ratio is equivalent
1. Compare the fractions by finding the LCD
2. Simplify the ratios
3. Compare by using cross products

2. Ratio, Proportions, Percent
Mr. Pontrella
Grade 6

3. Ratios, Rates, Proportions and Percent
Grade 6
Mr. Pontrella

4. Ratios We are comparing rectangles to triangles.
We use ratios to make comparisons between two things.
We are comparing rectangles to triangles.
Ratios can be written 3 ways.
1. As a fraction 3 5
2. Using the word to
3 to 5
3. Using a colon 3:5
equivalent ratios
Ratios that name the same comparisons
To see if to ratios are equivalent
1. Change each to a decimal and compare the decimals.
2. Reduce both ratios and compare.
3. Use cross products.

5. Rate: is a ratio of 2 measurements with different units
Rates
Rate: is a ratio of 2 measurements with different units
Here we are comparing days to inches
Example: It rained 4 inches in 30 days
The rate is 4 30
We can reduce to 2 15
Unit Rates
A rate that has 1 unit as its second term (denominator)
If a car travels 325 miles and uses 11 gallons of gas what is the mile per gallon?
This is an example of a unit rate. How many miles per 1 gallon?
Create a ratio Miles
Gallons
325 11
Since every fraction is a division problem we divide 325/ 11
Our Unit Rate is miles per gallon

6. Proportions We can write proportions in 2 forms. a:b = c:d
An equation that shows that two ratios are equal
We can write proportions in 2 forms.
a:b = c:d
If 2 ratios are equal then their cross product will be equal.
a * d = b * c

8. Using Proportions to Solve problems
A car travels 125 miles in 5 hours. How many miles will the car travel in 8 hours?
Solve using proportions.
125 = m
Proportion
Set an equation using cross products
125 * 8 = 5 * m
Simplify
1000 = 5m
Solve by inverse operation
(The opposite of multiplication is division )
1000 /5 = m
200 = m
In 8 hours a car can travel 200 miles

9. Scale Drawings and Proportions
On a map 1.5 inches is equal to 5 miles. If the distance in real life is 22 mile how big will it be on the map?
Proportions can help us with this problem. We know 1 ratio is 1.5 in: 5 m. We know 1 part of the second ratio is 22 m.
Proportion 1.5 in = X m
5 m m
Notice we lined up m to m and in to in
Cross Products x 22 = 5 x X
Simplify = 5X
22 miles is equal to 6.6 inches on the map
Inverse Operation 33/ = X
= X

10. Numbers and Their Pieces
Percents
Another form of writing a piece of a number is by using percents.
Percent means "out of 100.” With percents we are using a comparison of decimals and fractions to 100 pieces.
5 out of 100 = 5% = 0.05 = 1
10 out of 100 =10% = 0.1 = 1 20 10

11. Converting Percents and
Decimals
A decimal can be written as a percent, by moving the decimal point two places to the right like this:
Follow the same procedure for decimals larger than 1
2.35 = 2.35
= 235%
A percent can always be written as a decimal by moving the decimal point two places to the left like this:
68% = 68.
= 0.68
Follow the same procedure for percents larger than 100
345% = 345.
= 3.45

12. Converting Percents and Fractions
To convert the fraction 3 to a percent 5
To convert 138% to a fraction
Change the fraction to a decimal
Place the percent
over 100
0.6
5 3
138
Then simplify
Then move the decimal 2 places right
100 38 19
138 = 1 = = 1
0.6
60%
100 50
100

13. The Percent Proportion
Dinner cost $75 and you wish to leave a 20% tip. How much will the tip be?
We can use the percent proportion to solve.
P is the percentage ( a value that is a number for the percent
P = R B
B is the base or the original amount
R is the rate(the percent number over 100)
In this problem the Base is $75, the Rate is 20 over 100 and we are solving for the Percentage ( how much money is equal to 20%)
Cross products 75 x 20 = P x 100
P = 20 $
Simplify = 100P
Inverse operation 1500/ 100 = P
$15 = P
The tip will be $15

14. 3 Types or Percent
We have seen 1 type of percent problem. Let’s look at 2 others.
If we left a 20% tip which was $25, how much was the bill?
We know R is 20% and P is $25. We need to find B.
Proportion = 20 B
Cross products x 100 = 20 x B
Simplify = 20B
The dinner bill was $125
Inverse Operation / 20 = B
$125 = B

15. If Dinner cost $125 and we left a $35 tip what percent of the bill was the tip?
P is $35, B is $125. We are trying to find R.
Proportion = R
Cross Products 35 x 100 = x R
Simplify = R
The tip was 28% of the bill
Inverse Operation 3500/ 125 = R
28% = R