425

10011 0010 1010 1101 0001 0100 1011

Basic Math Skills Review

Fractions

425

1

0011 0010 1010 1101 0001 0100 1011

Introduction to Fractions

The block below is divided into three equal parts. One of three of the sections is shaded. We use the fraction ⅓ to represent the comparison of one shaded section out of three sections. Read this as “one-third.”

425

1

0011 0010 1010 1101 0001 0100 1011

Introduction to Fractions

• An easy way to recall the parts of a fraction is the “part” over the “whole.” In math terms, the “part” is called the numerator and the “whole” is the denominator. The line is called the bar.

(Read this fraction as three-fourths or three quarters)

4

3Numerator

Denominator

425

1

0011 0010 1010 1101 0001 0100 1011

Improper Fractions

• The numerator is more than the denominator.

• Its value is more than one.

2

37

12

9

35

425

1

0011 0010 1010 1101 0001 0100 1011

Mixed Numbers

• A mixed number is when a whole number is written next to a fraction.

3

21

8

510

425

1

0011 0010 1010 1101 0001 0100 1011

Rewriting Mixed Numbers

To rewrite a mixed number as an improper fraction:

1. Multiply the whole number by the denominator of the fraction.

2. Add the product to the numerator.

3. Take the result and write it over the original denominator.

425

1

0011 0010 1010 1101 0001 0100 1011

Rewriting Mixed Numbers

To rewrite a mixed number as an improper fraction:

rdenominato

numerator r denominato # whole

6

23

6

563 becomes

6

53

425

1

0011 0010 1010 1101 0001 0100 1011

Rewriting Improper Fractions

Improper fractions can be rewritten as mixed numbers. To do this:

1. Divide the numerator by the denominator.

2. The quotient is the whole number of the mixed fractional notation.

3. The remainder is the numerator of the fraction part.

4. The denominator remains the same.

425

1

0011 0010 1010 1101 0001 0100 1011

Improper Fractions

? why 4

36 becomes

4

27

6

3

24

274 Divide the denominator into the numerator.

The remainder is written as the numerator of the fraction part.

The denominator remains the same.

425

1

0011 0010 1010 1101 0001 0100 1011

Prime Numbers

A prime number is a whole number that has exactly two different factors: itself and one. This is a list of all prime numbers less than 100.

2 3 5 711 13 17 19

23 29 313741 43 47 53

59 61 6771 73 79 83

89 97

425

1

0011 0010 1010 1101 0001 0100 1011

Composite Numbers

• Numbers greater than one that have more than two factors are called composite numbers.

The numbers 15 and 18 are composite.3 ∙ 5 = 15 3 and 5 are factors of 15.1 ∙ 15 = 15 1 and 15 are also factors of 15

In set notation, the factors are listed as: {1, 3, 5, 15}The factors of 18 are: 1 ∙ 18

2 ∙ 9 3 ∙ 6

In set notation, they are written as: {1, 2, 3, 6, 9, 18}

425

1

0011 0010 1010 1101 0001 0100 1011

Remember This:

• One and zero are neither prime nor composite numbers.

425

1

0011 0010 1010 1101 0001 0100 1011

Prime Factorization

• A prime factorization is a an expression of a number as a product in which every factor is a prime number.

For example,

8 = 2•2•2

12 = 2•2•3

425

1

0011 0010 1010 1101 0001 0100 1011

Division Method

• Divide the number by a small prime factor of that number until the quotient is one.

answer 2) 18line 3) 9

3) 3The divisor of each is the prime factors.

Write as a product of these primes.

2 • 3 • 3 = 18 or2 • 32= 18

425

1

0011 0010 1010 1101 0001 0100 1011

Least Common Multiples (LCM)

A multiple of any number is the product of that number and another factor. When adding or subtracting fractions, the LCM is called the Least Common Denominator (LCD).

Example: The first four multiples of five are:5, 10, 15, 20

To find the Least Common Multiple (LCM) between two or more numbers, you must use

prime factorization.

425

1

0011 0010 1010 1101 0001 0100 1011

Greatest Common Factor (GCF)The Greatest Common Factor (GCF) is a number

that divides evenly into all the numbers you are given in a problem. The GCF is used for simplifying fractions.

For example, the GCF of 16 and 12 is 4.

2) 12 16

2) 6 82) 3 4

2) 3 2

3) 3 1

1 1

When the numbers stop having factors in common, you have found the GCF. When each number has been divided down to 1, you have found the LCM.

425

1

0011 0010 1010 1101 0001 0100 1011

Simplifying Fractions

• The simplest form of a fraction is when its numerator and denominator have no factors in common other than 1.

• Using the GCF to simplify fractions.

• Using prime factorization to simplify fractions.

8

202454

2

54

42

51

2

5

5

2

522

222

20

8

425

1

0011 0010 1010 1101 0001 0100 1011

Addition & Subtraction

Terms must have the same denominator in order to add or subtract.

Find the sum or difference of the numerators.

The denominator of the answer is:

– the same as the terms when adding or subtracting like fractions.

– the lowest common denominator (LCD) when adding or subtracting unlike fractions.

Always simplify to lowest terms.

425

1

0011 0010 1010 1101 0001 0100 1011

Examples

• Addition • Subtraction

24

71

24

31

24

15

24

1624

35

24

822424

8

5

3

2

24 is the LCD

Multiply both numerator and denominator to make

equivalent fraction

Add numerators only

24

171

24

31

24

202

24

311

24

452

241

242

8

11

6

52

Subtract numerators and whole numbers

425

1

0011 0010 1010 1101 0001 0100 1011

Multiplication of Fractions

There is no need to find the least common denominator.

In Multiplication: (“simplify, then multiply”)

1) Simplify the fraction “criss-cross” or “top to bottom.”

2) Multiply, from left to right, the numerators and denominators.

425

1

0011 0010 1010 1101 0001 0100 1011

Examples

5

2

5

2

1

1

20

14

7

4

20

14

7

4

5

2

1

1

Simplify

3

116

3

49

3

7

1

7

3

14

2

7

3

14

2

73

24

2

13

7

1

Simplify

Rewrite as improper fractions

Multiply straight across

Multiply straight across

425

1

0011 0010 1010 1101 0001 0100 1011

Division of Fractions

There is no need to find the least common denominator.

To divide:

1) Find the reciprocal of the divisor. (second fraction)

2) Multiply.

425

1

0011 0010 1010 1101 0001 0100 1011

What is a Reciprocal?

• The reciprocal of a fraction is simply the fraction “turned around” or “flipped over.” In more mathematical terms, invert the numerator and denominator of the fraction.

9

5The reciprocal of is

5

9

425

1

0011 0010 1010 1101 0001 0100 1011

Examples

6

5

3

1

2

5

3

4

8

5

3

4

8

54

3

8

5

1

2

You can only simplify when multiplying 7

32

65

133

13

7

5

197

13

5

197

61

5

43

Rewrite as improper fractions

425

1

0011 0010 1010 1101 0001 0100 1011

NOVA Math Placement Test

•The Math Placement test is given in the Testing Center.•There is a review book for the placement exam in the Annandale Library. (CG 3rd Floor)•It’s called Chart Your Success on the Compass Exam. •Brush-up on current skills, go through what you know. •Don’t try to teach yourself anything that you do not know.•Use the list of suggested websites to help you review.•Neither the Math Center nor the Tutoring Center will help you study for the exam.