Page 190 - NUMINO TG_6A
P. 190
12Increasing at the Same Rate Unit
2 . Solve the word problems using proportions. 2. The problems on this page will provide
a. The ratio of Ann’s money to Ryan’s money is 2 . variations on the operations already learned to
5
If Ann has $ 6, how much money do Ann and Ryan have in all? give a greater challenge. Solve the first
Ryan’s money = n They have $21 in all. problem for students.
Ann’s money 2 = 6 Example: 2a
Ryan’s money 5 n
Solve using proportions.
2 n=5 6
n = 15 Read out the problem and form an equation
Ryan has $15. based on the information.
How much money do Ann and Ryan have in all? 26
6 15 = 21
5n
4
b. The ratio of the width to the length of a rectangular backyard is 7 . Use cross products.
If the width of the yard is 12 m, what is the area of the backyard? 2n 5 6
length = n width 4 = 12 252 m2 2n 30
length 7 n
30
4 n = 7 12 n 2
n = 21
If the width of the yard is 12 m and the length is 21 m, n 15
the area is 12 21, which is 252 m2 .
Note to students that though the unknown
c. The ratio of the length to the width of a rectangular backyard is 6 . value is in a different place, the operation is
5 still the same.
If the width of the yard is 35 m, what is the area of the backyard? Have students solve the remaining problems.
width = n length 6 = n 1,470 m2
width 5 35
6 35 = 5 n
n = 42
35 42 = 1,470 m2
12. Increasing at the Same Rate 105
Some students may still have difficulty with the basic operations, not only of word problems, but ratios and
proportions in general. Provide the following set of tips to help students along.
Step 1: In order to solve ratios, you must change them from fractions to simple equations by multiplication.
Step 2: To change them, use the cross product method. Don’t worry if a variable exists, just act as if it fits
with the rest of the numbers.
Step 3: If a variable and a number are being multiplied, you can eliminate the multiplication symbol and just
place them together.
Step 4: If decimals are involved, simply treat them like any other number. Do not attempt to convert them to
fractions.
6A Unit 12 173
2 . Solve the word problems using proportions. 2. The problems on this page will provide
a. The ratio of Ann’s money to Ryan’s money is 2 . variations on the operations already learned to
5
If Ann has $ 6, how much money do Ann and Ryan have in all? give a greater challenge. Solve the first
Ryan’s money = n They have $21 in all. problem for students.
Ann’s money 2 = 6 Example: 2a
Ryan’s money 5 n
Solve using proportions.
2 n=5 6
n = 15 Read out the problem and form an equation
Ryan has $15. based on the information.
How much money do Ann and Ryan have in all? 26
6 15 = 21
5n
4
b. The ratio of the width to the length of a rectangular backyard is 7 . Use cross products.
If the width of the yard is 12 m, what is the area of the backyard? 2n 5 6
length = n width 4 = 12 252 m2 2n 30
length 7 n
30
4 n = 7 12 n 2
n = 21
If the width of the yard is 12 m and the length is 21 m, n 15
the area is 12 21, which is 252 m2 .
Note to students that though the unknown
c. The ratio of the length to the width of a rectangular backyard is 6 . value is in a different place, the operation is
5 still the same.
If the width of the yard is 35 m, what is the area of the backyard? Have students solve the remaining problems.
width = n length 6 = n 1,470 m2
width 5 35
6 35 = 5 n
n = 42
35 42 = 1,470 m2
12. Increasing at the Same Rate 105
Some students may still have difficulty with the basic operations, not only of word problems, but ratios and
proportions in general. Provide the following set of tips to help students along.
Step 1: In order to solve ratios, you must change them from fractions to simple equations by multiplication.
Step 2: To change them, use the cross product method. Don’t worry if a variable exists, just act as if it fits
with the rest of the numbers.
Step 3: If a variable and a number are being multiplied, you can eliminate the multiplication symbol and just
place them together.
Step 4: If decimals are involved, simply treat them like any other number. Do not attempt to convert them to
fractions.
6A Unit 12 173
