1.5 Dividing Whole Numbers Remember there are three different ways to write division problems 4 12 ÷ 3 = 4 3 / 12 12/3 = 4 All of these represent the same problem: 12 divided by 3 is 4.

There are some terms that are special to division that we should be familiar with: Quotient-the answer when we divide Dividend-the number being divided Divisor-the number being divided into something dividend / divisor = quotient dividend ÷ divisor = quotient quotient divisor / dividend

Division with zero Zero divided by any number Any number divided by zero Zero divided by any number is always and forever ZERO 0/99 = 0 0 ÷ 99 = 0 Any number divided by zero is always undefined. We cannot divide by zero. It is an illegal operation mathematically. 99/0 99 ÷ 0

Division and the number 1 Any number divided by itself Any number divided by 1 Any number divided by itself is equal to one. 9/9 = 1 99/99 = 1 Any number divided by one is equal to the number itself. 9/1 =9 99/1 =99

The connection Multiplication and Division are closely related. We can go back and forth between the two operations. 20/4 = 5 so 4 × 5 = 20 72 ÷ 9 = 8 so 9 × 8 = 72

We can also use multiplication to check division even when there is a remainder. Take: divisor x quotient + remainder = dividend 458 ÷ 5 = 91 r 3 divisor x quotient + remainder = dividend 5 x 91 + 3 = 455 + 3 = 458 It works!

Divisibility rules A number is divisible by: -2 if the ones digit is even -3 if the sum of the digits is divisible by 3 -5 if it ends in 5 or 0 -9 if the sum of the digits is divisible by 9 -10 if it ends in 0

1.6 Exponents 3 is your power or exponent; 2 is your base Read 2 to the 3rd power The exponent tells how many times the base appears as a factor. 2 x 2 x 2 = 8

1.6 Exponents Any number to the zero power = 1 20 = 1 1000 = 1 One to any power = 1 18 = 1

1.6 Exponents Any number that has no exponent written has an understood exponent of one 2=21 100=1001 Zero to any power = 1 18 = 1

1.6 Order of Operations Order of Operations exists because when there is more than operation involved, if we do not have an agreed upon order to do things, we will not all come up with the same answer. The order of operations ensures that a problem has only one correct answer.

1.6 Order of Operations Parenthesis (or grouping symbols) Exponents Multiplication or Division from Left to Right Addition or Subtraction from Left to Right PEMDAS

1.6 Order of Operations In the parenthesis step, you may encounter nested parenthesis. Below you will see the same problem written two ways: once with nested parenthesis and the other with a variety of grouping symbols (including brackets, braces, and parenthesis). (( 5 x ( 2 + 3 )) + 7 ) – 2 OR {[ 5 x ( 2 + 3 )] + 7 } - 2

1.6 Order of Operations Just a reminder that there are many ways to show multiplication. You will still see the “x” for times or multiply, but you will see other ways as well. 3(2) (3)2 (3)(2) 3 2

1.7 Rounding Whole Numbers To round we must remember place value

1.7 Steps for rounding Find the place you are rounding to and underline it Look at the digit to the right of the underlined place -if it is 5 or higher, the underlined number will go up; -if it is 4 or lower, the underline number will stay the same. Change all the digits the right of the underlined digit to zeros.

1.7 Rounding examples Round 478 to the nearest ten Find the tens place: 478 Look at the digit behind the 7 The 8 will push the 7 up to an 8 Fill in zeros 480

1.7 Rounding examples Round 46352 to the nearest thousand Find the thousands place: 46352 Look at the digit behind the 6 The 3 will not push the 6 up – leave it Fill in zeros 46000

1.7 Rounding examples Round 4963 to the nearest hundred Find the hundreds place: 4963 Look at the digit behind the 9 The 6 will push the 9 up to a 10 which rolls over and pushes the 4 up to a 5. watch out! Fill in zeros 5000

1.7 Rounding for estimating purposes Rounding to a given place-value Front-end rounding Round to hundreds place and add for an estimated answer. 949 900 759 800 + 525 + 500 2200 Front-end round as appropriate for an estimated answer. 3825 4000 72 70 565 600 +2389 + 2000 6670

1.8 Application Problems In most word problems, there are usually one or more words that indicate a particular operation. Being able to pick out these words is a key skill in being able to solve word problems successfully. What are some of these words?

1.8 Application Problems Words for Addition Plus, more, add, total, sum, increase, gain Words for Subtraction Less, difference, fewer, decrease, loss, minus Words for Multiplication Product, times, of, twice, double, triple Words for Division Quotient, divide, per Words for Equals Is, yields, results in, are

1.8 Application Problems Read the problem through once quickly Read a second time, paying a bit more attention to detail Make some notes Try to come up with a plan Do the math Label your answer