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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.


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


Find the difference of the following whole numbers:8092 and 2754

8 0 9 2– 2 7 5 4

The difference is 5338.


Find the product of the following whole numbers:3072 and 419

3072x 419

2764830720

1228800 The product is 1287168.1287168

Subtract 8


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.


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.


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.


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 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

False: The last digit is not even.

True: The last digit is zero.


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.


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


6 8

14 1915 = 15

Reduce the answer= 1 6


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


7 +15 15

2 3 . Prime factorization(3)(5) (2)(5)

1 1 / / / /

Cross cancel


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


35 Multiply 1

42 25 Improper 5 6 fraction

= 35Reduce

2 10 Change to15 3 reciprocal


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


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.


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


__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


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


.

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


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.


Solve applied problems using a variety of methods, including proportions and first degree equations.

Steps for solving application problems

Identify

Setup

Solve

Check

Explain


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.


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( ) ( )


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


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.


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:

<


Place <, > or = in the space between the numbers

35

35

(100%)

60%

0.601

0.601(100%)

60.1%


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%



27 B

=

30% of what number is 27?30

100=

30B = 27(100) Cross Multiply

30B = 2700 Solve

B = 90

The base is 90.


A150

What number is 40% of 150?40

100=

100A = 40(150) Cross Multiply

100A = 6000 Solve

A = 60

The amount is 60.


=

Interpret a chart or graph.Interpret a chart or graph.


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.


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:


Any Polygon: P = add all sides

Any Quadrilateral: P = add 4 sides

Rectangle: P = 2L + 2W

Triangle: A = a + b + c

Perimeter of Polygons:


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


Area: A = r2

Circumference: C = 2r or C = dr

r = radius, d = diameter, = 3.14

Circle formula:

r d


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.


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


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.



–5 + (–9)

n + n = n

–5 + (–9) = –14

negative 5 plus negative 9 equals negative 14

Add 5 + 9 and keep the negative sign.



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.



6 + (–9)


6 + (–9) = –3

positive 6 plus negative 9 equals negative 3




–6 + 8

n + p = subtract & find the sign

–6 + 8 = 2

negative 6 plus positive 8 equals positive 2




–7 + 3


–7 + 3 = –4

negative 7 plus positive 3 equals negative 4



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


Which addition rule applies to the expression 6 – 9


6 + (–9) = –3

positive 6 plus negative 9 equals negative 3



Which addition rule applies to the expression –6 – (–8)


–6 + 8 = 2

negative 6 plus positive 8 equals positive 2



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.


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.


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



3(4)

p(p) = p

3(4) = 12

positive 3 times positive 4 equals positive 12


Which rule applies to the expression –6

–2

n = p n

–6 = 3 –2

Negative 6 divided by negative 2 equals positive 3.



3(–8)

p(n) = n

3(–8) = –24

positive 3 times by negative 8 equals negative 24.


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.


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.


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


Givena + b = b + a


Commutative property


12 + 16 = 16 + 12

28 = 28


Givena(b + c) = ab + ac


Distributive property


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.


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.


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.


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


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


numbers.

Use the multiplication property of equality.Solve the equation. –5x = 20

–5x = 20 –5 –5

x = –4The solutionis x = –4


numbers.

Use the multiplication property of equality.Solve the equation. x 9

= –4

x9

9( ) = 9(–4)

x = –36The solutionIs x = –36


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.


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.


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

=


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)


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.


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.


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


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

End of review

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