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BASIC MATH

BASIC MATH. BASIC MATH. A. BASIC ARITHMETIC. Foundation of modern day life. Simplest form of mathematics. Four Basic Operations :. Addition plus sign Subtraction minus sign Multiplication multiplication sign

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BASIC MATH

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  1. BASIC MATH

  2. BASIC MATH A. BASIC ARITHMETIC • Foundation of modern day life. • Simplest form of mathematics. Four Basic Operations : • Addition plus sign • Subtraction minus sign • Multiplication multiplication sign • Division division sign x Equal or Even Values equal sign

  3. 1. Beginning Terminology • Numbers - Symbol or word used to express value or quantity. Numbers • Arabic number system - 0,1,2,3,4,5,6,7,8,9 • Digits - Name given to place or position of each numeral. Digits Number Sequence 2. Kinds of numbers Whole Numbers • Whole Numbers - Complete units , no fractional parts. (43) • May be written in form of words. (forty-three) Fraction • Fraction - Part of a whole unit or quantity. (1/2)

  4. 2. Kinds of numbers (con’t) • Decimal Numbers - Fraction written on one line as whole no. Decimal Numbers • Position of period determines power of decimal.

  5. B. WHOLE NUMBERS 1. Addition Number Line • Number Line - Shows numerals in order of value Adding on the Number Line • Adding on theNumber Line (2 + 3 = 5) Adding with pictures • Adding with pictures

  6. 1. Addition (con’t) Adding in columns • Adding in columns - Uses no equal sign 897 + 368 1265 5 + 5 10 Answer is called “sum”. Simple Complex Table of Digits

  7. ADDITION PRACTICE EXERCISES a. 222 + 222 318 + 421 d. 1021 + 1210 c. 611 + 116 739 727 2231 444 2. a. 813 + 267 924 + 429 411 + 946 c. 618 +861 1357 1479 1353 1080 3. a. 813 222 + 318 1021 611 + 421 d. 1021 1621 + 6211 c. 611 96 + 861 1353 2053 1568 8853 Let's check our answers.

  8. 2. Subtraction Number Line • Number Line - Can show subtraction. Subtraction with pictures Number Line Position larger numbers above smaller numbers. If subtracting larger digits from smaller digits, borrow from next column. 4 1 5 3 8 - 3 9 7 1 4 1

  9. SUBTRACTION PRACTICE EXERCISES a. 6 - 3 8 - 4 d. 9 - 5 e. 7 - 3 c. 5 - 2 4 4 3 3 4 2. a. 11 - 6 b. 12 - 4 d. 33 - 7 e. 41 - 8 c. 28 - 9 8 5 19 26 33 3. a. 27 - 19 b. 23 - 14 d. 99 - 33 e. 72 - 65 c. 86 - 57 66 8 9 7 29 Let's check our answers.

  10. SUBTRACTION PRACTICE EXERCISES (con’t) 4. a. 387 - 241 399 - 299 d. 732 - 687 c. 847 - 659 45 188 146 100 5. a. 3472 - 495 b. 312 - 186 d. 3268 - 3168 c. 419 - 210 126 2977 209 100 c. 47 - 32 6. a. 47 - 38 b. 63 - 8 d. 59 - 48 9 11 55 15 7. a. 372 - 192 b. 385 - 246 d. 368 - 29 c. 219 - 191 139 339 180 28 Let's check our answers.

  11. 3. Checking Addition and Subtraction • Check Addition - Subtract one of added numbers from sum. Check Addition Result should produce other added number. 5 + 3 8 - 3 5 73 + 48 121 - 48 73 2 + 8 10 - 8 2 Check Three or more #s • Check Three or more #s - Add from bottom to top. 927 318 426 183 927 To Add To Check • Check Subtraction - Add subtracted number back. Check Subtraction 62 - 37 25 + 37 62 103 - 87 16 + 87 103 5 - 4 1 + 4 5

  12. CHECKING ADDITION & SUBTRACTION PRACTICE EXERCISES 1. a. 6 + 8 b. 9 + 5 d. 109 + 236 c. 18 + 18 14 13 26 335 2. a. 87 - 87 b. 291 - 192 d. 28 - 5 c. 367 - 212 1 99 55 24 3. a. 34 + 12 b. 87 13 81 + 14 d. 21 - 83 c. 87 13 81 + 14 46 104 195 746 4. a. 28 - 16 b. 361 - 361 c. 2793142 - 1361101 0 22 1432141 Check these answers using the method discussed.

  13. CHECKING ADDITION & SUBTRACTION PRACTICE EXERCISES 1. a. 6 + 8 13 - 8 5 b. 9 + 5 14 - 5 9 d. 109 + 236 335 - 236 99 c. 18 + 18 26 - 18 8 2. a. 87 - 87 1 + 87 88 b. 291 - 192 99 + 192 291 d. 28 - 5 24 + 5 29 c. 367 - 212 55 + 212 267 b. 195 87 13 81 + 14 195 c. 949 103 212 439 + 195 746 3. a. 34 + 12 46 - 12 34 d. 21 + 83 104 - 83 21 4. a. 28 - 16 22 + 16 38 b. 361 - 361 0 + 361 361 c. 2793142 - 1361101 1432141 + 1361101 2793242 # = Right # = Wrong

  14. 4. Multiplication In Arithmetic • In Arithmetic - Indicated by “times” sign (x). Learn “Times” Table 6 x 8 = 48

  15. + 2 + 2 + 1 + 1 48 X 23 48 X 23 48 X 23 48 X 23 4 144 144 144 6 960 1104 4. Multiplication (con’t) • Complex Multiplication - Carry result to next column. Complex Multiplication Problem: 48 x 23 Same process is used when multiplying three or four-digit problems.

  16. MULTIPLICATION PRACTICE EXERCISES a. 21 x 4 81 x 9 d. 36 x 3 c. 64 x 5 108 729 320 84 2. a. 87 x 7 b. 43 x 2 d. 99 x 6 c. 56 x 0 86 609 0 594 d. 55 x 37 3. a. 24 x 13 b. 53 x 15 c. 49 x 26 2035 312 795 1274 Let's check our answers.

  17. MULTIPLICATION PRACTICE EXERCISES (con’t) 4. a. 94 x 73 b. 99 x 27 d. 83 x 69 c. 34 x 32 5727 1088 6862 2673 5. a. 347 x 21 b. 843 x 34 c. 966 x 46 28,662 7287 44,436 c. 111 x 19 6. a. 360 x 37 b. 884 x 63 55,692 13,320 2109 7. a. 493 x 216 b. 568 x 432 c. 987 x 654 106,488 245,376 645,498 Let's check our answers.

  18. 5. Division • Finding out how many times a divider “goes into” a whole number. Finding out how many times a divider “goes into” a whole number. 15 3 = 5 15 5 = 3

  19. Shown by using a straight bar “ “ or “ “ sign. • Shown by using a straight bar “ “ or “ “ sign. 1 times 48 = 48 48 “goes into” 50 one time. 48 5040 50 minus 48 = 2 & bring down the 4 48 goes into 24 zero times. Bring down other 0. 48 goes into 240, five times 5 times 48 = 240 240 minus 240 = 0 remainder 5. Division (con’t) 1 0 5 48 2 4 0 240 0 So, 5040 divided by 48 = 105 w/no remainder. Or it can be stated: 48 “goes into” 5040, “105 times”

  20. DIVISION PRACTICE EXERCISES 92 62 211 1. a. 7 c. 48 434 9 5040 b. 828 101 13 310 9 12 117 3720 2. a. b. 10 c. 1010 256 687 38472 3. a. b. 56 23 5888 67 98 13 871 4. a. b. 98 9604 123 50 789 97047 5. a. b. 50 2500 Let's check our answers.

  21. DIVISION PRACTICE EXERCISES (con’t) 9000 7 6. a. 3 21 27000 147 b. 61 101 32 88 1952 8888 7. a. b. 67 r 19 858 r 13 12883 8. a. b. 15 87 5848 22 r 329 12 r 955 352 8073 9. a. b. 994 12883 Let's check our answers.

  22. C. FRACTIONS - A smaller part of a whole number. A smaller part of a whole number. Written with one number over the other, divided by a line. 3 8 11 16 11 3 or 8 16 Any number smaller than 1, must be a fraction. 24 6 Try thinking of the fraction as “so many of a specified number of parts”. For example: Think of 3/8 as “three of eight parts” or... Think of 11/16 as “eleven of sixteen parts”. 1. Changing whole numbers to fractions. Multiply the whole number times the number of parts being considered. Changing the whole number 4 to “sixths”: 24 6 4 x 6 6 or 4 = =

  23. CHANGING WHOLE NUMBERS TO FRACTIONS EXERCISES 343 343 7 49 x 7 7 1. 49 to sevenths or = = 7 320 320 8 40 x 8 8 or = = 2. 40 to eighths 8 486 486 9 54 x 9 9 or = 3. 54 to ninths = 9 81 81 3 27 x 3 3 or = 4. 27 to thirds = 3 48 48 4 12 x 4 4 or = = 5. 12 to fourths 4 650 650 5 130 x 5 5 or = 6. 130 to fifths = 5 Let's check our answers.

  24. 2. Proper and improper fractions. Proper Fraction - Numerator is smaller number than denominator. 3/4 Improper Fraction - Numerator is greater than or equal to denominator. 15/9 3. Mixed numbers. Combination of a whole number and a proper fraction. 4. Changing mixed numbers to fractions. Change 3 7/8 into an improper fraction. • Change whole number (3) to match fraction (eighths). 24 24 8 3 x 8 8 3 = or = 8 • Add both fractions together. 7 + 24 31 = 8 8 8

  25. 9 2 8 2 1 2 + 4 x 2 2 = = = 24 4 27 4 3 4 + 8 x 4 4 = = = 304 16 311 16 7 16 + 19 x 16 16 = = = 95 12 84 12 11 12 + 7 x 12 12 = = = 93 14 9 14 + 84 14 6 x 14 14 = = = 321 64 320 64 1 64 + 5 x 64 64 = = = CHANGING MIXED NUMBERS TO FRACTIONS EXERCISES 1. 4 1/2 2. 8 3/4 3. 19 7/16 4. 7 11/12 5. 6 9/14 6. 5 1/64 Let's check our answers.

  26. 19/3 = 19 3 = 6, remainder 1 = 6 1/3 (a mixed number) 1. 37/7 = = 37 7 = 5, remainder 2 = 5 2/7 (a mixed number) 2. 44/4 = = 44 4 = 11, no remainder = 11 (a whole number) 3. 23/5 = = 23 5 = 4, remainder 3 = 4 3/5 (a mixed number) 4. 43/9 = = 43 9 = 4, remainder 7 = 4 7/9 (a mixed number) 5. 240/8 = = 240 8 = 30, no remainder = 30 (a whole number) 6. 191/6 = = 191 6 = 31, remainder 5 = 31 5/6 (a mixed number) Changing improper fractions to whole/mixed numbers. Change 19/3 into whole/mixed number.. CHANGING IMPROPER FRACTIONS TO WHOLE/MIXED NUMBERS EXERCISES Let's check our answers.

  27. 6. Reducing Fractions Reducing - Changing to different terms. Terms - The name for numerator and denominator of a fraction. Reducing does not change value of original fraction. 7. Reducing to Lower Terms Divide both numerator and denominator by same number. . . . . . . . . 8 2 =4 16 2 = 8 2 2 =1 4 2 = 2 4 2 =2 8 2 = 4 3 3 =1 9 3 = 3 Example: = & . . . . Have same value. 1 3 3 . . . . 9 3 9 8. Reducing to Lowest Terms Lowest Terms - 1 is only number which evenly divides both numerator and denominator. 16 = Example: 32 . . 16 2 =8 32 2 = 16 d. c. b. a. . .

  28. . 15 5 =3 20 5 = 4 . . . . 36 4 =9 40 4 = 10 . . . . . 24 6 =4 36 6 = 6 . . . 12 4 =3 36 4 = 9 . . . . 30 3 =10 45 3 = 15 . . . . 16 4 = 4 76 4 = 19 . . . REDUCING TO LOWER/LOWEST TERMS EXERCISES 1. Reduce the following fractions to LOWER terms: 15 a. to 4ths = 20 • Divide the original denominator (20) by the desired denominator (4) = 5.. • Then divide both parts of original fraction by that number (5). 36 b. to 10ths = 40 24 c. to 6ths = 36 12 d. to 9ths = 36 30 e. to 15ths = 45 16 f. to 19ths = 76 Let's check our answers.

  29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 =3 10 2 = 5 a. 3 3 =1 9 3 = 3 a. 6 2 = 3 64 2 = 32 a. 32 2 = 16 64 2 = 32 16 2 = 8 76 2 = 38 16 2 = 8 32 2 = 16 8 2 = 4 38 2 = 19 8 8 = 1 16 8 = 2 a. a. b. b. c. REDUCING TO LOWER/LOWEST TERMS EXERCISES (con’t) 2. Reduce the following fractions to LOWEST terms: 6 = a. 10 3 = b. 9 6 = c. 64 13 = d. Cannot be reduced. 32 32 e. = 48 16 f. = 76 Let's check our answers.

  30. 7 6 2 1 8 8 8 8 1 7 5 5 2 3 1 36 24 12 18 9 8 6 9. Common Denominator Two or more fractions with the same denominator. When denominators are not the same, a common denominator is found by multiplying each denominator together. 6 x 8 x 9 x 12 x 18 x 24 x 36 = 80,621,568 80,621,568 is only one possible common denominator ... but certainly not the best, or easiest to work with. 10. Least Common Denominator (LCD) Smallest number into which denominators of a group of two or more fractions will divide evenly.

  31. 1 7 5 5 2 3 1 36 24 12 18 9 8 6 1 1 1 4 1 3 1 1 7 24 16 12 12 20 8 15 6 10 2 x 5 2 x 2 x 5 3 x 5 3 x 2 x 2 x 2 2 x 2 x3 2 x 2 x 2 x 2 2 x 3 2 x 3 x 2 2 x 2 x 2 10. Least Common Denominator (LCD) con’t. To find the LCD, find the “lowest prime factors” of each denominator. 2 x 2 x 2 3 x 3 2 x 3 x 3 2 x 3 2 x 2 x 3 x 3 2 x 3 x 2 3 x 2 x 2 x 2 The most number of times any single factors appears in a set is multiplied by the most number of time any other factor appears. (2 x 2 x 2) x (3 x 3) = 72 Remember: If a denominator is a “prime number”, it can’t be factored except by itself and 1. LCD Exercises (Find the LCD’s) 2 x 2 x 3 x 5 = 60 2 x 2 x 2 x 2 x 3 = 48 2 x 2 x 2 x 3 = 24 Let's check our answers.

  32. 1 7 5 5 2 3 1 36 24 12 18 9 8 6 2 x 2 x 2 3 x 3 2 x 3 x 3 2 x 3 2 x 2 x 3 x 3 2 x 3 x 2 3 x 2 x 2 x 2 LCD = 72 3 2 5 8 9 12 . . . . 72 12 = 6 . . . . 72 8 = 9 72 9 = 8 5 x 6 = 30 12 x 6 = 72 3 x 9 = 27 8 x 9 = 72 2 x 8 = 16 9 x 8 = 72 11. Reducing to LCD Reducing to LCD can only be done after the LCD itself is known. Divide the LCD by each of the other denominators, then multiply both the numerator and denominator of the fraction by that result. 1 6 72 6 = 12 1 x 12 = 12 6 x 12 = 72 Remaining fractions are handled in same way.

  33. 2 x 2 x 3 x 5 = 60 2 x 2 x 2 x 2 x 3 = 48 2 x 2 x 2 x 3 = 24 24 6 = 4 48 12 = 4 60 10 = 6 1 1 3 1 x 4 = 4 6 x 4 = 24 6 1 x 4 = 4 12 x 4 = 48 12 3 x 6 = 18 10 x 6 = 60 10 24 8 = 3 48 16 = 3 60 15 = 4 1 1 4 . . . . . . . . . 1 x 3 = 3 8 x 3 = 24 8 1 x 3 = 3 16 x 3 = 48 16 . . . . . . . . . 4 x 4 = 16 15 x 4 = 60 15 24 12 = 2 48 24 = 2 60 20 = 3 1 1 1 1 7 4 1 1 3 1 1 x 2 = 2 12 x 2 = 24 12 1 7 1 x 2 = 2 24 x 2 = 48 24 7 x 3 = 21 20 x 3 = 60 24 20 16 12 12 20 8 15 6 10 2 x 5 2 x 2 x 5 3 x 5 3 x 2 x 2 x 2 2 x 2 x3 2 x 2 x 2 x 2 2 x 3 2 x 3 x 2 2 x 2 x 2 Reducing to LCD Exercises Reduce each set of fractions to their LCD. Let's check our answers.

  34. 12. Addition of Fractions All fractions must have same denominator. Determine common denominator according to previous process. Then add fractions. + 2 1 1 + 3 6 1 = = 2 4 4 4 4 Always reduce to lowest terms. 13. Addition of Mixed Numbers Mixed number consists of a whole number and a fraction. (3 1/3) • Whole numbers are added together first. • Then determine LCD for fractions. • Reduce fractions to their LCD. • Add numerators together and reduce answer to lowest terms. • Add sum of fractions to the sum of whole numbers.

  35. 3 + 3 2 1. + 7 2. = = 4 4 5 10 1 6 1 = + 11 7 4 = 4 2 10 10 10 1 1 = 10 2 + 9 + 1 3 15 5 4. 3. = = 5 32 4 16 5 + 1 = 6 39 9 + 30 = 32 32 32 23 + 15 8 = 7 20 1 20 20 = 32 3 3 + 7 1 6 = = 20 20 Adding Fractions and Mixed Numbers Exercises Add the following fractions and mixed numbers, reducing answers to lowest terms. Let's check our answers.

  36. - 6 14 20 = 24 24 24 - 1 5 To subtract fractions with different denominators: () 4 16 • Find the LCD... - 1 5 4 16 2 x 2 x 2 x 2 2 x 2 2 x 2 x 2 x 2 = 16 • Change the fractions to the LCD... - 4 5 16 16 • Subtract the numerators... - 1 4 5 = 16 16 16 14. Subtraction of Fractions Similar to adding, in that a common denominator must be found first. Then subtract one numerator from the other.

  37. Subtract the fractions first. (Determine LCD) - 1 2 4 10 2 3 3 x 2 = 6 (LCD) • Divide the LCD by denominator of each fraction. . 6 3 = 2 . 6 2 = 3 . . • Multiply numerator and denominator by their respective numbers. 2 2 4 1 3 3 = x = x 3 2 6 2 3 6 • Subtract the fractions. 4 3 1 = - 6 6 6 • Subtract the whole numbers. 10 - 4 = 6 • Add whole number and fraction together to form complete answer. 1 1 6 + 6 = 6 6 15. Subtraction of Mixed Numbers

  38. Subtract the fractions first. (Determine LCD) - 3 1 - 3 5 6 1 3 5 becomes 8 16 16 16 (LCD) = 16 • Six-sixteenths cannot be subtracted from one-sixteenth, so 1 unit ( ) is borrowed from the 5 units, leaving 4. 16 16 16 1 16 • Add to and problem becomes: 16 - 6 17 3 4 16 16 • Subtract the fractions. 17 6 11 = - 16 16 16 • Subtract the whole numbers. 4 - 3 = 1 • Add whole number and fraction together to form complete answer. 11 11 1 + 1 = 16 16 15. Subtraction of Mixed Numbers (con’t) Borrowing

  39. 2 - 1 1. = 5 3 5 - 6 6 5 1 15 = - 33 = 15 15 15 15 15 20 - 6 14 15 = 32 17 15 15 15 4 - 15 57 101 = 15 6 9 3 - = = 16 16 24 24 8 24 20 - 15 5 100 57 = 43 16 16 16 6 - 5 1 19 28 = 47 4 9 5 - 1 4 10 15 14 4 = 15 = 15 12 3 12 12 Subtracting Fractions and Mixed Numbers Exercises Subtract the following fractions and mixed numbers, reducing answers to lowest terms. 1 - 2 4. 15 = 33 3 5 - 15 5. 1 5 - 3 57 101 = 2. = 16 4 8 12 - 2 1 28 = 3. 47 - 6. 5 3 14 10 5 = 3 12 4 Let's check our answers.

  40. 4 3 X 4 16 4 12 3 = = X 4 16 4 12 3 = = X 4 16 64 4 12 3 = 64 4 16 . . 16. MULTIPLYING FRACTIONS • Common denominator not required for multiplication. 1. First, multiply the numerators. 2. Then, multiply the denominators. 3. Reduce answer to its lowest terms.

  41. 4 3 X 4 4 1 4 12 3 = X 4 1 4 3 4 12 3 = = 4 4 1 . . 17. Multiplying Fractions & Whole/Mixed Numbers • Change to an improper fraction before multiplication. 1. First, the whole number (4) is changed to improper fraction. 2. Then, multiply the numerators and denominators. 3. Reduce answer to its lowest terms.

  42. Example: 8 5 = X 3 16 1 8 5 = X 3 16 2 1 5 5 = X 3 2 6 1 1 12 1 3 1 1 = X = X 14 21 7 24 2 2 7 18. Cancellation • Makes multiplying fractions easier. • If numerator of one of fractions and denominator of other fraction can be evenly divided by the same number, they can be reduced, or cancelled. Cancellation can be done on both parts of a fraction.

  43. 3 16 2 1 2 1 5 5 27 50 7 10 72 33 2 25 3 Multiplying Fractions and Mixed Numbers Exercises Multiply the following fraction, whole & mixed numbers. Reduce to lowest terms. 1 3 4 1 1. 2. 26 = X = X 4 16 26 4 9 3. 2 4. = 3 X = X 5 5 3 35 3 4 9 1 5. 6. = = X X 4 35 5 10 1 7 2 5 = 7. X 8. 6 = X 12 3 11 77 9. 5 = X 15 Let's check our answers.

  44. 19. Division of Fractions • Actually done by multiplication, by inverting divisors. • The sign “ “ means “divided by” and the fraction to the right of the sign is always the divisor. Example: 3 1 15 3 5 3 becomes 3 4 = = X 5 4 4 1 4 20. Division of Fractions and Whole/Mixed Numbers • Whole and mixed numbers must be changed to improper fractions. Example: 3 1 51 17 3 2 3 1 becomes = = 16 3 + X 2 X 8 + 16 8 16 and 8 16 8 1 3 17 51 8 51 3 8 51 Inverts to 1 = X = X X 8 16 17 2 16 17 1 16 1 2 3 1 1 3 1 = X = 2 2 1 2 Double Cancellation

  45. 1 8 1 1 2 4 5 25 7 2 2 3 Dividing Fractions,Whole/Mixed Numbers Exercises Divide the following fraction, whole & mixed numbers. Reduce to lowest terms. 3 51 = 5 3 1. 2. = 8 16 8 6 1 7 144 18 15 = 3. 4. = 8 12 14 7 5. = 3 4

  46. 5 5 5 = = = .5 .005 10 1000 .05 100 999 1000 ( 1 + same number of zeros as digits in numerator) D. DECIMAL NUMBERS 1. Decimal System • System of numbers based on ten (10). • Decimal fraction has a denominator of 10, 100, 1000, etc. Written on one line as a whole number, with a period (decimal point) in front. 3 digits .999 is the same as

  47. 7 5 is written 5.7 10 Whole Number Decimal Fraction (Tenths) 7 55 is written 55.07 100 Whole Number Decimal Fraction (Hundredths) Decimal Fraction (Tenths) 77 555 is written 555.077 1000 Whole Number Decimal Fraction (Thousandths) Decimal Fraction (Hundredths) Decimal Fraction (Tenths) 2. Reading and Writing Decimals

  48. One place .0 tenths Two places .00 hundredths Three places .000 thousandths Four places .0000 ten-thousandths Five places .00000 hundred-thousandths 2. Reading and Writing Decimals (con’t) • Decimals are read to the right of the decimal point. .63 is read as “sixty-three hundredths.” .136 is read as “one hundred thirty-six thousandths.” .5625 is read as “five thousand six hundred twenty-five ten-thousandths.” 3.5 is read “three and five tenths.” • Whole numbers and decimals are abbreviated. 6.625 is spoken as “six, point six two five.”

  49. 3. Addition of Decimals • Addition of decimals is same as addition of whole numbers except for the location of the decimal point. Add .865 + 1.3 + 375.006 + 71.1357 + 735 • Align numbers so all decimal points are in a vertical column. • Add each column same as regular addition of whole numbers. • Place decimal point in same column as it appears with each number. .865 1.3 375.006 71.1357 + 735. 0 000 “Add zeros to help eliminate errors.” 0 “Then, add each column.” 0000 1183.3067

  50. 4. Subtraction of Decimals • Subtraction of decimals is same as subtraction of whole numbers except for the location of the decimal point. Solve: 62.1251 - 24.102 • Write the numbers so the decimal points are under each other. • Subtract each column same as regular subtraction of whole numbers. • Place decimal point in same column as it appears with each number. 62.1251 - 24.102 “Add zeros to help eliminate errors.” 0 38.0231 “Then, subtract each column.”

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