Page 188 - NUMINO TG_6A

12Increasing at the Same Rate Unit

2 . Solve each proportion with decimals. 2. This time the operations will be

1.5 a 1.5 a complicated by the addition of a decimal in
20 80 20 80
= = Cross products the proportion.

1.5 80 = 20 a Example: 1.5 a
120 = 20a 20 80
a=6
Use the cross products method.

1.5 80 20a

Simplify.

a. 1.2 = a b. 9 = 24 120 20a
30 50 1.5 b
Solve for a.

1.2 50 = 30 a 9 b = 1.5 24 a 120 , a 6
60 = 30a 9b = 36 20
a=2 b=4

c. 1.2 = c d. 2.5 = d Note to students that the addition of a
3 15 3.5 14 decimal does not mean that the operation
changes. It simply complicates the process
1.2 15 = 3 c 2.5 14 = 3.5 d of multiplication. Have students solve the
18 = 3c 35 = 3.5d rest of the problems individually.
c=6 d = 10

e. 1.5 = 2 f. 3.4 = 17
4.5 e f 14

1.5 e = 4.5 2 3.4 14 = f 17
1.5e = 9 47.6 = 17f
e=6 f = 2.8

12. Increasing at the Same Rate 103

Some students may incorrectly perform the cross product method, placing the variable in the wrong place

and resulting in an incorrect equation.

Example: Use cross products to solve a 12
5 30 .

Students may forget to cross the products, and instead simply multiply horizontally, resulting in this

equation.

12a 150, a 150 which is incorrect.
12

30a 60, a 2 which is correct.

6A Unit 12 171