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EL CENTRO COLLEGE
Developmental Math 0090Developmental Math 0090
REVIEWREVIEW
ECCECC
by Diana Moore
DMAT 0090, Objectives
DMAT 0090 has 20 course DMAT 0090 has 20 course objectives. The objectives objectives. The objectives correspond to course description correspond to course description stated in the college catalog.stated in the college catalog.
The only prerequisite for DMAT The only prerequisite for DMAT 0090 is an adequate assessment 0090 is an adequate assessment test score.test score.
DMAT 0090, Objective #1
Demonstrate knowledge of the Demonstrate knowledge of the base ten numeration system using base ten numeration system using both words and symbols.both words and symbols.
Demonstrate knowledge of the base ten numeration system using both words and symbols.
5 6 8 . 2 5Express this number in words.This number is:
five hundred sixty-eight and twenty-five hundredths
Consider place value
hun
dred
s
tens
ones
thou
sand
s
tent
hs
hund
redt
hs
thou
sand
ths
---- a
nd --
---
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
2 0 4 5 . 0 1 6
Consider place value
hun
dred
s
tens
ones
thou
sand
s
tent
hs
hund
redt
hs
thou
sand
ths
---- a
nd --
---
Use the operations of addition, Use the operations of addition, subtraction, multiplication and subtraction, multiplication and division on the set of whole division on the set of whole numbers.numbers.
DMAT 0090, Objective #2
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
16289
7 + 1203
12 0
1515 The sum is1515
7 8 _ /1 /12
5 3 3 8
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
8 0 9 2– 2 7 5 4
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
3072x 419
2764830720
1228800 The product is 1287168.1287168
Subtract 8
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
28 3698 multiply 1 x 28= 28
Subtract 5
Subtract 2
9 bring down
1 divide 3628
3 divide 8928
multiply 3 x 28= 84
multiply 2 x 28= 568 bring down
2 divide 5928
The quotient is 132 and the
remainder is 2.
Use the proper order of operations Use the proper order of operations to simplify numerical statements.to simplify numerical statements.
DMAT 0090, Objective #3
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: 176(in order from left to right)
Evaluate a given algebraic Evaluate a given algebraic expression with rational numbers.expression with rational numbers.
DMAT 0090, Objective #4
Evaluate a given algebraic expression with rational numbers.
Given x = 3, y = 7, and z = 9, evaluate the expression: 5x – (z – y)2
•Substitute 5(3) – (9 – 7)2
•Grouping symbols: 5(3) – (2)2 •Exponents: 5(3) – 4 •Multiply or divide: 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
Use both the division rules and Use both the division rules and prime factorization of whole prime factorization of whole numbers to find the least common numbers to find the least common multiple.multiple.
DMAT 0090, Objective #5
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.
6009 is divisible by 2.
4580 is divisible by 5.
True: 3 + 5 + 4 + 9 = 21 21 is divisible by 3
False: The last digit is not even.
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
13 3
3 93 273 81
13 3
3 92 18
81 = (3)(3)(3)(3)18 = (2)(3)(3)
(2)(3)(3)(3)(3)
LCM = 162
Use the operations of addition, Use the operations of addition, subtraction, multiplication, and subtraction, multiplication, and division on positive fractions or division on positive fractions or mixed numbers.mixed numbers.
DMAT 0090, Objective #6
Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers.
Add: 2 315 10
+
Prime factorization15 = (3)(5)10 = (2) (5) (2) (3) (5)LCD = 30
2 315 10( ) + ( )2
233
4 9 30 30
+
1330The sum is
6 8
Add: 3 2 5 3
+
5 and 3 areprime numbersLCD = 15
3 2 5 3( ) + ( )3
355
6 8 9 10 15 15
+
415
Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers.
6 8
14 1915 = 15
Reduce the answer= 1 6
Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers.
Subtract: 7 315 10
-
15 = (3)(5)10 = (2) (5) (2) (3)(5)LCD = 30
7 315 10( ) - ( )2
233
14 9 . 30 30-
5 .30
Subtract: 1 2 5 3
3 10 15 15 -8 5
8 5
8 5
-
5 and 3 areprime numbersLCD = 15
1 2 5 3( ) - ( )3
355
2 8 .15
Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers.
7 +15 15
2 3 . Prime factorization(3)(5) (2)(5)
1 1 / / / /
Cross cancel
Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers.
Multiply: 2 315 10
1 25 Multiply
The product is 1 . 25
(2)(3)(7) (5)(5) Prime factorization 5 (2)(3)
1 1 1 / / / / / / Cross cancel
Multiply: 2 1 . 5 68 4
Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers.
35 Multiply 1
42 25 Improper 5 6 fraction
= 35Reduce
2 10 Change to15 3 reciprocal
Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers.
Divide: 2 _ 315 10
2 (2)(5) Prime factorization(3)(5) 3
1 / / Cross cancel
4 9 Multiply
The quotient is 4 4 . 9
10 5 Change to 3 12 reciprocal
Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers.
Divide: 1 _ 2 . 3 5
(2)( 5) 5 Prime factorization 3 (2)(2)(3)
1/ / Cross cancel
25 Multiply 18
3 210 _ 12 Improper 3 5 fraction
= 1 718 Mixed number
Change fractions to decimals and Change fractions to decimals and perform the operations of addition, perform the operations of addition, subtraction, multiplication and subtraction, multiplication and division on decimal numbers.division on decimal numbers.
DMAT 0090, Objective #7
and
Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers.
25
Convert the following fractions to decimals.
= 5 2.0 2 0 0
0.416
= 6 1.000 6 40 36 4
0.166 = 0.16
Example 1 Example 2
25
= 0.416
_= 0.16
Line up the decimals points
11.56028.90027.000
+ 1.203
Find the sum of the following decimal numbers:
11.56, 28.9, 27 and 1.203
The sum is68.663
Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers.
__0_00000
optional: add zeros
11000 0
68.663
Line up the decimals points6 3 . 0 0
- 1 4 . 2 8
Find the difference of the following decimals numbers:
63 and 14.28
Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers.
0 0required: add zeros
The difference
Is 48.72
512 _ 9 0 / / 1/1_
4 8 . 7 2
Find the product of the following decimal numbers:
30.72 and 41.9
30.72x 41.9
27 64830 720
1228 800 The product is 1287.168.1287.168
Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers.
.
place the decimal point
multiply 7 x 25= 1 7 5
2.5 3.6 9
Subtract 11
Find the quotient of the following decimal numbers:
3.69 and 2.5
multiply 1 x 25= 2 5
Subtract 1 9
Subtract 1 5
9 bring down
1 divide 3625
4 divide 119 25
multiply 4 x 25= 10 0
0 add zero
0 bring down
7 divide 190250
add zero
0 bring down
2
Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers.
6 divide 150 25
The quotient is 1.476
Solve applied problems using a Solve applied problems using a variety of methods, including variety of methods, including proportions and first degree proportions and first degree equations.equations.
DMAT 0090, Objective #8
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 160 miles = 53 1/3 mph 3 hours
Setup: (53 1/3 mph)(5 hrs)
Solve 160 . 5 = 266 2/3 3 1
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 160 miles = x milesSetup 3 hours 5 hours
Solve 3(x) = 160(5)
3x = 800
x = 266 2/3
Explain: The car will travel 266 2/3 miles.
Solve 3 2 3 2 3 2( ) ( )
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 2 3 Explain:
You can fill 12 jars.
x = 8
x = 8
x = 12
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
2x = 14
x = 7
second number x+5 = 12
Explain: The two numbers are 7 and 12.
Use percents to describe common Use percents to describe common fractions and decimals, to make fractions and decimals, to make comparisons between numbers and comparisons between numbers and to solve for the rate, base, and to solve for the rate, base, and amount in applied problems.amount in applied problems.
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.
Convert the following to percents
3535
(100%)
60%
Example 2:0.175
0.175(100%)
17.5%
Example 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.
Place <, > or = in the space between the numbers
35
35
(100%)
60%
0.601
0.601(100%)
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
1325
=
What percent of 25 is 13?R
100=
25R = 13(100) Cross Multiply
25R = 1300 Solve
R = 52
The rate is 52%
rate amount 100 base
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.
27 B
=
30% of what number is 27?30
100=
30B = 27(100) Cross Multiply
30B = 2700 Solve
B = 90
The base is 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.
A150
What number is 40% of 150?40
100=
100A = 40(150) Cross Multiply
100A = 6000 Solve
A = 60
The amount is 60.
rate amount 100 base
=
Interpret a chart or graph.Interpret a chart or graph.
DMAT 0090, Objective #10
The bar graph above illustratesthe number of cars sold in the first seven months of 2001.
How many cars were sold in March?
Approx. 35 cars
How many cars were sold in June
and July?
Approx. 15 + 20 = 35 cars
How many more cars were sold in
April than May?
Approx. 58 – 45 = 13 cars
Interpret a chart or graph.
70
60
50
40
30
20
10
0 J F M A M J J
In which month were the most
cars sold?
January, 60 cars were sold
Use the formulas for perimeter and Use the formulas for perimeter and area of common geometric figures area of common geometric figures including, triangles, quadrilaterals, including, triangles, quadrilaterals, and circles.and circles.
DMAT 0090, Objective #11
Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles.
Rectangle: A = LW
Parallelogram: A = bh
Triangle: A = 1 bh 2
Trapezoid: A = 1 h(a + b) 2
Area of Polygons:
Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles.
Any Polygon: P = add all sides
Any Quadrilateral: P = add 4 sides
Rectangle: P = 2L + 2W
Triangle: A = a + b + c
Perimeter of Polygons:
Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles.
Given the polygon: 3 ft
5 ft 4 ft 5 ft
8 ft
Identify the figure:___________________.trapezoid
Find the area:_______________________.
Find the perimeter:___________________.
1 h(a+b) = 4(3+8)2 2 = 22 ft2
add all sides8+5+3+5 = 21 ft
Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles.
Area: A = r2
Circumference: C = 2r or C = dr
r = radius, d = diameter, = 3.14
Circle formula:
r d
Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles.
Given the Circle:
Identify the figure:___________________.circle with radius
Find the area:_______________________.
Find the circumference:_______________.
r2 = 3.14(5)2 = 78.5 ft2
2r = 2(3.14)(5) = 31.4 ft
5 ft
Use operations with signed (real) Use operations with signed (real) numbers.numbers.
DMAT 0090, Objective #12
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.
Identify numerical coefficients, Identify numerical coefficients, variables and constants.variables and constants.
DMAT 0090, Objective #13
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
Identify and apply the commutative, Identify and apply the commutative, associative and distributive associative and distributive properties.properties.
DMAT 0090, Objective #14
Identify and apply the commutative, associative and distributive properties.
Givena + (b + c) = (a + b) + c
Identify the property.
Associative property
Complete the statement.
4 + (7 + 9) = (4 + 7) + 94 + 16 = 11 + 9 20 = 20
Identify and apply the commutative, associative and distributive properties.
Givena + b = b + a
Identify the property.
Commutative property
Complete the statement.
12 + 16 = 16 + 12
28 = 28
Identify and apply the commutative, associative and distributive properties.
Givena(b + c) = ab + ac
Identify the property.
Distributive property
Complete the statement.
8(3 + 9) = 8(3) + 8(9)8(12) = 24 + 72 96 = 96
Combine like terms with the Combine like terms with the distributive property.distributive property.
DMAT 0090, Objective #15
Combine like terms with the distributive property.
Simplify the expression:2x – 3(4x – 1) + 5
2x – 3(4x – 1) + 5
2x – 12x + 3 + 5 distribute –3
–10x + 8 add like terms
The simplified expression is –10x + 8
Demonstrate that a given number is Demonstrate that a given number is a solution to a first degree a solution to a first degree equation.equation.
DMAT 0090, Objective #16
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
–36 –36
The solution is x = –5
Both sides have the same value.
Solve first degree equations of the Solve first degree equations of the formform a + x = ba + x = b ax = bax = b a(bx + c) = da(bx + c) = dWhere a, b, c, and d are rational Where a, b, c, and d are rational
numbers.numbers.
DMAT 0090, Objective #17
Solve first degree equations of the form a + x = b ax = b a(bx + c) = dWhere 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 solutionis x = –3
Solve first degree equations of the form a + x = b ax = b a(bx + c) = dWhere 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 = 9The solutionis x = 9
Solve first degree equations of the form a + x = b ax = b a(bx + c) = dWhere a, b, c, and d are rational
numbers.
Use the multiplication property of equality.Solve the equation. –5x = 20
–5x = 20 –5 –5
x = –4The solutionis x = –4
Solve first degree equations of the form a + x = b ax = b a(bx + c) = dWhere a, b, c, and d are rational
numbers.
Use the multiplication property of equality.Solve the equation. x 9
= –4
x9
9( ) = 9(–4)
x = –36The solutionIs x = –36
Solve first degree equations of the form a + x = b ax = b a(bx + c) = dWhere a, b, c, and d are rational
numbers.
Use the both property of equality.Solve the equation. 3(x – 8) = 36
distribute 3x – 24 = 36 addition 3x – 24 + (24) = 36 + (24)simplify 3x = 60division 3 3Simplify Solution x = 20
Plot points on the rectangular Plot points on the rectangular coordinate system; identify x and y coordinate system; identify x and y intercepts for a given graph.intercepts for a given graph.
DMAT 0090, Objective #18
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)
C(5,–1)
D(0,3)
E(2,0)
F(–3,5)
A
BC
D
E
F
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-interceptIs (0,–3)
Compute average, median and Compute average, median and mode on a given set of data.mode on a given set of data.
DMAT 0090, Objective #19
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 + 295
257 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)
Solve for a variable other than A in Solve for a variable other than A in an area formula for a rectangle, an area formula for a rectangle, triangle, or parallelogram.triangle, or parallelogram.
DMAT 0090, Objective #20
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: LW = A
L = 12A = 48
Solve the equation:12W = 48 W = 4The 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.
H = 10A = 50
Solve the equation: (10B) = 50
Use the formula:
BH = A12
The base is 10 feet.
12
5B = 50 B = 10
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.
H = 10A = 50
Solve the equation: 10B = 50 B = 5
The base is 5 feet.
Use the formula:
BH = A
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