algebraic ratios
TRANSCRIPT
ALGEBRAIC RATIOS
The number of boys =
The number of girls =
If we compare boys to girls we get
___ boys to _____ girls.
WHAT DO WE CALL A COMPARISON BETWEEN TWO OR MORE QUANTITIES?
RATIOWe just found the RATIO of boys to girls.
Is the ratio of girls to boys the same ?
No, when writing a ratio, ORDER matters.
AIM:
What is a ratio?
IT’S FRIDAY NIGHT AND YOUR FRIENDS ARE HAVING A PARTY……
The ratio of girls to guys is 2 to 12.
Would you want to attend the party?
HOW MANY BASKETBALLS TO FOOTBALLS ARE THERE?
For every 4 basketballs there are 6 footballs.
The ratio is 4 to 6.
WHAT ARE SOME OTHER WAYS WE CAN WRITE THE RATIO OF BASKETBALL TO FOOTBALLS?
4 to 6
4 : 6
4 6
First quantity to Second quantity
First quantity : Second quantity
First quantity divided by the second quantity (as a fraction).
Every ratio can be written in 3 ways:
Careful!!
Order matters in a ratio.
4 to 6
Is NOT the same as
6 to 4
WRITE THE RATIO OF SANDWICHES TO COKE BOTTLES 3 DIFFERENT WAYS. 6:8 , 6 to 8, and 6
8
Since a fraction can be simplified, We can simplify the ratio 6/8 to 3/4. The ratio of sandwiches to coke bottles can also be expressed as 3 : 4 or 3 to 4.
In other words, ratios can be simplified to form equivalent ratios.
EQUIVALENT RATIOS Simplify the following ratios:
4 to 8 10 to 8 8 to 10
Step 1 – Write the ratio as a fraction
Step 2 – Simplify the fraction (Find the greatest common factor (GCF) of both numbers and divide the numerator and denominator by the GCF).
Step 3 – Write the equivalent ratio in the same form as the question
4 = 4 / 4 = 1 = 1 to 2
8 8 / 4 2
GCF = 4
EQUIVALENT RATIOS CAN BE FORMED BY MULTIPLYING THE RATIO BY ANY NUMBER.
For example, the ratio 2 : 3 can also be written as 4 : 6 (multiply original ratio by by 2) 6 : 9 (multiply original ratio by by 3) 8 : 12 (multiply original ratio by by 4)
The ratio 2 : 3 can be expressed as 2x to 3x (multiply the original ratio by any number x)
COMPOUND RATIOS
A ratio that compares more than 2 quantities is called a compound ratio.
Example: A cake recipe says the ratio of cups of milk,
sugar, and batter are 1:2:4. This means that there is one cup of milk for every two cups of sugar and four cups of batter.
A BAG CONTAINS 18 YELLOW, BLUE, AND RED MARBLES. THE RATIO OF YELLOW
TO BLUE TO RED MARBLES IS 4 : 2 : 3.
1) Write the ratio of yellow to blue marbles in simplest form.
2) What is the ratio of yellow to red marbles?3) How many yellow marbles are there?
4 : 2 can be simplified to 2 : 1
4 : 3
Yellow : Blue : Red is 4 : 2 : 3
Since any multiple of this is an equivalent ratio, this can also be written as 4x : 2x: 3x
Let 4x = yellow, 2x = blue , 3x = red
4x + 2x+ 3x = 18
9x = 18
X= 2
Since the question asks for yellow marbles,
there are 4x or 4 (2) = 8 yellow marbles.
PRACTICE PROBLEM # 1It takes Max ¼ of an hour to ride his bike to school,
and it takes Riley 21 minutes to walk to school. Write a ratio comparing Max’s time to Riley’s
time.
PRACTICE PROBLEM #2
A TV normally sells for $400 is on sale for $340. The tax on the reduced price is $23.80, so the total cost with tax is $363.80.
What is the discount rate? What is the tax rate? Including tax, how much would a customer
save by buying the TV on sale?
PRACTICE WORD PROBLEMS1) You go to a party where
the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form.
2) Explain what this ratio tells us.
(1)28 / 56 = 1 / 2
The ratio of boys to girls is 1 to 2
(2) For every 1 boy there are 2 girls at the party.
PRACTICE WORD PROBLEMS
(1) Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.
(2) Explain what this ratio tell us.
CHALLENGE QUESTION
Suppose a team has won 15 of it’s first 38 games. How many games must it win in a row to bring its winning percentage to at least .500?