Transcript whole numbers

CHAPTER 1 REVIEW
SECTION 1.1
A set is a collection of objects.
The set of natural numbers is {1,2,3,4,5,….}
The set of whole numbers is {0,1,2,3,4,5,…}
Whole numbers are used for counting objects (such as money!)
However, they do not include fractions or decimals.
The digits in a whole number
have place value.
Data comparisons
can be shown in tables
1999 Quarterly Financial Data for NIKE
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
Year
164
69
124
95
or graphs
200
3 4 5
5 7 6
4 0 2
8 9 7
4 1 5
150
ThreeDigit
Groups
(separated
by commas)
Ones group
Thousands group
Millions group
Billions group
Trillions group
100
50
0
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
Rounding Whole Numbers:
Step 1: Locate the “rounding digit”, which is the digit at the place value you are rounding to.
Step 2: Look at the digit directly to the right of the rounding digit. This is the test digit. If the test digit is
< 5 (less than 5), keep the rounding digit the same and change all digits to the right of it to 0.
If the test digit is ≥5 (greater than or equal to 5), then increase the rounding digit by 1 and change all
the digits to the right of it to 0.
Expanded Notation: When a number’s digits are written with their place value names.
30,542 = 30 thousands + 5 hundreds + 4 tens + 2 ones
Verbal Form: 30,542 = Thirty thousand, five hundred forty-two.
(Notice we don’t use the word “and”.)
Standard Notation uses only digits (0 through 9) and commas to state the number.
16 million = 16,000,000
SECTIONS 1.2 and 1.3
Addition Terms: The numbers being added are called addends.
Subtraction Terms: The number you are taking away is the
subtrahend, the number you are subtracting from is the minuend, and
the answer is the difference.
Multiplication Terms: The numbers being multiplied together are the
factors. The result of the multiplication is the product.
Division Terms: The number you are dividing by is the divisor. The
number you are dividing into is the dividend. The answer to the
division problem is the quotient. The amount over if the dividend is
not exactly divisible by the divisor is the remainder.
1. Subtraction is the inverse of addition:
If a - b = c, then c + b = a
So if 10 - 3 = 7, then 7 + 3 = 10
Check subtraction by adding your difference answer to the subtrahend. Your new answer should
be the minuend.
2. Division is the inverse of multiplication:
If a ÷ b=c, then c x b = a
So if 8 ÷ 2=4, then 4 x 2 = 8
Check division like this: Quotient X Divisor + Remainder = Dividend.
Multiply your answer to the division problem by the number you are dividing by, then add the
remainder. Your answer should equal the number you divided into.
3. Addition and multiplication follow the commutative
properties:
a + b = b + a, so 8 + 3 = 3 + 8
a x b = b x a, so 5 x 2 = 2 x 5
Check division like this: Quotient X Divisor + Remainder = Dividend.
Multiply your answer to the division problem by the number you are dividing by, then add the
remainder. Your answer should equal the number you divided into.
The perimeter of a rectangle or a square is the distance around it. This is found
by adding up the lengths of all its sides. P = length + length + width + width
The area of a rectangle or square is is the amount of material needed to "cover"
it completely. This is found by the product of its length and width: A = l x w.
SECTION 1.4
Prime Factors and Exponents
A prime number is a whole number, greater, greater then 1, that
has only 1 and itself as factors.
Whole numbers greater than 1 that are not prime are called
composite numbers.
Whole numbers Divisible by 2 are EVEN numbers. Whole
numbers not divisible by 2 are ODD numbers.
The prime factorization of a whole number is the product of its
prime factors. This is found by starting with any two factors of
the number and then factoring each of those numbers until you
have nothing left but prime numbers at the bottom “roots” of the
factorization “tree”.
Example: The prime factorization of
2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5 = 22●32 ●52
2700
100
27
9
3
10
3
3
2
10
5 2
5
SECTION 1.5
ORDER OF OPERATIONS
Please: do all operations within parentheses and other grouping symbols (such as [
], or operations in numerators and denominators of fractions) from innermost
outward.
Excuse: calculate exponents
My,Dear: do all multiplications and divisions as they occur from left to right
Aunt,Sally: do all additions and subtractions as they occur from left to right.
Example:
20 – 2 + 3(8 - 6)2 Expression in parentheses gets calculated first
= 20 – 2 + 3(2)2 Next comes all items with exponents
= 20 – 2 + 3(4) Next in order comes multiplication. Multiplication and Division always come before
addition or division, even if to the right.
= 20 – 2 + 12
Now when choosing between when to do addition and when to do subtraction, always go
from left to right, so do 20-2 first, because the subtraction is to the left of the addition.
= 18 + 12
= 30
Now finally we can do the addition.
SECTION 1.6
An equation is a statement that two expressions are equal.
A variable is a letter that stands for a number.
Two equations with exactly the same solutions are called equivalent equations.
To solve an equation, isolate the variable on one side of the equation by
“undoing” the operation performed on it.
If the same number is added to (or subtracted from) both sides of an equation, an
equivalent equation results.
Example:
x – 5 = 2 gives the same solution as x – 5+ 5 = 2 + 5
which is x + 0 = 7, or x = 7.
Check by substituting the result for x into the original equation and seeing if it is true. 7-5 = 2 ? Yes.
Problem-Solving Strategy:
1. Analyze the problem. What are you trying to find? What’s the given info?
2. Form an equation. Let a variable = what you’re trying to find. Use this
variable in your equation using the given information.
3. Solve the equation by getting the variable by itself on one side.
4. Check the result by substituting the result for the variable into the original
equation and seeing if the equation is true.