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Chapter 1: Whole Numbers

Chapter 1: Whole Numbers. 1.1 Introduction to Whole Numbers. The Place Value System. • Numbers are composed of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. • The numbers 0, 1, 2, 3, 4, 5,… are called the whole numbers .

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Chapter 1: Whole Numbers

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  1. Chapter 1: Whole Numbers

  2. 1.1 Introduction to Whole Numbers

  3. The Place Value System • Numbers are composed of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. • The numbers 0, 1, 2, 3, 4, 5,… are called the whole numbers. • For large numbers, commas are used to separate digits into groups of three called periods. 4,058,614 Numbers written in this way are said to be in standard form.

  4. The Place Value System • The position of each digit within a number determines the place value of the digit. • The digit 5 in the number 4,058,614 represents 5 ten-thousandths.

  5. Expanded Form • A number can also be written by writing each digit with its place value unit. 287 = 2 hundred + 8 tens + 7 ones This is called expanded form.

  6. The Number Line and Order • Whole numbers can be visualized as equally spaced points on a number line. • A number is graphed on a number line by placing a dot at the corresponding point.

  7. The Number Line and Order • The number to the left is less than the number to the right. • The number to the right is greater than the number to the left. • “<” denotes “is less than” • “>” indicates “is greater than”.

  8. Exercise 1 Determine the place value of the underlined digit: 51,033,201 A). ones B). thousands C). hundred thousands D). millions

  9. Exercise 2 Convert the number to standard form: Two million, six hundred forty-seven thousand, five hundred twenty A). 2,647,520 B). 2,000,647,520 C). 2,647,020 D). 26,475,020

  10. Exercise 3 Insert the appropriate inequality. Choose from < or >. A). 14 < 13 B). 14 > 13

  11. 1.2 Addition of Whole Numbers

  12. Addition of Whole Numbers • The result of an addition problem is called the sum. • The numbers being added are called addends.

  13. Addition of Whole Numbers Using a Number Line • To add 5 and 3, begin at 0 and move 5 units to the right. • Move an additional 3 units to the right. • The final position is the sum.

  14. Addition of Whole Numbers To add whole numbers, • line up the numbers vertically by place value. • Add the digits in corresponding place positions. Example:

  15. Addition of Whole Numbers The sum of the digits in a given place position is sometimes greater than 9. If this occurs, we must carry or regroup. Add: 35 + 48 13 ones = 1 ten + 3 ones

  16. Properties of Addition

  17. Translations and Applications Involving Addition

  18. Perimeter • The perimeter of any polygon is the distance around the outside of the figure. • To find the perimeter, add the lengths of the sides.

  19. Exercise 4 Add the whole numbers. A). 111 B). 101 C). 113 D). 121

  20. Exercise 5 Translate the English phrase into a mathematical statement and simplify. 5 more than 18 A). 22 B). 13 C). 23 D). 24

  21. Exercise 6 Find the perimeter. A). 73 B). 35 C). 28 D). 30

  22. 1.3 Subtraction of Whole Numbers

  23. Subtraction of Whole Numbers • The result of a subtraction is called the difference. • The number being subtracted is called the subtrahend. • The number from which the subtrahend is subtracted is called the minuend.

  24. Subtraction Using a Number Line • To evaluate 7 – 4, • start from the point corresponding to the minuend (7). • move to the left 4 units. • The resulting position is the difference. • Check the result by addition. 7 – 4 = 3 because 3 + 4 = 7

  25. Subtraction of Whole Numbers • Write the numbers vertically, with the minuend on top. • Starting with the ones column, subtract digits having corresponding place values.

  26. Subtraction with Borrowing When a digit in the subtrahend is larger than the corresponding digit in the minuend, “regroup” or borrow a value from the column to the left. 9 tens = 8 tens + 10 ones

  27. Translations and Applications Involving Subtraction

  28. Exercise 7 Subtract the whole numbers. A). 6 B). 14 C). 16 D). 12

  29. Exercise 8 Translate the English phrase into a mathematical statement and simplify. 72 less than 1090 A). 1022 B). 1008 C). 1162 D). 1018

  30. Exercise 9 In landscaping a yard, Lily would like 26 plants for a border. If she has 18 plants in her truck, how many more will she need to finish the job? A). 8 B). 12 C). 6 D). 10

  31. 1.4 Rounding and Estimating

  32. Rounding Whole Numbers Round 3741 to the nearest hundred. 1). Identify the digit one position to the right of the given place value. 3741 2). If the digit in step 1 is a 5 or greater, add one to the digit in the given place value. Then replace each digit to the right of the given place value by 0. 3). If the digit in step 1 is less than 5, replace it and each digit to its right by 0. 3700 The number 3700 is 3741 rounded to the nearest hundred.

  33. Estimation • Use rounding to estimate the result of numerical calculations. • Example, to estimate the following sum, round each addend to the nearest ten. The estimated sum is 90 (the actual sum is 92).

  34. Exercise 10 Round the number to the given place value. 9384; hundreds A). 9300 B). 9400 C). 9500 D). 9380

  35. Exercise 11 Estimate the sum by first rounding each number to the nearest ten. A). 170 B). 180 C). 160 D). 100

  36. Exercise 12 Estimate the difference by first rounding each number to the nearest hundred. A). 0 B). 150 C). 200 D). 100

  37. 1.5 Multiplication of Whole Numbers

  38. Introduction to Multiplication Multiplication is repeated addition, and we use the multiplication sign × to express repeated addition more concisely. 12 + 12 + 12 is equal to 3 × 12 5 + 5 + 5 + 5 + 5 + 5 is equal to 6 × 5 In the statement 3 × 12 = 36: • The expression 3 × 12 is read “3 times 12”. • The numbers 3 and 12 are called factors. • The number 36 is called the product.

  39. Introduction to Multiplication • The symbol · may also be used to denote multiplication, such as 3·12 = 36. • Two factors written adjacent to each other with no operator between them also implies multiplication. 2y is understood to be 2 times y • Parentheses are used to denote multiplication between numerical factors. All of the following denote 3 times 12. (3)12 = 36 or 3(12) = 36 or (3)(12) = 36

  40. Properties of Multiplication

  41. Properties of Multiplication

  42. Properties of Multiplication Distributive Property of Multiplication When multiplying a factor times a sum, the factor can be “distributed” to each addend before summing. Example:

  43. Multiplying Many-Digit Whole Numbers When multiplying numbers with several digits, it is sometimes necessary to carry or “regroup”.

  44. Multiplying Many-Digit Whole Numbers

  45. Multiplying Many-Digit Whole Numbers Example:

  46. Multiplying Many-Digit Whole Numbers • The numbers 40, 300 and 1500 are called partial sums. • The product is found by adding the partial sums. • The product is 1840.

  47. Multiplying a Many-Digit Number by a Many-Digit Number

  48. Multiplying a Many-Digit Number by a Many-Digit Number

  49. Multiplying a Many-Digit Number by a Many-Digit Number

  50. Multiplying a Many-Digit Number by a Many-Digit Number Example:

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