PROPORTIONAL REASONINGA POWERFUL CONCEPT

RATIOS & PROPORTIONS

A proportion is a statement that two ratios are equal.

RATIOS & PROPORTIONS

EXAMPLE#1: Is a proportion?15

6

5

2

Find the cross products.

65152 30 = 30 TRUEIf TRUE, the

statement is a proportion.

RATIOS & PROPORTIONSEXAMPLE#2: Is a proportion?

5

3

7

4

Find the cross products.

3754 20 = 21 FALSEIf FALSE, the

statement is NOT a proportion.

RATIOS & PROPORTIONSAre the following proportions?

7

3

9

4

20

9

9

4

27

12

9

4

18

8

9

4

3974 2728

FALSE – Not a proportion

99204 8180

FALSE – Not a proportion

129274 108108

TRUE – this is a proportion

89184 7272

TRUE – this is a proportion

PROPORTION OR NOT?

37=2763

PROPORTION OR NOT?

49=763

Solving Proportions2 Ways:

1st - We can find equivalent fractions to solve proportions.

2nd - We cross multiply to solve proportions.

Solving ProportionsLet’s try using

equivalent fractions to solve

proportions.

Solving ProportionsWe can find equivalent fractions to solve proportions

Solving ProportionsWe cross multiply to solve proportions

RATIOS & PROPORTIONSEXAMPLE#4: Solve the proportion:

10

4

5

Find the cross products.

4510 x2010 x

10 10

2x

Divide both sides by 10.

RATIOS & PROPORTIONSEXAMPLE#6: Solve the proportion:

Find the cross products.

4186 c726 y

6 6

12x

Divide both sides by 10.

=

Steps in solving practical problems using proportion

1. ---------- = -------------2. Label the two quantities you are

comparing3. Plug in the given values and

solve.

How many pizzas?Ms. Marx bought 9 pizzas for 25 students. Tonight, 300 students will be attending a Math night to sharpen their math skills. How many pizzas would Ms. Marx need to buy for the students?

How many Pizzas ?1. ------------ = ---------------2. Label 3. Plug in given values and solve.

=

Your turnFour students went to see a movie for $30.00. How much would 20 students spend if they want to watch the same movie.

A possible solution =

Scale factor is a proportion

Inches = 15 = Centimeters 38.1 x

25

Percent is a Proportion too!Percent is “out of 100”. Percent of a number is used in tax,

tip, discount and lots of other everyday math!

One way to find the percent “of” a number is to change % to a decimal and multiply!

What is 20% of $50.00? Change 20% to a decimal: 0.20 x 50 = 10

What is 4.5% of 20? Change 4.5% to 0.045 x 20 = 0.9

Setup of a Percent Proportion

Is = partOf = wholeThe Percent Proportion puts the % into a

decimal.This can be used to find the Percent of a

number.

is

ofpercent

100

TaxIn Virginia, the state sales tax is 6.5%. You

want to buy a $195 bicycle in Virginia. How much is the tax?

READ the question! This is ONLY asking for the tax.

Change 6.5% to a decimal = 0.0650.065 x 195 = 12.675Money is always rounded to the nearest hundredth!(penny)6.5% of $195 is $12.68 OR

Set up a proportionTo solve for the tax.X = 12.675 = $12.68

=

DiscountDiscount is the Percent of a NumberMrs. Parker buys a new Beach Chair for

$35.00. She gets a 25% discount for being a teacher. What is the sale price of the beach chair?

First find 25% of $35.00. 0.25 x 35 = $8.75 This is the amount SUBTRACTED from $35.00. (Savings)

$35.00 - $8.75 = $26.25 for the chair.Sometimes the question asks for the amount

discounted and other times for the sale price.

TipMrs. Roan treats the Math teachers to lunch

at Flip Flops. The bill was $67.58 and she wants to leave a 20% tip. How much is the tip?

What is 20% of $67.58.Change 20% to 0.20 x 67.58 = 13.516Money rounded to the hundredth = $13.52

for the tip.Check the question. Are they asking for the

tip amount or the total including the tip?

Consumer MathRemember to READ THE QUESTION! (What are they asking?)

For tax and tip, find the %, then ADD for total cost.

Sales Price with Discount, find % then SUBTRACT for final price.