solve??

Step 1

2. Cross multiply

3. Isolate the variable

**Ratios & Proportions**

**First,**

**A comparison between two or more numbers or items**

2 boys

3 girls

4 clear beads

20 beads

Proportion

- An equation containing two ratios that are equal

=

2:3

4:20

You can use Cross Multiplication to see if the two are proportional

1

3

9

3

3(3) = 1(9)

9 = 9

These ratios are proportional

So what happens when we don't know one of the numbers in a proportion?

x

4

12

16

=

1. Set up a proportion

3 steps...

SWBAT use

cross multiplication

in order to

solve proportions

2 to 3

4 to 20

Three ways to express ratios:

1. Using the word "to"

2. Using a colon":"

3. As a fraction

=

?

?

What is the ratio of ties to bow ties?

Now let's look at how to set up a proportion.....

=

5 fingers

2 hands

10 fingers

1 hand

=

must be in the same units

must be in the same units

**What if....**

How many fingers compared to

how many hands

5 fingers

1 hand

**What if we ride bikes for**

40 minutes and make it

5 miles...how long would

we make it if we rode for

60 minutes?

40 minutes and make it

5 miles...how long would

we make it if we rode for

60 minutes?

You are thinking...

I can't do that!

It's too hard.

Yes u can!!

What are the quantities we are comparing?

miles to minutes

miles : minutes

miles

minutes

Find an equal ratio

5 miles to 40 minutes = x miles to 60 minutes

5 miles : 40 minutes = x miles : 60 minutes

5 miles

40 min

x miles

60 min

=

Cross multiply

means

extremes

5

x

40

60

=

5 (60)

300

40 (x)

40(x)

300

=

40(x)

We need to isolate the variable...

big words for get the variable (x) by itself.

What is the opposite of multiplication?

DIVISION

300 = 40 (x)

To get the "x" isolated, divide

each side by 40

300

40

That's our answer!

7.5!

We can ride

7.5 miles in

60 minutes

When you put it all together...

5 miles

40 minutes

x miles

60 minutes

=

Extremes

5(60) = 300

Means

40(x)

40(x) = 300

40(x) 300

40 40

Step 1

Set up the proportion

Step 2

Multiply

means x extremes

Step 3

Isolate the variable

=

x = 7.5

Miles on top

minutes on bottom

Next

we defined

PROPORTION

1

3

3

9

Check - is it equal?

means 3 x 3 = 9

and

extremes 1 x 9 = 9

Yes

9 = 9 It

is

a proportion!

2:6

2 to 6

2 choco

package

Gage

Veronica

Zanyah

Seanterria

Aron

40x

40

7.5 =

x

=

=

300

=

40x

Our proportion is...

5 miles 7.5 miles

40 minutes 60 minutes

=

we defined "Ratio"

3 to 16

3:16

3 orange

16 total m&ms

Domne't