Ratios and Proportions

Warm Up - Simplify

108)a

2

11b

21

3)c

36

2

22

7

21

Ratio – comparison of two numbers by division.

Proportion – an equation stating that two ratios are equal.

Ratio# boys to # girls

# boys : # girls#

#

boys

girls

Ratios are equal if the cross products are equal.

24 4

30 5

120120

430524

:

xx

Check

Solve24

15 16

n

5.2216

360

16

16

36016

)15)(24(1616

24

15

n

n

n

n

n

2

45Or

Solve3 1

5 7

x x

16

7

716

5721

5)13)(7(75

13

x

x

xx

xx

xx

Solve 8 3

4 1 2 5x x

4

37

374

3124016

)14(3)52(852

3

14

8

x

x

xx

xxxx

Seth earns $152 in 4 days. At that rate, how many days will it take him to earn $532?

daysx

x

xx

14

2128152

)532(4152

532

4

152

Lanett drove 248 miles in 4 hours. At that rate, how long did it take her to drive 93 miles?

hoursx

x

xx

x

5.1

1488248

)372(4248

372

4

248

)93(

4

248

A blueprint for a house states that 2.5 inches equals 10 feet. If the length of a wall is 12 feet, how long is the wall on the blueprint?

inchesx

x

x

ft

x

ft

in

3

3010

)12)(5.2(10

12.10

.5.2

The ratio of the measures of the angles of a triangle is 2 :7 : 3. Find the measure of the smallest angle of the triangle.

Smallest Angle:

15

18012

180372

x

x

xxx

30)15(2

2x

The profits in a business are shared by three partners in the ratio 4 : 5 : 9. The profits for the year was $720,000. Determine the number of dollars received by the partner with the second largest share.

Find x:Find the 2nd largest shared holder’s profit:

000,40

000,72018

000,720954

x

x

xxx

000,200$

)000,40(5

5x

The ratio of the measures of the angles of a triangle is 3 : 4 : 2. Find the measure of the largest angle of the triangle.

Find x: The largest angle:

20

1809

180243

x

x

xxx

80

)20(4

4x

If the ratio of boys to girls in a geometry class is 3:1, and there are 28 students in the class, how many are boys?

Find x:Find the number of boys.

7

284

283

x

x

xx

Boys

xBoys

21)7(3

3:

The width of a rectangle is 3/5 of the length. The perimeter is 48 feet. Find the area of the rectangle.

lw5

3

.15

24016

240610

485

62

485

322

22

ftl

l

ll

ll

ll

Pwl

..135

)9(15

155

315

ftsqA

A

A

lxwArea