algebraic ratios

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ALGEBRAIC RATIOS

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Page 1: Algebraic Ratios

ALGEBRAIC RATIOS

Page 2: Algebraic Ratios

The number of boys =

The number of girls =

If we compare boys to girls we get

___ boys to _____ girls.

Page 3: Algebraic Ratios

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.

Page 4: Algebraic Ratios

AIM:

What is a ratio?

Page 5: Algebraic Ratios

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?

Page 6: Algebraic Ratios

HOW MANY BASKETBALLS TO FOOTBALLS ARE THERE?

For every 4 basketballs there are 6 footballs.

The ratio is 4 to 6.

Page 7: Algebraic Ratios

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

Page 8: Algebraic Ratios

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.

Page 9: Algebraic 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

Page 10: Algebraic Ratios

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)

Page 11: Algebraic Ratios

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.

Page 12: Algebraic Ratios

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.

Page 13: Algebraic Ratios

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.

Page 14: Algebraic Ratios

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?

Page 15: Algebraic Ratios

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.

Page 16: Algebraic Ratios

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.

Page 17: Algebraic Ratios

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?