Business Math Reviewer.pdf

Republic of the Philippines Department of Education REGION III - CENTRAL LUZON SCHOOLS DIVISION OF SAN JOSE DEL MONTE CITY SAPANG PALAY NATIONAL HIGH SCHOOL...

Republic of the Philippines Department of Education REGION III - CENTRAL LUZON SCHOOLS DIVISION OF SAN JOSE DEL MONTE CITY SAPANG PALAY NATIONAL HIGH SCHOOL Business Math 1st Quarter Reviewer Table of Contents 1. Fractions 2. Addition and Subtraction of Fractions 3. Multiplication and Division of Fractions 4. Decimals 5. Form Transformations 6. Real-life Problems Involving Fractions and Decimals 7. Ratio 8. Proportion 9. Direct and Inverse Proportion 10. Partitive Proportion 11. Mark-Up, Mark-On, and Mark-Down 12. Discount 13. Break-Even  1 Lesson 1: Fractions Fraction is a ratio of two integers in the form of a/b where b≠0. It is one or more of the equal parts into which a whole is divided “part of a whole”. This fraction is formally read as “one-half” but can also be read as “one over two”. There are two types of fraction, namely Proper Fraction and Improper Fraction. Proper Fraction is when the numerator is less than its denominator. Improper Fraction is when the numerator is greater than its denominator. And under improper fraction, Mixed Numbers is when a proper fraction has a whole number beside it. When the numerator is equal to its denominator, it is always equal to 1.  2 Lesson 2.1: Addition of Fractions If the denominators are the same, proceed. But if they are not the same, do the butterfly method. Remember that c≠0. If it’s a mixed number (there is a whole number), add them separately from the fraction. Or you can make it an improper fraction. Lesson 2.2: Subtraction of Fractions Same with addition. If the denominators are the same, proceed. But if they are not the same, do the butterfly method. Remember that c≠0. If it’s a mixed number (there is a whole number), subtract them separately from the fraction. Or you can make it an improper fraction.  3 Lesson 3.1: Multiplication of Fractions You can make this easier by canceling. This can be done only if a numerator and a denominator are divisible by the same number. Remember that b≠0 and d≠0. If you’re given a whole number, remember that it always has a denominator 1. Lesson 3.2: Division of Fractions In dividing fractions, reciprocate the divisor (right side of the division symbol) first. In doing so, your denominator will be your new numerator and your numerator will be your new denominator. Then, change the operation into multiplication. Remember that c≠0 and d≠0.  4 Lesson 4: Decimals Decimals are fractions with a denominator of 10, 100, 1000, or any multiple/power of 10. Lesson 4.1: Addition and Subtraction of Decimals In adding and subtracting decimals, you must align the decimals before you proceed to solve/perform the operation. Once you get an answer, place the decimal aligned with the other decimals. Lesson 4.2: Multiplication of Decimals In multiplying decimals, you must align the numbers to the right. Ignore the decimals and proceed to solve/perform the operation. Once you get an answer, count how many numbers are on the left side of both decimals then add. That’s how many times you are going to count from the right going to the left in order for you to know where to properly place the decimal.  5 Lesson 4.3: Division of Decimals For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division. Let us understand the conditions and rules for using this method using an example. Example: Divide 48.65 ÷ 3.5 Solution: In this division, the dividend and the divisor are decimals, so we need to convert the divisor to a whole number using the following steps. Step 1: the dividend is 48.65 and the divisor is 3.5. We need to change the divisor to a whole number and so we will multiply it by 10 so that the decimal point shifts to the right and it becomes a whole number. This means, 3.5 x 10= 35. Step 2: We need to treat the dividend in the same way as we had treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 48.65 × 10 = 486.5. In other words, we need to move both the decimal points to the right until the divisor becomes a whole number. Step 3: Now, we have 486.5 as the dividend and 35 as the divisor. This can be divided as we do the usual division and we get 13.9 as the quotient.  6 Lesson 5: Form-Transformation Fraction Convert Fraction to a Decimal Divide the numerator by the denominator. Convert Fraction to Percent Convert the fraction first to a decimal, then move the decimal point 2 places to the right and the % symbol. Decimal Convert Decimal to a Fraction Read the decimal and reduce the resulting fraction. Convert Decimal to Percent Move the decimal point 2 places to the right and add the % symbol. Percent Convert Percent to a Decimal Move the decimal point 2 places to the left and remove the % symbol. Convert Percent to a Fraction Remove the % sign and write the number “over" 100. Lowest term, if possible.  7 Lesson 6: Real-Life Problems Involving Fractions and Decimals Fractions Example: Jose worked in the hardware 8½ hours while Pepe worked 8¾ hours. How many hours did the two work? Solution: 8½ + 8¾ Add the two whole number then set aside. 8+8=16 Add the two fraction. ½+¾ (Dissimilar fraction means you can use butterfly method or determine the LCD and divide it by the denominator and multiply to the numerator.) ½+¾= 4+6/8= 10/8 If improper fraction convert it into mixed numbers. 10/8= 1 2/8= 1 ¼ (Lowest term if possible) Add the whole number and the fraction. 16+ 1 ¼ = 17 ¼ Answer: 17 ¼ hours  8 Decimals Example: If your total bill is ₱176.75, how much of it is the VAT? Multiply ₱176.75 to VAT which is equivalent to 12%. 176.75 12% =21.21 Answer: ₱21.21 is the VAT Lesson 7: Ratio Ratio- it is the comparison of two quantities. The numerator is called antecedent and the denominator is called consequent. There are 2 terms in ratio. Three types of Notation in Ratio Odds Notation- where the symbol “:" is reads as " is to” (a:b). Fractional Notation- b≠0 (a/b). Division Notation- (a÷b) Rate- it is the ratio that compares quantities of different units. When the rate has a denominator of 1, it is called a unit rate.  9 Lesson 8: Proportion Proportion- is a way of expressing the comparative relationship between a part, share, or portion with regards to measurement, amount or number. It is expressed as a relationship between two ratios. The ratios are separated by :: or an equal sign (=). Example: 1:3 = 4:12, which is read as “one is to three equals four is to twelve". There are 4 terms in proportion. The means are the inner numbers or the second and third terms of the proportion. The extremes are the outer numbers or the first and fourth terms of the proportion. In any proportion, the product of the means is equal to the product of the extremes. BC = AD  10 Lesson 8.1: Find the Unknown Whole Numbers 1) 1: 4 = n: 16 Multiply the means and extremes. 4(n)= 4n 1(16)= 16 Equate 4n=16 Divide both side by 4 to isolate n. 4n/4= 16/4 Answer: n=4 2) n: 15 = 1: 5 Multiply the means and extremes. 15(1)= 15 n(5)= 5n Equate 5n=15 Divide both side by 5 to isolate n. 5n/5= 15/5 Answer: n=3  11 Decimals Example: 7: n :: 3.5: 4 Multiply the means and extremes. n(3.5)= 3.5n 7(4)=28 Equate 3.5n= 28 Divide both side by 3.5 to isolate n. 3.5n/3.5= 28/3.5 Answer: n=8 Fractions Example: ¼: 5 :: n: 60 Multiply the means and extremes. 5(n)= 5n ¼(60)= 15 Equate 5n = 15 Divide both side by 5 to isolate n. 5n/5 = 15/5 Answer: n=3  12 Lesson 9: Direct and Inverse Proportion Direct Proportion- increase in one, increase in another; and decrease in one, decrease in another. y=kx (k is constant), y varies directly as x Example of Direct Proportion temperature and heat salary and hours worked electricity consumed and electricity bill Inverse Proportion- increase in one, decrease in another; and decrease in one, increase in another y=kx (k is constant), y varies inversely as x Example of Inverse Proportion speed and travel time workforce and completion time  13 Lesson 10: Partitive Proportion Partitive Proportion- whole is partitioned into two or more equal or unequal parts. Examples: whole pizza into slices water into containers class into groups Lesson 11: Mark-Up, Mark-On, and Mark-Down Mark-Up- is the amount added to the cost price to determine the selling price. Mark-On- is the amount added to the regular selling price. Mark-Down- is the amount subtracted from the selling price to determine the new price. Formulas: Lesson 12: Discount Trade Discount- are reduction from list price, it is typically offered between manufacturer and wholesaler or between wholesaler and retailer. list price- suggested price of an item which was set by the manufacturer/supplier  14 Trade Discount = List Price x Trade Discount Rate Discount Series- (multiple discounts) can be converted to single equivalent discount rate (SEDR), which will give the same total discount as the discount series when taken separately rather than computing it one at a time. Lesson 13: Break-Even Profit- the amount left ehen you subtract all the expenses from the revenue (or sales). Profit = Income - Expense income > expense, there is profit income < expense, there is loss income = expense, there is break-even Break-Even- the break-even point is the volume of sales for which total revenue equals total costs where profit is equal to zero. total revenue = total costs total costs = fixed costs + variable costs