Last week we looked at the first type of question you will
encounter on the MSP placement Exam:
Simplifying Expressions Using the correct Order of Operations
Taking time to review fractions and decimals will be very helpful to you
since some of the order of operation questions will include both fractions and decimals. The Power
Point presentation has a special review section of helpful videos for you to watch at home.
This week we are going to review solving equations using specific types of
fractions and decimals : Rate, Ratio, Proportion, and Percent
You will need to know how to multiply, divide, find common factors, and simplify fractions.
Re-write the following fractions in simplest form:
1) 2/16
1/8
Easy right?
2) 3/27
1/9
3) 45/9
5
4) 56/154
4/11
 Let’s watch a quick video about rates and ratios (Video 1)
h ps://www.khanacademy.org/math/arithme c/rates‐and‐ra os/ra os_and_propor ons/v/simplifying‐rates‐and‐ra os Now you Try:
5) There are 50 text books for every 10 students.
Ratio 5:1
Rate: There are 5 books for every student
6) The restaurant uses 256 ounces of soda for every 36 customers.
Ratio 64:9
Rate: 64 ounces of soda are used for every 9 customers
7)There are 575 butterflies in the zoo for every 135 visitors.
Ratio 115:27
Rate: There are 115 butterflies for every 27 visitors
Try a Digital Challenge!
Find links to additional problems by visiting:
http://mathscienceprepgcc.wordpress.com/welcome/cohort2/exam-preparation-seminars/
 Let’s watch a video about Writing Proportions (Video 2)
h ps://www.khanacademy.org/math/algebra/ra o‐propor on‐topic/ra os_algebra/v/wri ng‐propor ons Prac ce these: h ps://www.khanacademy.org/math/algebra/ra o‐propor on‐topic/ra os_algebra/e/wri ng_propor ons Writing Proportions
8) 9 markers cost $12.78, write an equation that would help determine the cost of 4 markers.
9) 5 notebooks cost $9.05, write an equation that would help determine the cost of 13 notebooks.
10) 12 pencils cost $2.75, write an equation that would help determine the cost of 71 pencils.
Solving Proportions - Surprise You are doing Algebra!
Solve all of the following equations for x, write your response x =
11)
12)
13)
10X = 5(7)
7x = 90
5x = (8)7
10 X = 35
x = 90/7
5x = 56
X = 3.5 or 35/10
14)
x - 56/5 or 11.2
15)
16)
6(x-7) = 9(8)
5(x+3) = 80
5(x+8) = 60
6x—42 = 72
5x + 15 = 80
5x + 40 = 60
+42 +42
-15
-15
-40 -40
6x = 114
5x = 65
5x = 20
X = 114/6 = 19
X = 65/5 = 13
x = 20/5 = 4
Simplifying Simple Algebraic Equa ons
 Let’s watch a video about Equations (Video 3 & 4)
Video 3: h ps://www.khanacademy.org/math/algebra/solving‐linear‐equa ons‐and‐inequali es/why‐of‐algebra/v/why‐we‐do‐the‐
same‐‐thing‐to‐both‐sides‐‐simple‐equa ons Video 4: h ps://www.khanacademy.org/math/algebra/solving‐linear‐equa ons‐and‐inequali es/why‐of‐algebra/v/why‐we‐do‐the‐
same‐‐thing‐to‐both‐sides‐‐two‐step‐equa ons (write down the problems from the videos)
For these exercises, do not convert fractions to decimals.
17) 8x + 1 = 7
6/8
20) 7x + 2 = 3
1/7
23) 8x + 1 = 6x + 6 5/2
18) 6x-5 = 6
11/6
21) 7x+2=3
1/7
24) 6x‐5 = 8x + 2 7/2
19)2x + 9 = 10
1/2
22) 4x+2=36
17/2
25) 2x + 9 = 10x + 6 8/3 Ratio and Proportion Word Problems
 Let’s watch a video about solving word problems with proportions
h ps://www.khanacademy.org/math/arithme c/rates‐and‐ra os/ra os_and_propor ons/v/ra o‐word‐problem‐
exercise‐example‐1
17) Alex and Jay each have an mp3 player. Alex had 2/7 as many songs as Jay.
when Jay accidentally erased 36 songs from his mp3 player, Alex then had
twice as many songs as Jay. How many songs did Jay originally have?
18) The ratio of Julian’s money to Philip’s money was 1 : 2. When Julian received 24 dollars form
his sister, Philip then had only half as much money as Julian. How much money did Philip have?
19) Erin and Skylar were playing a logic game. Skylar had 1/2 as many points as Erin. When Skylar
scored 30 more points, she then had twice as many points as Erin. How many points did Erin have?
20) Terry and Claire each had a stamp collection. Claire had 2/9 as many stamps as Terry. When
Terry lost 88 stamps, Claire then had twice as many as Terry. How many stamps were in Terry’s
collection at first?
Exactly Like the Exam:
These questions are just like the type of rates, ratios, and percentage problems you will see
on the placement exam.
1) The soccer team won 12 out of its first 18 games. What is the ratio of games lost to
games played in simplest form? 18 –12 = 6 then 6:18 = 1:3
2) Circle Yes or No to indicate if the following sets of ra os are equivalent. 980 : 18 and 240 : 2 Yes No 36 : 3 and 324 : 27 Yes No 64 : 4 and 80 : 5 Yes No 3) Find the value of n for the following equa ons: N = 84/5
n = 60
n = 500/3
4) In a hospital, 24 ml of a drug are mixed with 1.2 liters of water to form a drug‐water solu on. Following this ra o, how many ml of water would be needed to mix with 1.2ml of drug? 24x = 1.2 (1200)
24x = 1440
X = 60
60ml water is needed to mix with 1.2 ml of drug.
5) Find .6% of 36 Postponed un l next Session
6) 360 students are in the gym for a basketball game. 50% of the students are Freshmen, 30% are Sopho‐
mores, a er excusing the Freshmen and Sophomores, 75% of the remaining students were juniors, once the juniors were excused how many students remained in the gym? Postponed un l next Session