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Business Math Chapter 1

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Business Math Chapter 1

  1. 1. CHAPTER 1 : Fundamental Operation of Arithmetic 1.1 Fraction 1.2 Ratio and Proportion 1.3 Percentage
  2. 2. 1.1 FRACTION   WHAT IS FRACTION? Two numbers separated by a horizontal or sloping line. Numerator, N 2 E.g. Two seventh = 2/7 = 7 Denominator, D Types of fraction Types Definition Proper fraction Numerator < denominator Improper fraction Numerator = or > denominator Mixed fractions Whole number + common fraction Equivalent fractions Two fractions that have equals values Examples
  3. 3. 1.1 FRACTION IMPROPER Divide N by D as far as possible and express remainder as a proper fraction Conversion improper to mixed MIXED Multiply the whole number by D, add N. Place the total over N.
  4. 4. 1.1 FRACTION OPERATION ON FRACTIONS 1. ADDITION & SUBTRACTION Same Denominators  Just add / minus the numerator Different Denominators  Find a common denominator, then add / minus and simplified the answer to the lowest term.  Example: Evaluate the followings; a) 1 + 3 + 6 5 5 5 3 1 b) + 7 5 2 2 c) − 5 3 3 2 d) 2 + 5 4 5
  5. 5. PRACTICE 1 1. Add together : 2 1 a) + 3 5 5 1 b) + 8 9 3 2 1 c) + + 8 5 3 2 3 d) 3 + 4 3 5 1 1 1 e) 5 + 4 + 3 2 3 5 2. Subtract the following: 2 1 a) − 3 4 3 2 b) − 4 5 7 1 c) 5 −3 16 3 1 3 d) 5 − 2 3 4 1 3 e) 7 − 3 2 5
  6. 6. 1.1 FRACTION OPERATION ON FRACTIONS 2. MULTIPLICATION  3. DIVISION Product of the numerators  Invert the divisor and divide by the product of the change the division sign to denominators. multiplication. p r p×r × = q s q×s   Can be simplified if possible before multiplying. Mixed fractions have to be converted into improper fractions before multiply. p r p s p× s ÷ = × = q s q r q× r
  7. 7. PRACTICE 2 Calculate each of the following: 5 4 1) × 8 7 5 2 2) ÷ 6 3 1 3 3) × 4 5 3 5 4) 1 × 4 8 7 3 5) ÷ 8 4 1 3 ÷ 8 4 1  1 2 7) ÷ 1 ×  4  8 5 6)1 2 2  7 8) 1 × 2  − 3 5 5  8 2 2 1 1 9) ×  −  + 5 3 4  2 1 4  2 10)  2 + 1  ÷ 5 5 5  3
  8. 8. 1.1 FRACTION OPERATION ON FRACTIONS 4. POWERS   5. SQUARE ROOTS Raise both the numerator & the denominator to that power.  a  n a n   = n b b 3 Example;  2  = 23 = 8   3 5 5 125   Invert the divisor and change the division sign to multiplication. a a = b b Example; 16 = 16 = 4 81 81 9
  9. 9. 1.1 FRACTION OPERATION ON FRACTIONS 6. PRACTICAL APPLICATION  A girl spends 3/4 of her pocket money and has 90cents left. How much did she have to start with? 3 1 1 − = = 90 cents 4 4 1 = 4 × 90 = 360 cents ∴ The girl had RM 3.60 to start with.  A group, of school children went to a hamburger bar, 2/5 of them bought hamburgers only, 1/4 bought chips only and the remainder bought drinks only What fraction bought food? 2 1  What fraction bought drinks? 1)Food = +  5 4 8 + 5 13 = = 20 20 13 20 20 − 13 7 = = 20 20 2)Drink = 1 −
  10. 10. PRACTICE 3 1. 2. 3. 4. 5. Jane takes 5 ¾ minutes to iron a blouse. How many blouses can she iron in 23 minutes? The profit of a business are RM 29 000. It is shared between two partners A & B. If A receives 9/20 of the profits, how much money does B receive? A man sells his car for RM 16 200 and as a result, loses one tenth of the price he paid for it. What price did he pay for it? 5/8 of a fence has been built. If there is still 40 feet to be built, how long will the fence be? A man left three eight of his money to his wife & half the remainder to his son. The rest was divided equally between his five daughters. Determine what fraction of the money each daughter received.
  11. 11. 1.2 RATIO & PROPORTION       WHAT IS RATIO ? Comparison of 2 numbers or quantities as quotient. Represent by x/y or x : y. Generally reduced to lowest terms like fraction (by dividing the HCF of the numbers). Derived from quantities measured in the same units Its just number, don’t have unit. Its express the relationship between 2 or more factors (or numbers)
  12. 12. 1.2 RATIO & PROPORTION   WHAT IS RATIO ? E.g. Simplify the ratio 200g : 1 kg (different units) = 200g : 1000g =1:5 Example: Expressed the following ratio to the lowest 78 3 term; a) 78 : 52 = = 52 2 5 3 : = 8 8 12 8 c) to 13 13 d) 10 cm 2 : 10 mm 2 b)
  13. 13. 1.2 RATIO & PROPORTION     1.   WHAT IS PROPORTION ? The equality of 2 ratios E.g. 5 : 2 = 25 : 10 To solve problems dealing with proportion, we use cross multiplication. Types of proportion: Direct proportion 2. If increase or decrease at the  same rate. E.g. If we buy rice at RM 2 for 2 kg, then we expect to pay RM 4  for 4 kg. Inverse proportion If an increase (decrease) in one quantity produces a decrease (increase) in a second quantity in the same time. E.g. 5 men building a wall take 20 days. If 4 men, it will take only 25 days.
  14. 14. 1.2 RATIO & PROPORTION  WHAT IS PROPORTION ? Examples: 5 x = 75 1. Find the value of x for 5 : 25 = 3 : x. 5 = 3 ⇒ 25 2. If a : b = 5 : 3, find a. b : a b. a : (a – b) c. b : (a + b) d. (a – b) : (a + b) 1. If a : c = 3 : 4, and a : b = 4 : 5, find b : c x x = 15
  15. 15. 1.3 PERCENTAGE    WHAT IS PERCENTAGE ? Express a quantity as the number of parts in 100 parts. Written as fraction, e.g. 20 percent = 20 % = 20/100 = 0.20 Conversion: Then move dec. point 2 places to the right x 100% ÷ 100% Fractions Percentage x 100% Decimal ÷ 100% Then move dec. point 2 places to the left
  16. 16. 1.3 PERCENTAGE  Example: Express each number as a fraction, decimal and percent. a. 86% b. 5.6% c. 8 ½% d. 0.025 e. 1.5 f. 9/8 g. 17/1000

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