Success step english 4

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– CBEST MINI-COURSE – 13 5 1 improper fractions before multiplying. With 6 2 , 7 − 66 multiply the denominator, 2, by the whole number, 6, 7 to get 12, then add the numerator, 1, for a total of 13. 1. Notice the common denominator Place 13 over the original denominator, 2. The result is 13 of the fractions: 7 2. 2. Add that number to the numerator of the top fraction: 5 + 7 = 12 13 − 1 = 12 3. Subtract one from the top integer: HOT TIP When you’re working with two fractions where the 4. Subtract as usual: 12 172 numerator of one fraction can be divided by the same −6 6 number as the denominator of the other fraction, you can 7 reduce even before you multiply: 66 61 × 51 = 13 16 7 × 2 3 2 3 Divide both the 2 and the 16 by 2: HOT TIP 16 8 104 2 13 When adding or subtracting fractions, you can use the × =3= 34 3 12 3 laser beam method. 1. First change to improper fractions, then multiply crosswise: When multiplying or dividing a fraction and an 18 7 3 3 1 1 + = 6 6 7 7 integer, place the integer over 1 and proceed as if it were a fraction. 2. Next, multiply the denominators: 6 × 7 = 42 3. Add or subtract the top numbers as appropriate and 1 13 1 13 = 61 13 × × place them over the multiplied denominator to get your = = 2 1 2 2 2 answer: 7 + 18 = 25 25 Choosing an Answer 42 When you come up with an answer where the numer- ator is more than the denominator, the answer may be M ultiplying and Dividing Fractions given in that form, as an improper fraction. But if the When multiplying fractions, simply multiply the answers are mixed numbers, divide the denominator numerators and then multiply the denominators: into the numerator. Any remainder is placed over the original denominator. In the case of 208 , 208 divided 5 7 35 × 6 = by 6 is 34 with a remainder of 4 yielding 34 4 . This 6 8 48 6 answer probably will not be there, so reduce 4 to 2 . If When dividing, turn the second fraction upside- 6 3 208 2 6 is not an answer choice, 34 3 probably will be. But down, then multiply across: don’t worry about having to choose between these two answers. Since they signify the same amount, the test 1 2 1 3 3 ÷ × is the same as = 2 3 2 2 4 would not be valid if both 208 and 34 2 were there 6 3 unless the question speciﬁcally asked for a fully When working with problems that involve mixed reduced answer. numbers such as 6 1 × 5 1 , change the numbers to 2 3 103
– CBEST MINI-COURSE – Practice It’s a good idea to put them on ﬂash cards for memorization. Have you improved your skills with fractions? Try these for practice: Common Measurements 51 42 61 1. You will be asked to ﬁgure problems using measure- + + = 2 3 6 ments of length, weight, and volume as well as speed, 2. 3 161 × 1 319 = time, and temperature. Here are the common meas- urements you may be asked to use. Knowledge of the 3. 5 3 − 2 1 = metric system was not on the CBEST when this book 4 2 went to print. 4. 8 1 − 2 5 = 8 8 Weight Measurements 5. A recipe called for 2 3 cups of ﬂour. Jessica 4 Weight measurements are usually measured on a scale. wanted to triple the recipe. How much ﬂour would she need? 1 pound = 16 ounces a. 7 3 4 1 ton = 2,000 pounds b. 7 7 8 c. 8 1 Liquid and Dry Measurements 4 Liquid and dry measurements are usually made in a d. 8 1 2 measuring spoon, cup, or larger container. Think of e. 8 3 4 the dairy department of your grocery store. Units smaller than a cup probably will not be on the test. Answers 1. 16 1 . The common denominator is 6 or 12. 3 1 cup = 8 ounces 40 3 171 2. 11 or 1 pint = 2 cups = 16 ounces 31 3. 1 quart = 2 pints 4 51 4. 1 quart = 4 cups = 32 ounces 2 1 3 2 gallon = 2 quarts 5. Jessica needs to multiply 2 4 cups of ﬂour times 3. 1 23 × 3 = 11 3 33 = 81 × gallon = 4 pints = 8 cups = 2 4 4 1 4 4 1 gallon = 64 ounces 2 For more practice, look at some of the books in 1 gallon = 2 half gallons the “More Help” section. 1 gallon = 16 cups = 4 quarts 1 gallon = 128 ounces M ath 5: Measurement, Distance Perimeter, and Area Distance is measured by rulers or tape measures. Miles are measured by odometers. There are certain numbers, formulas, and measure- ments, such as decimal equivalents, area formulas, and 1 foot = 12 inches weight conversions that you will be expected to have at 1 yard = 3 feet your ﬁngertips when working some CBEST problems. 1 yard = 36 inches 104
– CBEST MINI-COURSE – Sample Measurement Question 1 mile = 5,280 feet 1. Samuel, a friend of yours, has an uncle in the 1 mile = 1,760 yards wholesale fertilizer business. “And I don’t even Square and Cubic Measurements have a garden,” he remarked to you one day. The Here are some conversions you should know. You two of you decide to make a garden in a 21 feet won’t need to know any of the larger numbers on the by 25 feet patch in his back yard. You suggest he CBEST. For example, you won’t need to memorize put 4 inches of his uncle’s fertilizer on the top 1,728—just be able to ﬁgure it out if you need it. and then dig it in. He asks you to help him decide how much to order. Try to solve your 1 square foot = 144 square inches friend’s problem in cubic feet and write down 1 cubic foot = 12 × 12 × 12 inches your answer. or 1,728 cubic inches You give Samuel your answer and he calls his 1 yard = 3 feet uncle. His uncle is most obliging, but insists that 1 square yard = 9 square feet since he’s a wholesale dealer, he can only accom- 1 cubic yard = 27 cubic feet modate orders in cubic yards. He also warns Samuel that his fertilizer does not smell very Temperature good, and needs to be dug in right away. You re- Temperature is measured by a thermometer in degrees. ﬁgure your calculation in terms up cubic yards. The only tricky thing here is to know that the differ- You ﬁnally come up with a ﬁgure and Samuel ence between 40 below 0 and 65 above 0 is not 25, but calls his uncle. What is the amount he orders? 105. If you can’t visualize the distance between 40 a. 9,600 cubic yards below and 65 above 0, a rereading of Math Lesson 2 on b. 58.3 cubic yards negative numbers might help. c. 19.4 cubic yards d. 6.5 cubic yards Speed e. none of these Speed is usually measured by speedometers in miles per hour. Time, distance, and rate problems are dis- Answer cussed in Math Lesson 7. Look for your answer below and read to discover the exciting conclusion. Time Time is measured by a clock or by a calendar. You can a. 9,600 cubic yards. Suddenly, it grows dark. You try ﬁgure out the number of seconds in an hour (3,600) by looking out the window, but fertilizer is stacked multiplying 60 seconds by 60 minutes. up against the window as high as you can see. You can’t even get out of your house. You changed 1 minute = 60 seconds everything to inches and divided by 36 because 1 hour = 60 minutes = 3,600 seconds there are 36 inches in a yard, so how could you 1 day = 24 hours = 1,440 minutes have been wrong? 1 week = 7 days = 168 hours b. 58.3 cubic yards. Suddenly, it grows dark. Your 1 year = 12 months = 52 weeks = 365 days windows are covered with fertilizer. Fertilizer is 105
– CBEST MINI-COURSE – piled to the roof and the garden is buried. You changed inches to feet and divided by 3, so where did you go wrong? c. 19.4 cubic yards. There is a pile of fertilizer about three feet high covering your garden. This is more than you expected so you pile it up and give it to your neighbors. You were clued into the cube idea and divided by 9, so why didn’t you get it right? d. 6.5 cubic yards. You spread exactly 4 inches on top of the garden with a rake. Quickly, you and Practice Samuel dig the fertilizer under. You feel proud Try your hand at some additional measurement that you could get the right answer to a compli- problems. cated math problem. e. You couldn’t ﬁnd your answer so you redo your 2. Casey bought 3 lbs. 5 oz. of boneless chicken at math. You choose the closest answer. $1.60 per pound. How much did she pay? a. $0.50 In this volume problem, three dimensions need b. $4.80 to be multiplied to get a cubic measurement, but they c. $5.30 need to be in the same units of measurement. You can’t d. $8.80 multiply 21 feet by 4 inches. In this case, it is easiest to e. $12.00 change the 4 inches into feet. Four inches is 1 of a foot 3 and 1 of 21 is 7, times 25 is 175, the answer to the ﬁrst 3. Frank cut 2′8′′ off a 6′3′′ board. How much was 3 part of the question. Now that you’re working in cubic left? feet, you need to convert to cubic yards. a. 3′5′′ Suppose you had a square with sides of one yard b. 4′5′′ each. Since there are 3 feet in a yard, a square yard c. 3′7′′ d. 4′7′′ would include 9 square feet. e. cannot be determined 4. Eight scouts each need two 3′ dowels for some banners they are making. Before being cut, the dowels are 10 feet long. How many dowels should the scoutmaster buy? a. 2 b. 3 c. 4 d. 5 Now suppose you made your square into a cube. e. 6 You would have 3 layers of 9, or 27 square feet. So since you need 175 cubic feet of fertilizer, you should divide by 27 cubic feet: 175 ÷ 27 ≈ 6.5 cubic yards. 106
– CBEST MINI-COURSE – 5. Three full containers each held one of the fol- Answers 2. This problem can be solved at least two ways. You lowing amounts: one ounce, one cup, and one can turn the ounces into 156 of a pound and mul- quart. If all three containers were dumped into a tiply 1.60 × 3 156 . Alternately, you can multiply gallon jar, how much room would be left? 1.60 by 3, then multiply 1.60 by 156 and add the 9 a. 2 16 pints two together. Choice c is the answer. 5 176 pints b. 3. When subtracting 8 inches from 3 inches, borrow 6 156 pints c. one foot from the 6 feet. Add 12 inches to the 3 9 15 pints d. inches to get 15′′. 15 − 8 = 7 and 5 − 2 is 3. The 16 14 15 pints e. answer is c. 16 4. The trick here is to realize that the 10’ dowels are 6. A strip of wallpaper 5 yards long measured 5 really only good for 9’ since the scouts need 3’ inches wide. How many square feet of wallpaper pieces. The scouts need a total of 48’: 8 × 2 × 3 = were there? 48. Five dowels would only be good for 45’, but six a. 6.25 dowels would provide more than enough (54’). b. 8.3 The answer is e. c. 60 5. There are 128 ounces in a gallon. 128 − 1 oz. = d. 12.4 127. 127 − 8 oz. (1 cup) = 119 oz. 119 − 32 oz. e. 19.7 (1 qt.) = 87 oz. There are 16 ounces in 1 pint, so 87 7 16 = 5 16 pt. The correct answer is b. 7. Cooking a turkey takes 20 minutes for every 6. The easiest way to do this one is to change every- pound in an oven heated to 350 degrees. If a thing to feet to begin with. 5 yards is 15 feet × 152 turkey weighing 20 pounds has to be ready by 2:00 P.M., at the latest, when should the turkey be = 6.25. The answer is a. 7. Multiply 20 × 20 to get the total time. Convert the put in the pre-heated oven? a. 6:20 A.M. answer, 400, from minutes to hours by dividing by b. 6:40 A.M. 60, to get 6 2 , or 6 hours, 40 minutes. From noon 3 c. 7:00 A.M. to 2 p.m. is 2 hours. Subtract the remaining 4 d. 7:20 A.M. hours and 40 minutes from 12 noon; think of 12 e. 7:40 A.M. noon as 11 plus 60 minutes. 11:60 − 4:40 = 7:20 A.M. HOT TIP Perimeter and Area Formulas On the CBEST, there is usually one question that goes Rectangle something like this: Area: length times width (A = lw). One side times A school of 240 children want to go on a ﬁeld trip. A bus can hold 50 children. How many buses are needed? the other side tells you how many ﬁt inside. 4 Among the answers are 4, 4 5 , and 5. Four buses would Perimeter: 2 length + 2 width (2l + 2w). To meas- 4 not be enough. There is no such thing as 5 of a bus. So ure all the way around something rectangular, 5 is the answer. you need to include 2 lengths and 2 widths— that’s all four sides. 107
– CBEST MINI-COURSE – Square you don’t have to worry about converting it to a num- ber. But if π is not found in the answers, and the ques- Measuring the area and perimeter of a square is basi- tion calls for an approximate answer, substitute 3 for π. cally the same as a rectangle, only the length and width The question may tell you to use 272 or 3.14. are the same measurement. Area: πr2. Square the radius and look at the answers. Area: side × side If π is not found in the answers, multiply by 3. In Perimeter: side × 4 the example above, A = π42 or 16π. Circumference: 2πr. Circumference is to a circle what Triangle perimeter is to a rectangle. Multiply the radius by Remember that a triangle is half a rectangle. 2 and look for the answers. If π is not in the Area: 1 b × h. Multiply the height and the base. answer choices, multiply by 3. In the example 2 above, the circumference is 2π4, or 8π. Since the triangle is half, divide by two. Note: The height of a triangle is not always one of the Other Areas sides. For example, in triangle ABC which fol- Cut the ﬁgure into pieces, ﬁnd the area of each, and lows, side AB is not the height, BD is the height. AC is the base. To ﬁnd the area, ignore all the add. If you’re asked to ﬁnd the area of a ﬁgure with a numbers but the base and the height. The base piece cut out of it, ﬁnd the area of the whole ﬁgure, can be found by adding 4 and 8: 4 + 8 = 12. The ﬁnd the area of the piece, and subtract. height is 5. 1 × 5 × 12 = 620 or 30. 2 Other Perimeters For any perimeter, just add the outside lengths all the way around. Practice 8. Find the area of a circle with a diameter of 6. Perimeter: Add the sides all around: 12 + 6 + 9 = 27 a. 36π b. 24π Circle c. 16π d. 9π e. 6π The diameter of a circle goes from one point on the circle, through the middle, and all the way across to another point on the circle. The radius (r) is half of the diameter. When working with π, consider the follow- ing: The symbol π is usually found in the answers so 108