Basic Math Skills Review

1. Basic Math Skills Review Fractions

2. 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.”

3. Introduction to Fractions Numerator • 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) Denominator

4. Improper Fractions • The numerator is more than the denominator. • Its value is more than one.

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

6. 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.

7. Rewriting Mixed Numbers To rewrite a mixed number as an improper fraction:

8. 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.

9. Improper Fractions Divide the denominator into the numerator. The remainder is written as the numerator of the fraction part. The denominator remains the same.

10. Prime Numbers A primenumber 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 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

11. 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}

12. Remember This: • One and zero are neither prime nor composite numbers.

13. 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

14. Division Method • Divide the number by a small prime factor of that number until the quotient is one. answer 2) 18 line 3) 9 3) 3 The divisor of each is the prime factors. Write as a product of these primes. 2 • 3 • 3 = 18 or 2 • 32= 18

15. 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 firstfour 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.

16. 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 8 2) 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.

17. 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.

18. 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.

19. Examples • Addition • Subtraction 24 is the LCD Multiply both numerator and denominator to make equivalent fraction Add numerators only Subtract numerators and whole numbers

20. 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.

21. Examples Rewrite as improper fractions Simplify Simplify Multiply straight across Multiply straight across

22. 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.

23. 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. The reciprocal of is

24. Examples Rewrite as improper fractions You can only simplify when multiplying

25. 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.