Pre-algebra - Whole Numbers and Operators Flashcards
Review Major Concepts for Whole numbers and the Use of Operators.
What are ‘Natural Numbers’?
Natural numbers are one through infinity.
What are ‘Counting Numbers’?
Counting numbers are one through infinity.
What are ‘whole numbers’?
Whole numbers are the numbers zero through infinity.
What is a ‘place value’?
The position of a digit in a larger number.
What is ‘standard form’?
A number that is written using the symbols 0 through 9.
What is a ‘period’ of a number?
When a number is written in standard form, each group of digits separated from the other digits by a comma (or commas) is called a period.
How are periods of a number used in math?
- Periods are used to denote the beginning of a major place value, such as ones, thousands, millions, billions, …
- When writing a number in words, the amount of each period is stated: “three billion seven hundred eighty-six million four hundred fifty-one thousand two hundred ninety-four (ones).
What does ‘expanded form’ mean?
- Expanded Form means to take each number of a large quantity and write down its value according to its place value.
- The Expanded Form of a large number separates each digit according to its place value.
- Adding up the number in expanded form should provide the number in standard form: 20,000 + 6000 + 400 + 20 + 9 = 26,429.
What is ‘rounding’ a number?
- Taking an approximate value from an exact number is called rounding.
- A rounded number is always rounded to a given place value.
- 37 is closer to 40 than it is to 30. 37 rounded to the nearest ten is 40.
List the main four types of operators for whole numbers.
Addition
Subtraction
Multiplication
Division
What is ‘addition’?
- Addition is the process of finding the total of two or more numbers.
- Addition is the combining of two or more quantities to form a greater quantity.
How do you add large numbers?
To add large numbers, begin by arranging the numbers vertically, keeping the digits of the same place value in the same column. Add each of the numbers of each column from right (the lesser number column) to left (the greater number column).
What is ‘carrying’?
When the sum of the digits in a column exceeds 9, the addition will involve noting the lesser place value in that column and moving (or carrying) the excess place value to the next column to the left.
What is Cumulative Property of Addition?
Two numbers can be added in either order; the sum will be the same.
What is the Associative Property of Addition?
Grouping (with parenthesis) an addition in any order gives the same result.
What is the Addition Property of Zero?
Zero added to any number does not change the number.
What is ‘subtraction’?
Subtraction is the process of finding the difference between two numbers OR it is the process of finding the remainder between two numbers.
What is a ‘minuend’?
The minuend is the base number which is subtracted from.
What is a ‘subtrahend’?
The subtrahend is the number which is used to subtract from the base number (minuend).
What is a ‘difference’?
The difference is the remaining quantity after the subtraction process is complete.
What is ‘borrowing’?
When the lower digit is larger than the upper digit, subtraction will involve borrowing. Using the number to the left top number, lower that number by 1 and add 10 to the right top number. With the borrowing method, the right top number is enough as minuend.
What is ‘multiplication’?
Multiplication is used to find the total number of objects when divided into several groups when each group contains the same number of objects.
What is the ‘multiplicand’?
The multiplicand is the number of objects in each group.
What is the ‘multiplier’?
The multiplier is the number of groups.
What is the ‘product’?
The product is the total number of objects in all the groups.
What is a ‘factor’?
A factor is either the multiplicand or multiplier that are multiplied to obtain a product.
What is the Commutative Property of Multiplication?
Two numbers can be multiplied in either order; the product will be the same.
What is the Associative Property of Multiplication?
Grouping numbers (with parenthesis) to be multiplied in any order gives the same result.
What is the Multiplication Property of One?
Multiplying a number by 1 does not change the number.
What is the Multiplication Property of Zero?
A number multiplied by zero is zero.
What is ‘division’?
Division is used to separate objects into equal groups.
What is the ‘dividend’?
The number that is being divided (i.e. separated into parts).
What is the ‘divisor’?
The number that is used to divide (i.e. separate into parts) another number (i.e. the dividend).
What is the ‘quotient’?
The number that is the result of a division problem.
What is the Property of One in Division?
Any whole number, except zero, divided by itself is 1.
What is the Property of Zero in Division?
Zero divided by any whole number other than zero is zero.
What is an ‘exponent’?
A number that indicates how many times another number (the factor) appears in a multiplication statement.
Which is the factor, and which is the Exponent in: 65?
In 65, the 6 is the factor and 5 is the exponent.
How to you say 65 or 64?
How to you say 65 or 64?
Six to the fifth power or six to the fourth power.
How do you say 62?
62 is six squared OR six to the second power.
How do you say 63?
63 is six cubed OR six to the third power.
How do you say 61?
61 six OR six to the first power.
How do you calculate an exponent notation?
Write out the number of factors according to the exponent and multiply.
What is the Order of Operations Agreement?
Order of Operations Agreement are the rules of calculating complex (mixed) calculations.
What are the steps of Order of Operations Agreement?
What are the steps of Order of Operations Agreement?
Step 1. Perform operations inside grouping symbols such as parentheses.
Step 2. Simplify exponential expressions.
Step 3. Do multiplication and division as they occur from left to right.
Step 4. Do addition and subtraction as they occur from left to right.
What is a whole number factor of another number?
Whole-number factors of a number divide that number evenly (there is no remainder).
How do you find a whole number factor of another number?
Divide a number by 1, 2, 3, 4, 5… The numbers that divide evenly are whole number factors.
What is a prime number?
A number is a prime number if its only whole-number factors are 1 and itself.
What is a composite number?
A number that is not prime.
Is the number 1 a prime number?
No.
What is Prime Factorization?
The prime factorization of a number is the expression of the number as a product of its prime factors.
What is a T-Diagram?
A T-Diagram is a bar shaped like a capital T used for Prime Factorization. On top of the T-Diagram is the original number. To the left of the T-Diagram are the prime Factors and to the right is the remainder when divided by the prime factor.
What is the process of Prime Factorization?
Start with the original number and if it is even, divide by 2; if it is divisible by 3, divide by 3, so on…
