Writing a Ratio

Write the ratio 3 feet (ft) to 8 inches (in) as a fraction in simplest form.

A ratio is a comparison of 2 values.

Compare these 2 values as a fraction.

3 ft

8 in Convert to the same unit.Hint: Always convert to the smaller unit.

=36 in

8 in

•12 =

Now, reduce

=9 in

2 in

9

2

There are other ways to write a ratio, also.

9 in

2 in

or

9 2

or 9:2

or 9 to 2

Finding a Unit RateIn 1987, Bo Jackson ran the 40 yd (yard) dash in 4.12 s (seconds).

In 1989, Deion Sanders ran the 60 yd dash in 6.68 s.Who ran at a faster rate?

To compare these runners, find each players yards second

sBoBo DeionDeion

40 yd

4.12 s

=9.708

≈ 9.7 yd s

60 yd

6.68 s

=8.982

≈ 9.0 yd s

Bo Jackson ran at the faster Bo Jackson ran at the faster rate.rate.Emerald’s 11 oz (ounce) can of almonds sells for $7.69.

Planters 5 oz bag of Trail Mix sells for $3.25. Which has the lower unit rate?

EmeraldEmerald’s’s

$7.69

11 oz=0.699≈$0.70

ozPlantersPlanters

$3.25

5 oz0.65 ≈$0.65

oz

ProportionsDana earned a salary of $27,000/mo, and Teresa earned a

salary of $6,500/mo. Dana paid $10,530 in income taxes, but Teresa paid $1,625 in income taxes. Did they pay a

proportional amount of taxes?When two ratios are equal, they form a

proportion So, let’s set Dana’s ratio of tax salary

Dana Teresa

=10,53027,000

1,6256,500 ... equal to Teresa’s ratio of

tax salary

Now, find the cross products.

•=68,445,000

= 43,875,000

Are they Are they equal?equal?

No -- the No -- the ratios ratios don’t don’t

form a form a proportioproportio

nn

Writing & Solving ProportionsJack’s recipe makes 2.25 pounds (lb) of chili, and it calls for 1.5 tablespoons of lime juice. If he wanted to make 5.1 lb of chili,

how many tablespoons of lime juice should he use?

To write a proportion, each ratio must be set up the same way.

juice

Chili #1

=2.251.5

5.1

l chili

Now, find the cross products.

Jack should use 3.4 Jack should use 3.4 tablespoons of lime juice.tablespoons of lime juice.

Let’s set up both ratios as

Chili #2

•

2.25 •

l

= 5.1 • 1.5

2.25l= 7.6

52.25 2.25

l= 3.4

Simplify, then solve

Scale ModelsHarmony MS has the longest bus rides in the county. Here’s a map showing the route from Loudoun Heights (next to Harper’s Ferry) to Harmony. If their map length is 1 3 inches apart, then how far apart are they actually apart?

4

Let’s make a proportion.

For scale model problems, your proportion will have:

scale ratio = distance ratio

actual

map

this is what the map tells

you in the corner

this is distance

between the 2 places

actual

map=

m

Since we don’t like fractions, let’s

change them to decimals.

0.25 • m = 1.75 • 20.25m

= 3.50.25 0.25

m = 14

...so the

actual distance is 14 miles. 0.2

5 1.75

Finding a Scale RatioThe longest drive in the contiguous U.S. is from Key West, FL to Seattle, WA. If the actual distance of the drive is 3,450 miles, what is the scale of the map. You’ll need a ruler with inches for this one.

Set up your proportion.

scale ratio = distance ratio

=

Usually, scale ratios scale ratios set the first value as 1

1 in

Measure to find the mapmap distancedistance between

them.

Solve.

in

3450 = a

a = so, the scale is1 in = mi

Using a Map’s Scale Ratio

Set up your proportion. scale ratio = distance ratio

=Measure the distancedistance in cm.

cm

Now, measure the map’s scalescale ratioratio in cm...

... and fill it in your scalescale ratioratio.

cm

a

Solve. a a ==

The distance between Lisbon, Portugal and Vladivostok, Russia is The distance between Lisbon, Portugal and Vladivostok, Russia is miles. miles.

José and Rosa, from Lisbon, Portugal, are going to visit the grandparents, in Vladivostok, Russia,

for the holidays.. What will be the actual distance of their drive?