Ratios in theReal World
What are some examples of ratios used in
real-life?
In this lesson, you will learn about ratios in
geometry and review techniques you can
use to solve geometric and real-life
problems with ratios.
4.
Vocabulary
Ratio a tob
If a and b are two quantities that are measured in the
same units, then the ratio of “a to b" is or a : b.
b
Proportion
An equation that equates two ratios
Extremes
In the proportion — a and d are the extremes
Means b d
In the proportion = , b and c are the means
b d
5.
To simplify ratios
withunlike units,
convert to like
units so that the
units divide out.
a. 16 kg
soo g
Simplifying Ratios
Then simplify the
fraction if
possible.
b. 7 ft
21 yd
6.
Writing o Ratio
Gotlt‘7 A bonsai tree is 18 in. wide and stands 2 h tall. Yhat is the ratio of the
width of the boncai to its height?
14. The bonsat is tn. wide and tall.
J 5. Write the same raöo three different ways.
â
Widtl 0f b0flSüi t0 X0lght 0f
b0fiSai
7.
8
Got if? Thelengths of the s!des ol a lrtart$le are' In the z•xtended
ratlo J : 7 : 9. The perlmeer 1s 60 cm. t’hat are thr lengths ol the sldes?
16. fahrl the trtanglc at IAe rtght. Use the extended ratlo to»zIte
an expression for cach side length.
J7. Compleie thr model to write an equation.
Relate is
18. Use the jusuñcattons below to ñnd the value of. .
4z 4 + 60
Combine llke terms
Dvtde each side by
19. Use the value off t‹› find cach side length.
4.y 1 7 T •
e 20. xc lengths of the sides of the trtangle are cm, cm, and cm.
8.
On Your Own
Theperimeter of rectangle JKLM is 56 cm.
The ratio of JK:KL is 4:3. Find the length
and width of the rectangle.
P 2/ +
2w
9.
Properties of Proportions
CrossProduct Property
The product of the extremes equals the product of the
means.
Y , then ad bc.
b d
Reciprocal Property
If 2 ratios are equal, then their reciprocals are also
equal.
If
a
c
b d
then b d
a
10.
Additional PropeGies ofProportions
I
f
' ,
then
b
b
d
c
d
If źż
— "
ñ" d
then ^+ b
+
d
b " d
11.
Use the CrossProducts Property to verify Property
(3).
fi C is equivalent to ad —
bc.
b d
a+b c+d
b d
is equivalent to (n -F b)d
ad ^
= bd — bc +
bd ad —
bc
So, b
——
d
is equivalent to
a+b c+d
b
d
Using
Proportions
About 15 ofevery 1000 liplit bulbs assembled at the Brite Lite Company are
defective. If the Brite Lite Company assembles approximately 13.000 light bulbs
each day. about hon many are defective?
Set up a proportion to solve the problem. Let. represent the number of defectire
light
bulbs per day.
15 .v
1000
13, 000
15(13.000) =
1000.v
195. 000=
1000.v
191 000 = v
1000
191 = .r
Cross Products Property
Simplify.
Divide each side by 1000.
Solve for the variable.
About 195 of the 13.000 light bulbs assembled each day are defectie.
14.
On Your Own
4.About 45 of every 300 apples picked at the Newbury Apple Orchard are
rotten. If 3560 apples were picked one week. about how many apples were
rotten?
5. About 56 of every 700 picture framesput together on an assembly line have
broken pieces of glass. If 60.000 picture frames are assembled each month,
about how many will has e broken pieces of glass?
Using Proportions
The ratioof width to length of a rectangle is 7 :
10.
The width of the rectangle is 91 cm. Write and
solve a proportion to find the length.
The ratio of the two acute angles in a right
triangle is 5 : 13. What is the measure of each
angle in the right triangle?
