Transcript TODAY IN ALGEBRA…  Warm Up: Review solving Multi-step equations  STATs for Mid-Ch.3 Test  Learning Goal: 3.5 You will find ratios and write.

TODAY IN ALGEBRA…
 Warm Up: Review solving Multi-step
equations
 STATs for Mid-Ch.3 Test
 Learning Goal: 3.5 You will find ratios
and write and solve proportions
 Independent Practice
WARM UP: Simplify and solve.
1. −104 = −5𝑝 − 3𝑝
−104 = −8𝑝
−8
−8
𝟏𝟑 = 𝒑
3. 2𝑎 − 6 𝑎 − 4 = −4
2𝑎 − 6𝑎 + 24 = −4
−4𝑎 + 24 = −4
−24 − 24
−4𝑎 = −28
−4
−4
𝒂=𝟕
2. 2𝑣 + 5𝑣 − 8 = 13
7𝑣 − 8 = 13
+8 + 8
7𝑣 = 21
7
7
𝒗=𝟒
5
5 6
4. ∙ 5 − 4𝑔 = −18∙
6 5
−18∙5 6
6
5 − 4𝑔 =
5 − 4𝑔 = −15
−5
−5
−4𝑔 = −20
−4
−4
𝒈=𝟓
HOW DID YOU “SHAPE” UP??
Results for ALL of my Algebra classes:
GRADE
A/AB+/B/BC+/C/CD+/D
F
Average
NUMBER OF STUDENTS WHO TOOK THE Mid-CH.3 TEST (33
pts)
1ST PERIOD
6TH PERIOD
TOTAL
9
9
3
1
6
34.36
0
2
3
8
12
4
10
7
10
22
3.5 RATIOS AND PROPORTIONS: WRITING AND SIMPLIFYING
RATIOS
RATIO: uses division to compare two quantities.
𝑎
Can be written 3 ways: 𝑎 𝑡𝑜 𝑏 , 𝑎: 𝑏 ,
𝑏
EXAMPLE 1: A volleyball team PRACTICE 1: Derek has 44 CDs
plays 14 home matches and and his brother has 52 CDs.
10 away matches.
a. Find the ratio of Derek’s
a. Find the ratio of home
CDs to his brother’s CDs.
44 𝟏𝟏
𝐷𝑒𝑟𝑒𝑘 ′ 𝑠 𝐶𝐷𝑠
matches to away matches.
=
=
′
ℎ𝑜𝑚𝑒 𝑚𝑎𝑡𝑐ℎ𝑒𝑠 14 𝟕
𝐵𝑟𝑜𝑡ℎ𝑒𝑟 𝑠 𝐶𝐷𝑠 52 𝟏𝟑
=
=
𝑎𝑤𝑎𝑦 𝑚𝑎𝑡𝑐ℎ𝑒𝑠 10 𝟓 b. Find the ratio of Derek’s
b. Find the ratio of home
CDs to their CDs together.
matches to all matches.
′ 𝑠 𝐶𝐷𝑠
44 𝟏𝟏
𝐷𝑒𝑟𝑒𝑘
𝟕
ℎ𝑜𝑚𝑒 𝑚𝑎𝑡𝑐ℎ𝑒𝑠 14
=
=
=
=
96 𝟐𝟒
𝑡𝑜𝑡𝑎𝑙 𝐶𝐷𝑠
24 𝟏𝟐
𝑎𝑙𝑙 𝑚𝑎𝑡𝑐ℎ𝑒𝑠
3.5 RATIOS AND PROPORTIONS: SOLVING PROPORTIONS
WITH CROSS MULTIPLICATION
PROPORTION: an equation that states two RATIOs are equal.
𝑎
𝑐
=
𝑏
𝑑
EXAMPLE 2: Solve the proportion.
Solve by CROSS MULTIPLICATION
Solve the one-step equation
11
6
=
𝑥
30
11 ∙ 30 = 6 ∙ 𝑥
330 = 6𝑥
6
6
𝟓𝟓 = 𝒙
3.5 RATIOS AND PROPORTIONS: SOLVING PROPORTIONS
WITH CROSS MULTIPLICATION
PRACTICE:
𝑤
4
9
𝑚
𝑧
5
1.
=
2. =
3.
=
35
7
𝑤 ∙ 7 = 35 ∙ 4
7𝑤 = 140
7
7
𝒘 = 𝟐𝟎
2
12
9 ∙ 12 = 2 ∙ 𝑚
108 = 2𝑚
2
2
𝟓𝟒 = 𝒎
54
9
𝑧 ∙ 9 = 54 ∙ 5
9𝑧 = 270
9
9
𝒛 = 𝟑𝟎
3.5 RATIOS AND PROPORTIONS: WRITING AND SOLVING
PROPORTIONS
EXAMPLE 2: Write the
PRACTICE: Write the sentence
sentence as a proportion.
as a proportion. Then solve
Then solve the proportion.
the proportion.
5 is to 7 as a is to 49
5
7
=
𝑎
49
5 ∙ 49 = 7 ∙ 𝑎
245 = 7𝑎
7
7
𝟑𝟓 = 𝒂
y is to 20 as 9 is to 5
𝑦
20
=
9
5
𝑦 ∙ 5 = 20 ∙ 9
5𝑦 = 180
5
5
𝒚 = 𝟑𝟔
3.5 RATIOS AND PROPORTIONS: SOLVING PROPORTIONS
WITH CROSS MULTIPLICATION AND DISTRIBUTION
EXAMPLE 3: Solve the proportion.
Solve by CROSS MULTIPLICATION
Distribution FIRST
Solve the two-step equation
5
13
=
𝑘−4
39
5 ∙ 39 = 13 ∙ (𝑘 − 4)
195 = 13(𝑘 − 4)
195 = 13𝑘 − 52
+52
+ 52
247 = 13𝑘
13
13
𝟏𝟗 = 𝒌
3.5 RATIOS AND PROPORTIONS: SOLVING PROPORTIONS
WITH CROSS MULTIPLICATION AND DISTRIBUTION
PRACTICE: Solve the proportion.
6+𝑛
60
=
15
90
Solve by CROSS MULTIPLICATION (6 + 𝑛) ∙ 90 = 60 ∙ 15
90(6 + 𝑛) = 900
Distribution FIRST 540 + 90𝑛 = 900
Solve the two-step equation −540
− 540
90𝑛 = 360
90
90
𝒏=𝟒
HOMEWORK #5:
Pg. 165: 1-41 odd
If finished, work on other assignments:
HW #1: Pg. 137: 1-49 odd
HW #2: Pg. 144: 1-27 odd
HW #3: Pg. 150: 1-35 odd
HW#4: 157: 3-27 odd 44-46