______Confident
Chapter/Lesson: Chapter 7 Lesson 3 Page: 308
______Ok
Objective/Title: Equivalent Ratios
______Lost
Important Terms
Quick Solve
Ratio: compares 2 numbers or
measurements
Find what you are multiplying or dividing
by in order to get the equivalent
numerator or denominator (whichever one
it already gives you)
Equivalent: representing the same
amount
Multiply or divide by the EXACT same
number that you came up with on step
#1.
It is NOT necessary to simplify
Practice Questions
Find the missing term.
1. 72
144
=
n8
16
2. 21 =
n 28
147
196
3. 5
16
=
5. 4
6
=
y 20
30
6. 12
3
=
m4
1
7. 15
9
9. 2
5
=
p 10
25
10. 18
6
=
6
d2
11. 12
3
Compare = or ≠
13. 3
9
= 15
5
14. 12
4
≠
4
1
15. 4:3
=
25
n 80
=
8:6
=
5
p3
4. 5
8
8. 7
14
4
q1
12. 56
8
16. 5 to 20
=
=
10
k 16
=
t1
2
= y 14
2
10 to 40
Notes and Examples
1. Find what you are multiplying or dividing by in order to get the equivalent numerator or
denominator that is already given in the problem.
example;
3
4
n
12
12 is the equivalent denominator of 4. To get from 4 to 12;
I must multiply by 3.
×3
2. Multiply or divide by the EXACT same number you multiplied or divided by on step #1 in
order to determine the missing number.
×3
example;
3
4
n (3 × 3 = 9)
12
Since I multiplied by 3 on the denominator, I
must also multiply by 3 on the numerator.
×3
n = 9 , so the ratio 9 is equivalent to the ratio 3
12
4
3. It is NOT necessary to simplify equivalent ratios.
Are the two ratios a proportion?
Cross multiply, diagonally from bottom to top
*If they are the same = they are a proportion
*If they are different ≠ they are not a proportion
14
35
14
35
2
5
=
14 × 5 = 70
35 × 5 = 70
2
5
From first fraction to second fraction
Smaller to larger = × (multiply)
Larger to smaller = ÷ (divide)
37
______Confident
Chapter/Lesson: Chapter 7 Lesson 4 Page: 310
______Ok
Objective/Title: Proportions
______Lost
Important Terms
Quick Solve
Proportion: shows that two ratios are
equivalent
Cross multiply (multiply the numerator of
one ratio by the denominator of the other
ratio.)
Ratio: compares 2 numbers or
measurements
Divide by the numerator or denominator
that was not part of the problem from
step 1.
Equivalent: representing the same
amount
You can solve SOME proportions just like
you would solve equivalent ratios.
Practice Questions
Find the missing term.
1. 5
2
=
10
a4
5. e 18 = 6
15
5
9. 24 =
j 36
8
12
2. 3 =
h1
9
3
3. 12 =
c4
6. 3 =
21
k2
14
7. 120
30
10. 100
20
=
5
x1
3
1
=
4. 7 =
m 14
s 20
5
8. 30
25
11. f 24 = 8
15
5
12. 5
5
2
4
=
u 12
10
= 7
p7
Do the two ratios form a proportion? Yes or No
13. 5
15
Yes
10
30
No
14. 2
3
Yes
4
9
No
15. 12
3
Yes
No
6
2
16. 3
8
Yes
No
12
32
Notes and Examples
1. Cross multiply. Multiply the numerator of one ratio by the denominator of the other
ratio. It helps to draw a diagonal line to connect the two numbers.
example:
8 =
16
5
h
16 × 5 = 80
2. Divide the product (from step 1) by the numerator or denominator that was not part
of the problem from step 1. I used the 16 and the 5, so the only number I have left to
use is the 8.
example:
10
80
8
h = 10
3. You can solve SOME proportions just like you solve equivalent ratios. If you can
multiply or divide to get from one numerator (or denominator), then you can solve the
proportion like equivalent ratios
÷6
example
18
n
=
3
1
I can divide easily by 6 in order to get from 18 to 3, therefore I can solve this
proportion just like equivalent ratios. The number n is a number I can divide by 6 to
get to 1. I multiply 6 x 1 to get to n
6×1=6
n=6
Are the two ratios a proportion?
Cross multiply, diagonally from bottom to top
*If they are the same = they are a proportion
*If they are different ≠ they are not a proportion
14
35
14
35
2
5
=
14 × 5 = 70
35 × 5 = 70
2
5
38