Rational Numbers 5-1 to 5-7 Kane Oct 2007

Factors

Vocab… Factor “a” is a factor is of “b” if “a” will divide evenly into “b” Prime number Any number with only two factors; 1 and itself. (Is 1 a prime?) why or why not? No, the number 1 only has one factor:1*1=1 The first 5 prime numbers are: Composite number Any whole number with more than 2 factors.

Find all the prime numbers between 1-100 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 51, 52, 53, 54, 55, 56, 57, 58, 59, 60 61, 62, 63, 64, 65, 66, 67, 68, 69, 70 71, 72, 73, 74, 75, 76, 77, 78, 79, 80 81, 82, 83, 84, 85, 86, 87, 88, 89, 90 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Practice Tell if each number is prime or composite: Ex1: 36 Ex2: 81

Vocab (operations) Prime factorization Writing a number as the product of prime numbers ie: the prime factorization of 20 = 2*2*5 Greatest Common Factor (GCF) The largest factor that any two composite numbers have in common.

Examples: Prime Factorization (find the prime factorization of each number) Ex5: 315 Ex6: 72

Examples: Find the GCF Ex7: Find the GCF of 60 and 72 Find the prime factorization of each number Find the common factors: 60: 72: Find the product of the common factors:

Rational Numbers Chapter 5-2

Vocabulary Rational Number Simplest form Any number that can be written as a fraction Simplest form When the GCF of the numerator and the denominator is the number 1.

Ez-xamples Ex1 write 54/60 in simplest form. To simplify completely divide both numbers by their GCF 54 = 2*3*3*3 60 = 2*2*3*5 Or just divide by factors that you know. The GCF is 6

Ex2: Change the fraction from a mixed number to an improper fraction. Step 1: multiply the whole number by the denominator. Step 2: Add the numerator to the product of the whole number and the denominator. Step 3: Put the new sum over the original denominator

Equivalent Fractions Ex3: to come up with fractions with equal value multiply the original fraction by any number over itself.

Equivalent Fractions and Decimals The decimal equivalent for these fractions is?? Chapter 5 - 3

Vocab! Terminating Decimal Any decimal that ends Repeating Decimal a decimal that has a repeating pattern.

Writing Fractions as Decimals Ex1: Billy just started playing baseball. After a few games he started to think he was pretty good. In 8 games he got up to bat 20 times. Of those times he got a hit 9 times. What is his batting average?

Decimal to Fraction Ex2: to turn a decimal into a fraction put the number over the place value and simplify .025 is 25 thousandths or

Repeated Decimals Ex3: The rules are a little different when dealing with repeated decimals. To change a repeated decimal to a fraction use the line-9 rule. Step 1: figure out how many digits are in the repeated pattern. In this case it is 2. Step 2: take the repeated pattern and set it as the numerator of a fraction Step 3: Count the number of decimal places the pattern takes up. Put the numerator over that many 9s. For example if it just the tenths place only use one 9, if it is the hundredths use two 9s and so on. .45 goes to the hundredths place so we will only need two 9s 99 Step 4: simplify!

Least Common Multiple Chapter 5 - 4

Vocab… Multiple: Any number you can get by multiplying two numbers together. ie: 5*4 = 20 so 20 is a multiple of both 4 and 5 Least Common Multiple (LCM) The first multiple that any two numbers have in common. Least common denominator The LCM of the denominators, of two or more fractions.

Examples!! Ex1: Find the LCM of 36 and 30 -step 1: prime factor each #. -step 2: select the largest version of each factor. -step 3: multiply out each of the selected factors 180 is the LCM

In order to compare rational numbers (fractions) give them common denominators. Ex2: put in numerical order step 1: find the LCM of the denominators step 2: change both fractions so they have a denominator of 48 and 15 16

Ex3: put the numbers .053, .38, and .275 becomes To compare decimals make sure that they all have the same number of decimal places. Hint: line up decimal points & fill empty spaces with zeros (0s) Ex3: put the numbers .053, .38, and .275 becomes

What if you have a decimal and a fraction?? Ex4: compare 0.32 and 5/16 You have to make them both either fractions or both decimals. (Hint): It is usually easier to turn the fractions into a decimal. we compare Therefore

Adding and Subtracting Like Fractions Chapter 5 - 5

What is the rule for adding and subtracting like fractions?? Ex1: Ex2:

Adding and Subtracting Unlike Fractions Chapter 5 - 6

What is the rule for adding and subtracting unlike fractions? Ex1: -7 12

Ex2:

Multiplying and Dividing Rational Numbers Chapter 5-7

Multiply: make sure all mixed numbers are changed to improper fractions Multiply straight across the top and straight across the bottom, then simplify Ex1: SIMPLIFY

Rules for Dividing Step 1: take the reciprocal of the second fraction Step 2:change division to multiplication Step 3: multiply across Ex2: becomes

Scientific Notation Chapter 2 Section 11

Vocab… Scientific Notation When a very large or very small number is written as a product of two factors. The first number must be greater than or equal to 1 but less than ten. The second number must be a power of ten (10x)

Vocab… Standard Form Normal number format. The same as we are used to seeing

For these examples change the scientific notation to standard form. Ex 1: 2.63 X 106 2.63 X 1,000,000 2,630,000 Ex 2: 8.9 X 104 8.9 X 10,000 89,000

Examples For these examples change standard notation to scientific notation Is really 259,000,000.0 To get a number greater than 1 and less than 10 move the decimal left 8 times 2 59,000,000.0 Because we moved the decimal 8 spaces the power of 10 will be 108 2.59 X 108 .