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Instructor: Dr.Gehan Shanmuganathan

Instructor: Dr.Gehan Shanmuganathan. Learning Outcomes. 1-1. Read whole numbers. Write whole numbers. Round whole numbers. Read and round integers. Read whole numbers. 1-1-1. Section 1-1. Place Value and Our Number System.

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Instructor: Dr.Gehan Shanmuganathan

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  1. Instructor: Dr.Gehan Shanmuganathan

  2. Learning Outcomes 1-1 • Read whole numbers. • Write whole numbers. • Round whole numbers. • Read and round integers.

  3. Read whole numbers 1-1-1 Section 1-1 Place Value and Our Number System • Our system of numbers, the decimal number system uses 10 symbols called digits: • 0,1, 2, 3, 4, 5, 6, 7, 8, and 9. • Place-value system: a number system that determines the value of a digit by its positionin a number.

  4. Read whole numbers HOW TO: Section 1-1 Place Value and Our Number System • Beginning with the ones place on the right, the digits are grouped with three digits in each group. • For example: 286,418,917 • Each group is called a period.

  5. Understanding place value HOW TO: Section 1-1 Place Value and Our Number System • Each period has a name and a ones place, a tens place, and a hundreds place. • In a number, the first period from the left mayhave fewer than three digits. • In many cultures, the periods are separated by commas.

  6. Understanding place value HOW TO: Section 1-1 Place Value and Our Number System • Identify the period name of the leftmost group. • Read the three digit number from left to right. • Name the period. • 4,693,107 would read four million six hundred ninety-three thousand one hundred seven.

  7. Exceptions… Section 1-1 Place Value and Our Number System • Do not read or name a period that is all zeros. • 34,000,892 would read thirty-four million, eight hundred ninety-two. • Do not name the units period (892). 34, 000, 892

  8. When reading whole numbers, remember… HOW TO: Section 1-1 Place Value and Our Number System • The period name will be read at each comma. • Period names are read in the singular: • (“thousand” not “thousands”). • Hundreds is not a period name. • Do not say the word “and” when readingwhole numbers. • Calculator displays ordinarily do not show commas; insert them when writing the number.

  9. Write whole numbers 1-1-2 Section 1-1 Place Value and Our Number System • Begin recording digits from left to right. • Insert a comma at each period name. • Every period after the first period must havethree digits. • Insert zeros as necessary.

  10. 8, million 903, thousand422 (units) An Example… Section 1-1 Place Value and Our Number System Eight million, nine hundred three thousand, four hundred twenty-two… …is written 8,903,422.

  11. Round whole numbers 1-1-3 Section 1-1 Place Value and Our Number System • Rounding to a specificplace: • Identify the place. • “nearest hundred”, for example. • Look at the digit immediately to the right. • Is it 5 or higher? Round up. • Is it 4 or lower? Specified digit stays the same. • All digits to the right of the specified placebecome zeros.

  12. Examples… Section 1-1 Place Value and Our Number System Round to the nearest hundred: 4,856 10,527 234,567 8,648,078 4,900 10,500 234,600 8,648,100

  13. Key Terms… Section 1-1 Place Value and Our Number System • Addends • The numbers being added. • Sum or total • The answer or result of addition.

  14. Key Terms… Section 1-1 Place Value and Our Number System • Commutative property of addition • Two or more numbers can be added in either order without changing the sum. • Example: 8 + 3 = 3 + 8 = 11 • Associative property of addition • When more than two numbers are being added, the addends can be grouped by two at a time in any way. • Example: 5 + (2 + 1) = (5 + 2) + 1 = 8

  15. Read and round integers 1-1-4 Section 1-1 Place Value and Our Number System • In the business world we sometimes want to express numbers that are smaller than 0. • These are referred to as negative numbers. • When the set of whole numbers is expanded to include negative numbers, this set is called theset of integers.

  16. Read and round integers HOW TO: Section 1-1 Place Value and Our Number System • When reading integers: • The rules are the same as for reading whole numbers. • State the word negative or minus to read a numberless than zero. • When rounding integers: • The rules are the same as for roundingwhole numbers.

  17. An Example… Section 1-1 Place Value and Our Number System Read the number for the U.S. national debt: - $11,936,042,802,503 Negative eleven trillion, nine hundred thirty-six billion, forty-two million, eight hundred two thousand, five hundred three dollars.

  18. -$11,936,042,802,503 The trillions digit is 1. -$11,936,042,802,503 The digit to the right is 9. An Example… Section 1-1 Place Value and Our Number System Round the previous exampleto the nearest trillion: 9 is more than 5, so increase the 1, by 1, to get 2.Replace all digits to the right of 2 with zeros. -$12,000,000,000,000 The answer is -$12 trillion.

  19. Learning Outcomes 1-2 • Add and subtract wholenumbers. • Add and subtract integers. • Multiply and divide integers. • Apply the standard order ofoperations. to a series of operations.

  20. Add and subtract whole numbers 1-2-1 Section 1-2 Operations With Whole Numbers and Integers • To add whole numbers, write the numbers in a vertical column, aligning digits according to their place values. • Beginning with the ones column, add the place digits. • Add, if necessary, to the tens column. • Repeat the operation, adding to the hundreds column, if necessary, until you have reached the farthest column of digits to the left.

  21. An Example… Section 1-2 Operations with Whole Numbers and Integers Add 1 1 2 2 • Add the ones column. • Place 8 at the bottom ofthe ones column. • Carry the 2 to the tens column. • Place the 4 in the tens column. • Carry the 2. • Finish the operation. 6 4 9 4 8 Answer: 64,948

  22. Estimating HOW TO: Section 1-2 Operations with Whole Numbers and Integers • Estimate: to find a reasonable approximateanswer for a calculation. • Use estimating as a quick tool when an exactnumber is not required. • Round whole numbers to the place desiredfor an estimate.

  23. Sales for last week’sconcession stand. Monday: $219 Tuesday: $877 Wednesday: $455 Thursday: $614 Friday: $980 An Example… Section 1-2 Operations with Whole Numbers and Integers What was the week’s total to the nearest hundred? = $3,200 $200 + $900 + $500 + $600 + $1000

  24. Subtract whole numbers HOW TO: Section 1-2 Operations with Whole Numbers and Integers • When subtracting whole numbers, the order ofthe numbers is important. • Therefore, subtraction is not commutative. 9 – 4 ≠ 4 – 9 • Grouping in subtraction is important. • Subtraction is not associative. (8 - 3) -1 = 5 – 1 = 4 but 8 - (3 -1) = 8 - 2 = 6 4 ≠ 6

  25. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Minuend • The beginning amount or number thata second number is being subtracted from. • Subtrahend • The number being subtracted. • Difference • The answer or result of subtracting. • Borrow • Regroup digits in the minuend by borrowing 1from the digit to the left of the specified place,and adding 10 to the specified place.

  26. 1 2 9 3 An Example… Section 1-2 Operations with Whole Numbers and Integers • Borrow 1 from the ten column, add 10 to the ones column. • Subtract 8 from 13. • Borrow 1 from the hundreds column,add 10 to the tens column. • Subtract 9 from 18. • Borrow 1 from the thousands column. • Subtract 5 from 11. Subtract 11 1 1 18 8 18 6 9 5 Answer: 695

  27. Using rounding in subtraction HOW TO: Section 1-2 Operations with Whole Numbers and Integers • Subtract 128 from 1,345 by rounding each number to the nearest hundred to estimatethe difference. • 128 would become 100. • 1,345 would become 1,300. • The estimated difference would be 1,200.

  28. Add and subtract integers 1-2-2 Section 1-2 Operations with Whole Numbers and Integers • To add two negative integers, add the numbers without regard to the signs. • Assign a negative to the sum. Last year Murphy’s Used Car Co. lost $23,000. This year they lost another $16,000. What is the total loss? -$23,000 + (-$16,000) = -$39,000 The two-year loss is -$39,000.

  29. Add and subtract integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers • To add a positive and a negative integer, subtract the numbers without regard to the signs. • Look at the numbers without the signs. • Choose the larger of these numbers; • Assign the sum the sign of the larger number.

  30. The final balance is -$72. An Example… Section 1-2 Operations with Whole Numbers and Integers Jeremy has a bank balance of $47,then writes a check for $89. What is the new balance,including a $30 overdraft fee? $47 + (-$89) = -$42 -$42 + (-$30) = -$72

  31. Multiply whole numbers HOW TO: Section 1-2 Operations with Whole Numbers and Integers • Numbers can be multiplied in any order without affecting the result • Commutative property of multiplication. 8 x 12 = 12 x 8 96 = 96

  32. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Multiplicand • The number being multiplied. • Multiplier • The number multiplied by. • Factor • Each number involved in multiplication.

  33. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Product • The answer or result of multiplication. • Partial product • The product of one digit of the multiplier andthe entire multiplicand.

  34. Multiply Multiplicand 7 9 Multiplier x 2 3 Partial product 2 3 7 Partial product 1 5 8 _ PRODUCT 1 8 1 7 An Example… Section 1-2 Operations with Whole Numbers and Integers 1

  35. Examples to try without a calculator… Section 1-2 Operations with Whole Numbers and Integers 418 x 107 = ? Answer: 44,726 88 x 120 = ? Answer: 10,560 348 x 27 = ? Answer: 9,396

  36. Multiply integers 1-2-3 Section 1-2 Operations with Whole Numbers and Integers • To multiply a negative and a positive integer, multiply the two integers without regard tothe signs. • Assign a negative sign to the product. What is the total loss generated fromselling 87 frames each for $2 below cost? 87 x (-$2) = -$174 The total loss is -$174.

  37. Multiply integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers • To multiply two negative or two positive integers, multiply the two integers without regard to the signs. • The product is positive. What is the product of (-16)(-3)? 16 x 3 = 48 The product is positive and is 48.

  38. Divide integers 1-2-4 Section 1-2 Operations with Whole Numbers and Integers • Division is used to find the number of equal parts into which a whole quantity can be separated. A $40 tip is shared equally among 5 servers. How much does each server receive? $40 ÷ 5 servers = $8 each.

  39. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Dividend • The number being divided or the total quantity. • Divisor • The number to divide by. • Quotient • The answer or result of the operation. • Whole-number part of the quotient • The quotient without regard to its remainder.

  40. Key Terms… Section 1-2 Operations with Whole Numbers and Integers • Remainder of quotient • A number that is smaller than the divisor thatremains after division is complete. • Partial dividend • The part of the dividend that is being consideredat a given step of the process. • Partial quotient • The quotient of the partial dividend and the divisor.

  41. Remainders HOW TO: Section 1-2 Operations with Whole Numbers and Integers • There will be a remainder if an amount is toosmall to be further divided by the divisor. • For example: 152 ÷ 3 = 50 R 2 • That amount may be expressed as… • A remainder (R 2). • A fraction. • A decimal.

  42. MORE Divide integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers STEP 1 Beginning with its leftmost digit, identifythe first group of digits of the dividendthat is larger than or equal to the divisor. 1235 ÷ 5 = ? • Is it 1?No. • Is it 12?Yes. • 5 goes into 12 two times.Place the 2 above the 2 in the dividend.

  43. MORE Divide integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers STEP 2 Multiply 2 by the divisor. Place 10 underthe 12 and subtract. The result is 2. 1235 ÷ 5 = ? STEP 3 Bring down the following digit whichis 3, and divide 5 into 23. STEP 4 The result is 4. Place the 4 directlyabove the 3 in the dividend.

  44. Divide integers HOW TO: Section 1-2 Operations with Whole Numbers and Integers STEP 5 Multiply 4 by the divisor. Place 20 underthe 23 and subtract. The result is 3. 1235 ÷ 5 = ? STEP 6 Bring down the last digit, which is 5,and divide 5 into 35. The result is 7. STEP 7 Place 7 directly above the 5. Youhave finished and the answer is 247.

  45. Examples to try without a calculator… Section 1-2 Operations with Whole Numbers and Integers Adams-Duke Realty Company estimates thatits losses for the year will be $36,000,000. What is the average loss per month? Answer: -$3,000,000 Divide the following: 63,500,000 ÷ 1,000 (mentally eliminate the ending zeros from both numbers) Answer: 63,500

  46. Apply the standard orderof operations to a series of operations 1-2-5 Section 1-2 Operations with Whole Numbers and Integers STEP 1 Perform all operations that are inside grouping symbols, such as parentheses. STEP 2 Perform all multiplications and divisions as they appear from left to right. STEP 3 Perform all additions and subtractions as theyappear from left to right.

  47. Examples to try… Section 1-2 Operations with Whole Numbers and Integers 15 – (4 + 7) = ? Answer: 4 (75 + 50 + 35 + 90) ÷ 5 = ? Answer: 50 45 - 4 x 9 = ? Answer: 9

  48. EXERCISES SET A

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