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1.5 Dividing Whole Numbers

Remember there are three different ways to write division problems

412 ÷ 3 = 4 3 / 12 12/3 = 4

All of these represent the same problem:12 divided by 3 is 4.

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There are some terms that are special to division that we should be familiar with:

Quotient-the answer when we divideDividend-the number being divided Divisor-the number being divided into something

dividend / divisor = quotientdividend ÷ divisor = quotient quotientdivisor / dividend

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Division with zero

Zero divided by any number• Zero divided by any number

is always and forever ZERO

• 0/99 = 0• 0 ÷ 99 = 0

Any number divided by zero• Any number divided by zero

is always undefined. We cannot divide by zero. It is an illegal operation mathematically.

• 99/0• 99 ÷ 0

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Division and the number 1

Any number divided by itself• Any number divided by

itself is equal to one.

• 9/9 = 1• 99/99 = 1

Any number divided by 1• Any number divided by one

is equal to the number itself.

• 9/1 =9• 99/1 =99

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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

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We can also use multiplication to check division even when there is a remainder.

Take: divisor x quotient + remainder = dividend

458 ÷ 5 = 91 r 3divisor x quotient + remainder = dividend 5 x 91 + 3 = 455 + 3 = 458 It works!

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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

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1.6 Exponents

323 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 = 11000 = 1

One to any power = 118 = 1

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1.6 Exponents

Any number that has no exponent written has an understood exponent of one

2=21

100=1001

Zero to any power = 118 = 1

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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.

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1.6 Order of Operations

Parenthesis (or grouping symbols)ExponentsMultiplication or Division from Left to RightAddition or Subtraction from Left to Right

PEMDAS

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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 ) – 2OR

{[ 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

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1.7 Rounding Whole Numbers

• To round we must remember place value

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1.7 Steps for roundingFind the place you are rounding to and

underline itLook 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.

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1.7 Rounding examples

Round 478 to the nearest tenFind the tens place: 478 Look at the digit behind the 7The 8 will push the 7 up to an 8Fill in zeros480

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1.7 Rounding examples

Round 46352 to the nearest thousandFind the thousands place: 46352Look at the digit behind the 6The 3 will not push the 6 up – leave itFill in zeros46000

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1.7 Rounding examples

Round 4963 to the nearest hundredFind the hundreds place: 4963Look at the digit behind the 9The 6 will push the 9 up to a 10 which rolls over

and pushes the 4 up to a 5. watch out! Fill in zeros5000

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1.7Rounding for estimating purposes

Rounding to a given place-value

Round to hundreds place and add for an estimated answer.

949 900

759 800+ 525 + 500

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Front-end roundingFront-end round as

appropriate for an estimated answer.

3825 4000 72 70 565 600+2389 + 2000

6670

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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?

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1.8 Application ProblemsWords for AdditionPlus, more, add, total, sum, increase, gainWords for SubtractionLess, difference, fewer, decrease, loss, minusWords for MultiplicationProduct, times, of, twice, double, tripleWords for DivisionQuotient, divide, perWords for EqualsIs, yields, results in, are

1.8 Application Problems

Read the problem through once quicklyRead a second time, paying a bit more attention

to detailMake some notesTry to come up with a planDo the mathLabel your answer