Transcript EL CENTRO COLLEGE

EL CENTRO COLLEGE
ECC
Developmental Math 0090
REVIEW
by Diana Moore
DMAT 0090,
Objectives
 DMAT
0090 has 20 course
objectives. The objectives
correspond to course description
stated in the college catalog.
 The
only prerequisite for DMAT
0090 is an adequate assessment
test score.
DMAT 0090, Objective #1
 Demonstrate
knowledge of the
base ten numeration system using
both words and symbols.

Demonstrate knowledge of the base ten
numeration system using both words
and symbols.
Consider place value
5 6 8 . 2 5
This number
is: in words.
Express
this number
five hundred sixty-eight and
twenty-five hundredths

Demonstrate knowledge of the base ten
numeration system using both words
and symbols.
Express this statement in numerical form.
two thousand, forty-five and sixteen
thousandths
Consider place value
2 0 4 5.0 1 6
DMAT 0090, Objective #2
 Use
the operations of addition,
subtraction, multiplication and
division on the set of whole
numbers.

Use the operations of addition,
subtraction, multiplication and division
on the set of whole numbers.
Find the sum of the following
whole numbers:
16, 289, 7 and 1203
12 0
16
289
7
+ 1203
1515
The sum is
1515

Use the operations of addition,
subtraction, multiplication and division
on the set of whole numbers.
Find the difference of the following
whole numbers:
8092 and 2754
7 8_
8/1 0 9/12
–2754
5338
The difference is 5338.

Use the operations of addition,
subtraction, multiplication and division
on the set of whole numbers.
Find the product of the following
whole numbers:
3072 and 419
3072
x 419
27648
30720
1228800
1287168
The product
is 1287168.

Use the operations of addition,
subtraction, multiplication and division
on the set of whole numbers.
Find the quotient of the following
whole numbers:
3698 and 28
132
28 3698
multiply 1 x 28= 28
Subtract
89
multiply 3 x 28= 84
Subtract
58
multiply 2 x 28=
56
Subtract
2
59
36
89
divide
divide
divide
28
28
28
bring
down
The quotient is
132down
and the
bring
remainder is 2.
DMAT 0090, Objective #3
 Use
the proper order of operations
to simplify numerical statements.
 Use
the proper order of operations
to simplify numerical statements.
Order of operations
•Grouping symbols
•Exponents
•Multiply or divide
(in order from left to right)
•Add or subtract
(in order from left to right)
 Use
the proper order of operations
to simplify numerical statements.
Simplify the expression:
82 + 7(6 – 2)2
•Grouping symbols:
82 + 7(4)2
•Exponents:
64 + 7(16)
•Multiply or divide:
64 + 112
(in order from left to right)
•Add or subtract:
(in order from left to right)
176
DMAT 0090, Objective #4
 Evaluate
a given algebraic
expression with rational numbers.
 Evaluate
a given algebraic
expression with rational numbers.
Given x = 3, y = 7, and z = 9,
evaluate the expression: 5x – (z – y)2
•Substitute
•Grouping symbols:
•Exponents:
•Multiply or divide:
5(3) – (9 – 7)2
5(3) – (2)2
5(3) – 4
15 – 4
(in order from left to right)
•Add or subtract:
11
(in order from left to right)
The value of the expression is 11
DMAT 0090, Objective #5
 Use
both the division rules and
prime factorization of whole
numbers to find the least common
multiple.

Use both the division rules and prime
factorization of whole numbers to find
the least common multiple.
Division Rules
Division by 2:
last digit is even
Division by 3:
sum of digits is divisible by 3
Division by 5:
last digit is 0 or 5

Use both the division rules and prime
factorization of whole numbers to find
the least common multiple.
Use the division rules and the given
number to determine the following.
3549 is divisible by 3.
True: 3 + 5 + 4 + 9 = 21
21 is divisible by 3
6009 is divisible by 2.
False: The last digit is not even.
4580 is divisible by 5.
True: The last digit is zero.

Use both the division rules and prime
factorization of whole numbers to find
the least common multiple.
Use prime factorization to find the
LCM of the following numbers:
81 and 18
1
33
3 9
3 27
3 81
1
33
3 9
2 18
81 =
(3)(3)(3)(3)
18 = (2)(3)(3)
(2)(3)(3)(3)(3)
LCM = 162
DMAT 0090, Objective #6
 Use
the operations of addition,
subtraction, multiplication, and
division on positive fractions or
mixed numbers.

Use the operations of addition,
subtraction, multiplication, and division
on positive fractions or mixed numbers.
Add:
2
3
+
15 10
Prime factorization
15 =
(3)(5)
10 = (2)
(5)
(2) (3) (5)
LCD = 30
2 2
15 2
( )
4
30
The sum is
3 3
+ 10
3
9
+
30
13
30
( )

Use the operations of addition,
subtraction, multiplication, and division
on positive fractions or mixed numbers.
Add:
3
5
6
3
+
5
3
3
8
2
3
5
5
2
3
6 ( )+ 8 ( )
6
9
15
14
+
19
15
10
15
8
= 15
4
15
5 and 3 are
prime numbers
LCD = 15

Use the operations of addition,
subtraction, multiplication, and division
on positive fractions or mixed numbers.
Subtract: 7
3
15 10
7 2
15 2
3
10
3
3
( )- ( )
14 - 9 .
30
30
Reduce the answer
5 . = 1
6
30
15 =
(3)(5)
10 = (2)
(5)
(2) (3)(5)
LCD = 30

Use the operations of addition,
subtraction, multiplication, and division
on positive fractions or mixed numbers.
Subtract:
1
5
8
1
5
3
3
-5
2
3
5
5
5
10
15
2
3
8 ( ) -5 ( )
7
8
3 +15 15 15
2
8.
15
5 and 3 are
prime numbers
LCD = 15

Use the operations of addition,
subtraction, multiplication, and division
on positive fractions or mixed numbers.
Multiply:
2
15
3
10
1
1
2/
/
(3)(5)
3/ . Prime factorization
/
(2)(5)
Cross cancel
1
25
The product is
1.
25
Multiply

Use the operations of addition,
subtraction, multiplication, and division
on positive fractions or mixed numbers.
Multiply:
8
2
5
42
5
4
1.
6
25
6
1 1
(2)(3)(7)
/ /
5/
Improper
fraction
1
(5)(5)
Prime factorization
/
/ /
Cross cancel
(2)(3)
35
1
= 35
Multiply
Reduce

Use the operations of addition,
subtraction, multiplication, and division
on positive fractions or mixed numbers.
Divide:
2 _ 3
15
10
2
15
2
/
(3)(5)
10
Change to
3
reciprocal
1
(2)(5)
Prime factorization
/
Cross cancel
3
4
9
The quotient is
Multiply
44 .
9

Use the operations of addition,
subtraction, multiplication, and division
on positive fractions or mixed numbers.
Divide:
1
3
1 _
3
10 _ 12
3
5
10
5
3
12
(2)(
/ 5)
3
25
18
2
2.
5
Improper
fraction
Change to
reciprocal
5
Prime factorization
/
Cross cancel
(2)(2)(3)
7
Multiply
18
Mixed number
=1
DMAT 0090, Objective #7
 Change
fractions to decimals and
perform the operations of addition,
subtraction, multiplication and
division on decimal numbers.

Change fractions to decimals and
perform the operations of addition,
subtraction, multiplication and division
on decimal numbers.
Convert the following fractions to
decimals.
Example 2
Example 1
0.4
0.166 = 0.16
2
1
= 5 2.0
= 6 1.000
5
6
20
6
0
40
_
1 = 0.16
36
2
= 0.4 and
6
4
5

Change fractions to decimals and
perform the operations of addition,
subtraction, multiplication and division
on decimal numbers.
Find the sum of the following
decimal numbers:
11.56, 28.9, 27 and 1.203
11000 0
11.560
__0
28.900
_00
27.000
000
+ 1.203
68.663
optional:
Line
up the
add zerospoints
decimals
The sum is
68.663

Change fractions to decimals and
perform the operations of addition,
subtraction, multiplication and division
on decimal numbers.
Find the difference of the following
decimals numbers:
63 and 14.28
5 12 _ 9 0
_
6/ 3/ . 10/10
-14.28
4 8 .7 2
required:
Line
up the
add zerospoints
decimals
The
difference
Is 48.72

Change fractions to decimals and
perform the operations of addition,
subtraction, multiplication and division
on decimal numbers.
Find the product of the following
decimal numbers:
30.72 and 41.9
30.72
x 41.9
27 648
30 720
1228 800
1287.168
The product
is 1287.168.
Change fractions to decimals and
perform the operations of addition,
subtraction, multiplication and division
on decimal numbers.
Find the quotient of the following
decimal numbers:
3.69 and 2.5
119
190
36
150
.
divide
divide
1 4 76
divide
divide
2525
2.5 3.6 9 0 0 2525
multiply 1 x 25= 2 5
The
quotient
add
zero
add
zero
bringisdown
Subtract
11 9
2
1.476
multiply 4 x 25= 10 0
bring down
Subtract
1 90
place the
multiply 7 x 25= 1 7 5
bring point
down
Subtract
1 5 0 decimal

DMAT 0090, Objective #8
 Solve
applied problems using a
variety of methods, including
proportions and first degree
equations.

Solve applied problems using a variety
of methods, including proportions and
first degree equations.
Steps for solving application problems
Identify
Setup
Solve
Check
Explain

Solve applied problems using a variety
of methods, including proportions and
first degree equations.
A car traveled 160 miles in 3 hours. If the
car continues at the same speed, how far
will he travel in 5 hours?
Identify
Setup:
Solve
160 miles = 53 1/3 mph
3 hours
(53 1/3 mph)(5 hrs)
160 . 5
3
1
= 266 2/3
Explain: The car will travel 266 2/3 miles.

Solve applied problems using a variety
of methods, including proportions and
first degree equations.
A car traveled 160 miles in 3 hours. If the
car continues at the same speed, how far
will he travel in 5 hours?
Identify
Setup
Solve
160 miles
3 hours
3(x)
3x
x
=
x miles
5 hours
= 160(5)
= 800
= 266 2/3
Explain: The car will travel 266 2/3 miles.

Solve applied problems using a variety
of methods, including proportions and
first degree equations.
How many 2/3 cup jars can be filled from
an 8 cup pitcher?
Identify 1 jar = 2/3 cup
total = 8 cup
x = number of jars
Setup
Solve
2x=8
3
3 2x = 3 8
2 3
2
( ) ()
x = 12
Explain:
You can fill
12 jars.

Solve applied problems using a variety
of methods, including proportions and
first degree equations.
The sum of two number is 19. One
number is 5 more than the other.
Identify The two numbers are x and x + 5
Setup
1st number + 2nd number = sum
Solve
x + x+5
= 19
2x + 5 = 19
Explain: The
2x = 14
two numbers
x = 7
are 7 and 12.
second number x+5 = 12
DMAT 0090, Objective #9
 Use
percents to describe common
fractions and decimals, to make
comparisons between numbers and
to solve for the rate, base, and
amount in applied problems.

Use percents to describe common
fractions and decimals, to make
comparisons between numbers and to
solve for the rate, base, and amount in
applied problems.
Convert the following to percents
Example 1:
3
5
3 (100%)
5
60%
Example 2:
0.175
0.175(100%)
17.5%

Use percents to describe common
fractions and decimals, to make
comparisons between numbers and
to solve for the rate, base, and amount
in applied problems.
Place <, > or = in the space
between the numbers
3
5
0.601
3 (100%)
5
0.601(100%)
60%
<
60.1%

Use percents to describe common
fractions and decimals, to make
comparisons between numbers and to
solve for the rate, base, and amount in
applied problems.
rate
amount
=
100
base
What percent of 25 is 13?
R = 13
100
25
25R = 13(100) Cross Multiply
The rate
25R = 1300
Solve
is 52%
R = 52

Use percents to describe common
fractions and decimals, to make
comparisons between numbers and to
solve for the rate, base, and amount in
applied problems.
rate
amount
=
100
base
30% of what number is 27?
30 = 27
100
B
30B = 27(100) Cross Multiply
The base
30B = 2700
Solve
is 90.
B = 90

Use percents to describe common
fractions and decimals, to make
comparisons between numbers and to
solve for the rate, base, and amount in
applied problems.
rate
amount
=
100
base
What number is 40% of 150?
40 =
A
100
150
100A = 40(150) Cross Multiply
100A = 6000
Solve
The amount
is 60.
A = 60
DMAT 0090, Objective #10
 Interpret
a chart or graph.
 Interpret
70
60
50
40
30
20
10
0
J
a chart or graph.
F
M
A
M
J
J
March?
In
which
most
morewere
carsthe
were
in
How
many
cars
were
sold
insold
June
The
barmonth
graph
above
illustrates
the July?
number
of cars sold in the
cars
sold?
April
than May?
and
Approx.
35 cars
firstApprox.
seven
months
2001.
January,15
60+
sold
58
– cars
45of=were
13 cars
20
35
DMAT 0090, Objective #11
 Use
the formulas for perimeter and
area of common geometric figures
including, triangles, quadrilaterals,
and circles.

Use the formulas for perimeter and area
of common geometric figures including,
triangles, quadrilaterals, and circles.
Area of Polygons:
Rectangle:
A = LW
Parallelogram:
A = bh
Triangle:
A = 1 bh
2
Trapezoid:
A = 1 h(a + b)
2

Use the formulas for perimeter and area
of common geometric figures including,
triangles, quadrilaterals, and circles.
Perimeter of Polygons:
Any Polygon:
P = add all sides
Any Quadrilateral:
P = add 4 sides
Rectangle:
P = 2L + 2W
Triangle:
A=a+b+c

Use the formulas for perimeter and area
of common geometric figures including,
triangles, quadrilaterals, and circles.
Given the polygon:
5 ft
3 ft
4 ft
5 ft
8 ft
trapezoid
Identify the figure:___________________.
1 h(a+b) = 4(3+8)
2
=
22
ft
2
2
Find the area:_______________________.
add all sides
Find the perimeter:___________________.
8+5+3+5 = 21 ft

Use the formulas for perimeter and area
of common geometric figures including,
triangles, quadrilaterals, and circles.
Area:
Circle formula:
A = pr2
Circumference:
r = radius,
C = 2pr
or C = dr
p = 3.14
d = diameter,
r
d

Use the formulas for perimeter and area
of common geometric figures including,
triangles, quadrilaterals, and circles.
Given the Circle:
5 ft
circle with radius
Identify the figure:___________________.
2 = 3.14(5)2
2
pr
=
78.5
ft
Find the area:_______________________.
2pr = 2(3.14)(5)
Find the circumference:_______________.
= 31.4 ft
DMAT 0090, Objective #12
 Use
operations with signed (real)
numbers.
 Use
operations with signed (real)
numbers.
Addition Rules
Add like signs
p+p=p
n+n=n
Subtract unlike signs
p + n = subtract & find sign
n + p = subtract & find sign
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
3+4
p+p=p
3+4=7
positive 3 plus positive 4 equals positive 7
Add 3 + 4 and keep the positive sign.
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
–5 + (–9)
n+ n = n
–5 + (–9) = –14
negative 5 plus negative 9 equals
negative 14
Add 5 + 9 and keep the negative sign.
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
15 + (–8)
p + n = subtract &
find the sign
15 + (–8) = 7
positive 15 plus negative 8 equals positive 7
Subtract 15 – 8 and use the sign of the
number with the largest absolute value.
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
6 + (–9)
p + n = subtract &
find the sign
6 + (–9) = –3
positive 6 plus negative 9 equals negative 3
Subtract 9 – 6 and use the sign of the
number with the largest absolute value.
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
–6 + 8
n + p = subtract &
find the sign
–6 + 8 = 2
negative 6 plus positive 8 equals positive 2
Subtract 8 – 6 and use the sign of the
number with the largest absolute value.
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
–7 + 3
n + p = subtract &
find the sign
–7 + 3 = –4
negative 7 plus positive 3 equals negative 4
Subtract 7 – 3 and use the sign of the
number with the largest absolute value.
 Use
operations with signed (real)
numbers.
Subtraction Rules: Change to addition
Subtract like signs
p – p change to p + n
n – n change to n + p
Add unlike signs
p – n change to p + p
n – p change to n + n
 Use
operations with signed (real)
numbers.
Which addition rule applies to the
expression 6 – 9
p + n = subtract &
find the sign
6 + (–9) = –3
positive 6 plus negative 9 equals negative 3
Subtract 9 – 6 and use the sign of the
number with the largest absolute value.
 Use
operations with signed (real)
numbers.
Which addition rule applies to the
expression
–6 – (–8)
n + p = subtract &
find the sign
–6 + 8 = 2
negative 6 plus positive 8 equals positive 2
Subtract 8 – 6 and use the sign of the
number with the largest absolute value.
 Use
operations with signed (real)
numbers.
Which addition rule applies to the
expression 3 – (–4)
p+p=p
3+4=7
positive 3 plus positive 4 equals positive 7
Add 3 + 4 and keep the positive sign.
 Use
operations with signed (real)
numbers.
Which addition rule applies to the
expression –3 – 7
n+ n = n
–3 + (–7) = –10
negative 3 plus negative 7 equals
negative 10
Add 3 + 7 and keep the negative sign.
 Use
operations with signed (real)
numbers.
Multiplication and Division Rules:
Multiply and divide like signs
p(p) = p
and
p/p=p
n(n) = p
and
n/n=p
Multiply and divide unlike signs
p(n) = n
and
p/n=n
n(p) = n
and
n/p=n
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
3(4)
p(p) = p
3(4) = 12
positive 3 times positive 4 equals
positive 12
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
–6
–2
n=p
n
–6 = 3
–2
Negative 6 divided by negative 2 equals
positive 3.
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
3(–8)
p(n) = n
3(–8) = –24
positive 3 times by negative 8 equals
negative 24.
 Use
operations with signed (real)
numbers.
Which rule applies to the expression
16
–4
p=n
n
16 = –4
–4
Positive 16 divided by negative 4 equals
negative 4.
DMAT 0090, Objective #13
 Identify
numerical coefficients,
variables and constants.
 Identify
numerical coefficients,
variables and constants.
Given the algebraic expression:
2x + 7y – 9
What are the coefficients?
2, 7, and –9
What are the variables?
x and y
What are the constant terms?
–9
DMAT 0090, Objective #14
 Identify
and apply the commutative,
associative and distributive
properties.

Identify and apply the commutative,
associative and distributive properties.
Given
a + (b + c) = (a + b) + c
Identify the property.
Associative property
Complete the statement.
4 + (7 + 9) = (4 + 7) + 9
4 + 16
=
11 + 9
20
=
20

Identify and apply the commutative,
associative and distributive properties.
Given
a+b=b+a
Identify the property.
Commutative property
Complete the statement.
12 + 16 =
28 =
16 + 12
28

Identify and apply the commutative,
associative and distributive properties.
Given
a(b + c) = ab + ac
Identify the property.
Distributive property
Complete the statement.
8(3) + 8(9)
8(3 + 9) =
8(12) =
24 + 72
96
=
96
DMAT 0090, Objective #15
 Combine
like terms with the
distributive property.
 Combine
like terms with the
distributive property.
Simplify the expression:
2x – 3(4x – 1) + 5
2x – 3(4x – 1) + 5
2x – 12x + 3 + 5
–10x + 8
The simplified expression is
distribute –3
add like terms
–10x + 8
DMAT 0090, Objective #16
 Demonstrate
that a given number is
a solution to a first degree
equation.

Demonstrate that a given number is a
solution to a first degree equation.
Given x = -5, show that x is the
solution to the equation:
7x – 1 = –36
7x – 1 = –36
7(–5) – 1
–36
Substitute
–35 – 1
–36
Simplify
Both sides
–36 –36
have the
The solution is x = –5
same value.
DMAT 0090, Objective #17
 Solve
first degree equations of the
form
a+x=b
ax = b
a(bx + c) = d
Where a, b, c, and d are rational
numbers.

Solve first degree equations of the form
a+x=b
ax = b
a(bx + c) = d
Where a, b, c, and d are rational
numbers.
Use the addition property of equality.
Solve the equation.
x+5=2
x + 5 + (–5) = 2 + (–5)
x+0
= –3
x
= –3
The solution
is x = –3

Solve first degree equations of the form
a+x=b
ax = b
a(bx + c) = d
Where a, b, c, and d are rational
numbers.
Use the addition property of equality.
Solve the equation.
–2 + x = 7
–2 + x + (2) = 7 + (2)
x+0
= 9
x
= 9
The solution
is x = 9

Solve first degree equations of the form
a+x=b
ax = b
a(bx + c) = d
Where a, b, c, and d are rational
numbers.
Use the multiplication property of equality.
Solve the equation.
–5x = 20
–5x = 20
–5
–5
x = –4
The solution
is x = –4

Solve first degree equations of the form
a+x=b
ax = b
a(bx + c) = d
Where a, b, c, and d are rational
numbers.
Use the multiplication property of equality.
Solve the equation.
x
= –4
9
9( x ) = 9(–4)
The solution
9
Is x = –36
x = –36

Solve first degree equations of the form
a+x=b
ax = b
a(bx + c) = d
Where a, b, c, and d are rational
numbers.
Use the both property of equality.
Solve the equation.
3(x – 8) = 36
distribute
addition
simplify
division
Simplify
3x – 24 = 36
3x – 24 + (24) = 36 + (24)
3x = 60
3
3
Solution
x = 20
DMAT 0090, Objective #18
 Plot
points on the rectangular
coordinate system; identify x and y
intercepts for a given graph.

Plot points on the rectangular
coordinate system; identify x and y
intercepts for a given graph.
Graph the ordered pairs.
A(2,4)
B(–3,–2)
F
A
D
C(5,–1)
E
D(0,3)
E(2,0)
F(–3,5)
B
C

Plot points on the rectangular
coordinate system; identify x and y
intercepts for a given graph.
Find the x and y intercepts.
The x intercept
is (1,0)
The y-intercept
Is (0,–3)
DMAT 0090, Objective #19
 Compute
average, median and
mode on a given set of data.
 Compute
average, median and
mode on a given set of data.
Find the average of the following
numbers: 76,29,42,81,and 29
average = total
n
76 + 29 + 42 + 81 + 29
257
=
5
5
The average is 51.4
 Compute
average, median and
mode on a given set of data.
Find the median of the following
numbers: 76,29,42,81,and 29
Write numbers in order.
Change: 76, 29, 42, 81, 29
To:
29, 29, 42, 76, 81
The median is 42.
(middle number)
 Compute
average, median and
mode on a given set of data.
Find the mode of the following
numbers: 76,29,42,81,and 29
Write numbers in order.(optional)
Change: 76, 29, 42, 81, 29
To:
29, 29, 42, 76, 81
The mode is 29.
(most number of occurrences)
DMAT 0090, Objective #20
 Solve
for a variable other than A in
an area formula for a rectangle,
triangle, or parallelogram.

Solve for a variable other than A in an
area formula for a rectangle, triangle,
or parallelogram.
The area of a rectangle is 48 square feet.
The length is 12 feet. Find the width.
Use the formula: L = 12
LW = A
A = 48
Solve the equation:
12W = 48
W=4
The width is 4 feet.

Solve for a variable other than A in an
area formula for a rectangle, triangle,
or parallelogram.
The area of a triangle is 50 square feet.
The height is 10 feet. Find the base.
Use the formula:
1
2 BH
H = 10
A = 50
=A
Solve the equation:
1 (10B) = 50
2
5B = 50
B = 10
The base is
10 feet.

Solve for a variable other than A in an
area formula for a rectangle, triangle, or
parallelogram.
The area of a parallelogram is 50 square
feet. The height is 10 feet. Find the base.
Use the formula:
H = 10
A = 50
BH = A
Solve the equation:
10B = 50
B=5
The base is 5 feet.
End of review
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