15 (See Example E later in this lab)

Transcription

1 Tallahassee Community College APPLICATIONS OF ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION In an earlier chapter, you learned some of the basics of working with applications. Many of the prior applications will be similar to these -- you'll just use the rules for fractions after you "set up" the problem! Two new things to look for are:. "A fraction of a number." This translates to the "fraction the number." EXAMPLE: of 0 means: 0 Now use the rule: 0 5 (See Example E later in this lab) (Review the meaning of a fraction in your text.). 5,, represent all of something. This value of "all of 5 something" is. (See Example D in this lab) Be sure that you really understand what happens in addition, subtraction, multiplication and division. Know how these operations are related. Then read the problem very carefully. Think about the situation and plan your strategy. What operation is implied? (There may be two or more operations!) What numbers do you know? What are you looking for? Can you estimate a reasonable answer? Translate the words into an arithmetic problem. Work it carefully. THINK about your answer. It should seem reasonable. It helps to draw a picture of the situation. EXAMPLES:

2 A. Shelves are cut from a foot board. How many ft. shelves can be cut? Will there be a left over part; if so, how big is it? METHOD I: Draw it. See each step as you "cut"! st cut nd 5 cut rd cut ft ft 5 ft = 5 = - = (st shelf) - (nd shelf) - = (rd shelf) ft. 5 ft. ft. extra ANSWER: There will be three shelves ft. long. The left over piece is ft. METHOD II: We want to know how many 's are in. We can divide by.

3 Now interpret the answer. The whole number tells how many full ft. shelves we can cut. The fraction means we can also get of shelf. To figure the extra length use of one shelf. of shelf (one shelf is ft.) of shelf (one shelf is ½ ft.) = ft. extra Be sure you understand that the quotient did NOT mean shelves and ft. left over. It's shelves which is shelves and of a shelf. METHOD III: This problem may bring to mind the concept Size of shelf No. of Shelves = Total Board? = (Now fill in what you know) When you don't know one of the factors, you divide the product by the known factor.

4 Now proceed as you did in METHOD II! OR using algebra, this is n n = n = n = n = Not all problems have this many ways to solve them! Common sense must be used. B. Find the missing dimension.? 0 in. in. The unknown length + 0 in. = in. + 0 in. = in. When we are missing an addend, we subtract the given addend from the total.

5 The missing length is 5 in. OR using algebra: 0 = = = 0 = 0 5 in. n + 0 = n = - 0 n = 5 The work for this is done above. C. A student has a part time job that pays $ an hour. The student worked hrs. on Monday, hrs. on Tuesday, hrs. on Friday, and hrs. on Saturday. Find how much he earned. Plan your strategy: Total earned = Hours worked $ for each hour FIRST: Add all hours THEN: Multiply by. (Be sure to include units in your answer) 5

6 + = = = 9 = = hrs. hrs. 9 9 = $ In an upcoming chapter, you'll learn to use decimals. This is approximately $.. If you divide 9 with your calculator, your answer is... This was rounded to the nearest cent. D. Max wrote of his paper last weekend and 5 of it Tuesday. Has he written all of the paper? If not, how much more of the paper must he write? + = Total written = This is less than, so the whole paper has not been written. (The whole paper is or. See page of this lab.) = 5 5 =? unwritten = Has not - = been written written written written E. In Example D, suppose the paper had to be 000 words. How many words

7 must still be written? You know: of the paper must be written This means: 000 words =? words 000 = 00 words 00 words must be written. (You can also see that or 000 would tell how many words have been written.) SOLVE: Be sure your answers seem reasonable. Ask for help if you get stuck--but try these on your own first.. John weighed 9 pounds before going on a diet. The first month he lost lbs. and the second month he lost the end of the second month. lbs. Find John's weight at. The total value of a house and lot is $0,000. The value of the lot is of this total value. Find the value of the lot. Find the value of the house..,500 people attended a high school football game. The stadium was full. What was the capacity of the stadium? (THINK: should the answer be more or

8 less than 00?). A developer bought acres of land for $00 an acre. How much did the land cost? 5. The developer set aside acres of his acres for a park and sold the rest. How many acres were left to sell?. How many acre lots can be developed with acres of land? (HINT: Find how many 's are in.). a. A developer sold his acre lots for $,000 each. Find the total selling price of lots. ($000 is the cost of lot.). b. Use your answers in # and in #a to find his profit on this land.(of course the developer had other expenses that we aren't considering!)

9 . Sarah kept a record of the gas used on a recent trip. She purchased the following amounts. gal., 0 gal., 9 5 gal. and gal. Find the total amount of gas she bought on the trip. 9. The Johnsons have a monthly income of $00. Their monthly house payments can be 5 of their monthly income. How much can they spend on house payments each month? 0. How many ft. shelves can be cut from a ft. board? What size will be left? ANSWERS: One way:. lb. Find 9 - ( + ) ADD FIRST!. $5,000 lot of 0,000 = lot's value $,000 house either 0,000-5,000 or 5 0,000 = value of house 9

10 capacity > capacity of capacity = 00? = 00 so 00 = capacity One way:. $9,900 $00 is ¾ acres for lots -. lots. a. $0,000 $,000 b. $9,00 profit 0,000-9, gal. of gas $5 monthly house payment shelves that are full shelves) 0

11 ft. each ( ft. left over) then = size of left over board You should continue to work on the applications in your text Ask tutors or your instructor to help you. Let this be the semester you learn to apply your math skills. After all, that's why you're learning to add, subtract, multiply and divide. You will use this!