Bus. Math. List of topics and Chapter 1.pptx

Introduction to Business Mathematics

1. Business Mathematics Specialized subject

2. List of Topics

3. L ist of Topics Chapter 1: Fundamental Operations on Fractions, Decimals, and Percents Chapter 2: Percentage, Ratio and Proportion Chapter 3: Buying and Selling Chapter 4: Salaries and Wages Chapter 5: Presentation and Analysis of Data

4. Chapter 1: Fundamental Operations on Fractions, Decimals and Percents

5. Lesson 1: Fraction

6. Lesson objectives At the end of the lesson, the students should be able to Demonstrates the understanding about fractions Recall the types of fractions they have learned Express a part as fraction of a whole Explain how fractions operate when the unit referred to is a group or a class.

7. Lesson 1: Fraction A fraction represents a part of a whole or a group. It is expressed as a quotient of two quantities, namely, the numerator and the denominator . The numerator (the number above the fraction bar) indicates the number of parts taken from the whole. The denominator (the number below the fraction bar) specifies the number of equal parts the whole is divided into.

8. Kinds of Fractions Proper Fractions Proper fraction is a fraction whose numerator is less than the denominator. This fraction has a value less than 1. The following are proper fractions: 2. Improper Fraction An improper fraction is a fraction whose numerator is greater than or equal to the denominator. This fraction has a value greater than or equal to 1. The following are improper fractions: 3. Mixed number A mixed number is a fraction which consists of a whole number and a proper fraction. The following are mixed numbers:  

9. A. Express the following as fractions of the units indicated 6 as part of a dozen 18 weeks as part of a decade 25 years as part of a century 2 quarts as part of a gallon 7 days as part of a week 400 kg as part of ton 5 years as part of a decade 1 inch as part of a foot 6 hours as part of a day 5 as part of 8-member team B. A class is composed of 30 students. There are 20 girls and 10 boys. What fraction of the class are girls? Boys?

10. Lesson 2: Addition of Fractions Lesson Objectives At the end of the lesson, the students should be able to: Add similar fractions Add dissimilar fractions Add mixed numbers; and Apply the knowledge of addition of fractions and mixed numbers in solving business problems, like total hours worked, total items sold etc.

11. Addition of Fractions Steps: To add fractions with the same denominator , add the numerators and write the sum over the common denominator. Then simplify or reduce the resulting fraction to its lowest term if possible. To simplify or reduce a fraction to its lowest term, divide the numerator and denominator by their greatest common factor (GCF). The GCF is the greatest factor that can divide two or more numbers. To find the GCF of two or more numbers, find all the factors of each number. Then identify the common factors of the numbers. Choose the greatest factor of those numbers afterward.

12. Example 1 Find the sum of the following fractions:  

13. Addition of Fraction Steps: To add fractions with different denominators , write them first as equivalent fractions by finding the least common denominator (LCD) of the fractions. The LCD is the least common multiple of the denominators of the fractions. To find the LCD of two or more fractions, list first the multiples of the denominators of each fraction until you find the smallest multiple that they have in common

14. Example 2 Add the following:  

15. Addition of Mixed numbers Steps: Change the mixed numbers into improper fractions and then Add: Example: Add the following mixed fractions  

16. Word problems involving addition of Fractions You need meters (m) of ribbon to make a large bow and m of ribbon to make a small bow. How much ribbon should you buy to make sure you have enough ribbon to make a large and a small bow?  

17. You were given a task to prepare three kinds of desserts for the Marketing Week. Based on the recipe, you will need 2 cups of flour for the pie, cups of flour for the cookies, and cups of flour for the cake. How much flour do you need to make the three desserts?  

18. James and Gabriel bought a farm measuring meters on one side, meters on the second side, meters, and meters on the fourth side. The couple wanted to fence the farm with barbed wires. They have 2 rolls of barbed wires of 500 meters per roll on hand. How many more meters of barbed wires do they need if they want to fence the farm four times.  

19. Olive is preparing for the Baptist of her daughter, Irene. She bought five dressed chicken weighing and kilograms each, respectively. What is the total weight of the chicken? At P75.00 per kilogram, how much will Olive have to pay for five dressed chicken? If she gave the seller two P500-bills, how much change is due her?  

20. Lesson 2: Subtraction of Fractions At the end of the lesson, the students should be able to: Subtract, similar, dissimilar fractions and mixed numbers. Subtract mixed numbers and whole numbers Apply the knowledge of subtraction of fractions, mixed numbers in different business applications.

21. Subtraction of Fractions To subtract fractions with the same denominator , subtract the numerators and write the difference over the common denominator. Example 1: Solve Subtract from Subtract from Subtract from  

22. Subtraction of Fractions Subtracting fractions with different denominators follows the same procedure as in adding fractions with different denominators. Write the fractions first as equivalent fractions by finding the LCD. Example 2: Subtract  

23. Subtraction mixed numbers To subtract from another mixed number, we follow the following rules. If the mixed numbers have similar fractional parts, we subtract the whole numbers then subtract the fractional parts following the rule for subtraction. If the mixed numbers have fractional parts which are not similar, then we change the fractional parts into similar fractions then proceed to subtraction. Example: Subtract the following.  

24. Subtraction of mixed numbers and whole numbers To subtract a mixed number from a whole number, convert one unit of the minuend into an improper fraction with the same denominator as the fraction in the subtrahend thus reducing the whole number in the minuend by one. The subtract. Example:  

25. Word Problems The Fernando family decided to hike to Dream Lake, approximately miles away. After an hour the lake was still miles away. How far did the group hike so far ?  

26. Try This Efren has started his small business by buying a small lot where he will raise pigs for a piggery that he envisions can supply the local market with meat and at the same time sell the piglets for those who would want to raise them as well as sell pigs for lechon . The total area of the lot he bought is 330 square meters. Efren used of the total area for pigs’ pen and of the lot for the little cabin of the helpers. What part of the total lot was left as the free space? What is the area used for the pigs’ pen and the area used for the helpers’ cabin? What is the area of the free space?  

27. Multiplication of Fraction Lesson Objectives: Multiply fraction by another fraction Multiply fraction by a whole number Multiply whole number by a mixed number Multiply mixed number by a mixed number Apply the knowledge of multiplication of fractions, mixed numbers, and whole numbers in solving business problems.

28. Multiplication of Fractions Steps: Change the mixed number (if any) to an improper fraction. Before you multiply, cross cancel (reduce the numerator of one fraction with the denominator of another fraction by dividing both by their GCF). Multiply the numerators, and then multiply the denominators. Convert the result (if improper fraction) to a mixed number. Reduce your answer in its simplest or lowest term

29. Example 1 Multiply the following fractions 3  

30. Example 2: Suppose your class was collecting money for your community extension activity. If of the class donated money and only of those who donated promised to serve voluntarily during the said activity, what part of the class promised to serve voluntarily during the said activity?  

31. Example 3 Your bakeshop received an order for two cakes. A recipe for a cake specifies cups of cake flour and cup butter. How much flour should you buy? How much butter?  

32. Example 4 The agreed capital of the partnership of Jasper, Irene and Alwin was P100, 000. They agreed that Jasper will contribute of the capital ; Irene ; and Alwin the remaining capital. What will be the capital contribution of each partner?  

33. Example 5 Audrey needs 95 kg. of potatoes. She buys 12 bags, and it is composed of 10 kg and 5 kg bags. How many 10 kg and 5 kg bags are there? What part of the 95 kg of potatoes are 5 kg bags? 10 kg bags?

34. Division of Fractions Objectives At the end of the lesson, the students should be able to Apply the concept of reciprocals by another fraction Divide fraction by another fraction Divide whole number by fractions Divide mixed numbers by mixed number Apply the knowledge of division to business problems.

35. Division of Fractions To divide two fractions, follow these steps: Change the mixed number (if any) to an improper fraction. Change the division sign to multiplication sign. Get the reciprocal of the divisor by interchanging its numerator and denominator. If possible, cross cancel before multiplying. Multiply the numerators, and then multiply the denominators. Convert the result (if improper fraction) to a mixed number. Reduce answer in its simplest or lowest term

36. Example 1: Divide the following fractions:  

37. Example 2: Your inventory shows that your warehouse has m of a certain fabric. You instructed your worker to cut the fabric into pieces of m each. How many pieces of m fabric would you have?  

38. Example 3: You bought a sack of fertilizer weighing 50 kilograms (kg). You were informed by a farm tenant that he needs kg of fertilizer for every 3 fruit-bearing trees on his farm. How many packs of kg fertilizer can you make out of a sack of 50 kg of fertilizer? How many fruit-bearing trees will be fertilized by the sack of fertilizer that you bought?  

39. Example 4 Amys ’ meat shop sells of 100 kgs. of pork each day. How many days it will take for Amy to sell 500 kgs.?  

40. Assessment A. Direction: Solve for the Indicated operation. 6. 7. 8. 9. 10.  

41. B. Solve the following problems: You got 20 items correctly in a 50-item test. What part of the test did you answer correctly? What part of the test did you not answer correctly? Forty-eight ABM students were included in the entrance interview for college. Three-fourths of them decided to take Accountancy. If of the remaining students opted for Entrepreneurship and the rest will take management courses in college, how many students will take each course?