Transcript PROP Lesson 06 Luke

Lesson 6
Write and Solve Proportions
1.
Ten boys and 15 girls ran a mile under seven minutes in
P.E.
a) Write the ratio of boys to girls who ran a mile under
seven minutes.
b) Write the ratio of boys to all students who ran a mile
under seven minutes.
c) Write the ratio of girls to all students who ran a mile
under seven minutes.
2.
The football team had a win to loss ratio of 5 : 2. What is
their ratio of wins to total games played?
Target:
Write and solve proportions.

Proportion: An equation stating two ratios are
equivalent.
2 x

Solve the proportion
using cross products.
3 15





Write the cross products.
Simplify the equation.
Divide both sides by 3.
3·x = 2·15
3x = 30
x = 10
2 ? 10

3 15
Check your answer.
10 simplifies to 2 , so the solution is correct.
15
3
6 1.5
Solve the proportion 
using cross products.
a 7




Write the cross products.
Simplify the equation.
Divide both sides by 1.5.
1.5·a = 6·7
1.5a = 42
a = 28
Check your answer.
6 ? 1 .5

28 a
1.5(28) ? 6  7
42  42
Determine whether the pair of ratios forms a proportion.
4
2
and
9
6
4 ? 2

9 6

Write the proportion using ≟.
Check using cross products.
Simplify.

24  18 so the ratios DO NOT form a proportion.


4·6 ≟ 9·2
24 ≟ 18
Determine whether the pair of ratios forms a proportion.
15
50
and
9
30




Write the proportion using ≟.
Check using cross products.
Simplify.
15 ? 50

9 30
15·30 ≟ 9·50
450 ≟ 450
The cross products are equal so the ratios form a
proportion.
Write a proportion for the following phrase and solve it: $4 in
30 minutes; $b in 45 minutes.

Write both ratios with dollars
in numerator and minutes in
denominator.
Write the cross products.
Simplify.
Divide both sides by 30.

$6 in 45 minutes



$4
$b

30 minutes
45 minutes
4·45 = 30·b
180 = 30b
6=b
Solve each proportion.
1.
2.
25 x

15 3
6 8

9 a
Determine whether the pair of ratios forms a proportion.
3.
4.
4
10
and
5
12
9
6
and
15
10
How would a chef use proportions? How would a
builder use proportions? How can you use proportions?