# JUMP Math: Teacher's Manual for the Fractions Unit

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6 page Section F-: Naming Explain how to represent a fraction. Step 1: Count the number of shaded regions 8 Step : Count the number of pieces the pie is cut into Remember, each step should be taught separately (allowing for repetition) unless your student is very quick. Here are some questions your student can try. What fraction of each figure is shaded? Teach your student how to draw 1 and 1 with circles. Teach them how to draw 1 as follows: Ask your student how they would draw 1 and 1 in a square box. Make sure they know that in drawing a fraction, you have to make all the pieces the same size. For instance, the following is not a good example of 1 :

7 page 7 Your student should be able to recognize when a shaded piece of pie is less than 1 of a pie. To see that the fraction is less than 1, continue one of the lines. Section F-: Adding Two With the Same Denominator Rule: Add the numerator and leave the denominator the same. For example, 1 + = 1 piece plus pieces gives pieces Make sure your student knows why the denominator does not change: the pie is still cut into pieces you are still adding up 1 size pieces. Allow for lots of practice. Only introduce one step at a time. Whenever possible, you should allow the student to figure out how to extend a concept to a case they haven t seen. This is easy to do with the addition of fractions. Ask your student what they might do if: There were three fractions with the same denominator? =?

9 page 9 + = Draw the above picture, and ask your student to write the new fractions corresponding to the way pies are now cut. Make sure they notice that 1 is the same as of the pie, and that 1 is the same as (and one out of three pieces is the same as two out of six). Once you have discussed this, your student can perform the addition. The one thing the student should take away from this explanation is that to produce pieces of the same size in both pies (which is necessary for adding fractions), one has to cut each pie into smaller pieces. (For more advanced students: the number of pieces you need to cut both pies into is equal to the lowest common multiple of the denominators see Section F-9). Tell your student you will now teach them a very easy way of changing the number of pieces the pie is cut into without having to draw the picture. Step 1: Multiply each denominator by the other one. The numerator also has to be multiplied, because now you are getting more pieces: x x x x Have your student practise this step before you go on. The student should just practise setting the right numbers in the right places. Remember you can make this step easier if necessary by having the student move one denominator at a time. Step : Perform the multiplication. x x = + x x Practise Step 1, then Step 1 and Step together, before you go on. Step : Perform the addition. + = Now have the student practise all three steps.

10 page 10 For students who know higher times tables, gradually mix in higher denominators like and 7 (make sure the smaller denominator does not divide the larger). NOTE: Two numbers are relatively prime if their least-common multiple (the lowest number they both divide into evenly) is their product. For instance, and are relatively prime but and are not (since the product of and is, while their least common multiple is 1). The method of adding fractions taught in this section is only really efficient for fractions whose denominators are relatively prime (as is the case for all of the examples directly above). For other cases, for instance when one denominator divides into the other or when both denominators divide into a number that is smaller than their product, more efficient methods can be found in sections F- and F-9. Section F-: Changing One Denominator Tell your student that sometimes you don t have to change both denominators (i.e. there s a short-cut) when you add fractions. How can you tell when you can do less work? Step 1: Check to see if the smaller denominator divides into the larger. Count up on your fingers by the smaller denominator and see if you hit the larger denominator if you do, the number of fingers you have up is what you multiply the smaller denominator by: = x x 10 Counting up by twos you hit 10. You have fingers up. This means x = 10 Multiply the smaller denominator by the number of fingers you have up Give lots of practice at this step before you move on. Step : Perform the multiplication. x = + 1 x Step : Perform the addition. + 1 =

13 page 1 For instance, with 1 of a pie and of a pie you get the same amount of pie. Each fraction has a representation in the smallest possible whole numbers. Finding this representation is called reducing the fraction. To check whether a fraction can be represented with smaller numbers, your student should first check if the numerator divides into the denominator. Step 1: Count up by the numerator to see if it divides into the denominator 1 Step : If yes, divide both the numerator and the denominator of the fraction by the numerator: = 1 1 Some students will need a good deal of practice with step 1. You might give your student a sheet of questions on which they simply have to count up by the numerator, checking to see if they say the denominator as they count. Once your student has mastered the steps above, let them know that if the numerator of a fraction does not divide the denominator, they should still check to see if any smaller number divides both. If they find a number that goes into the numerator and the denominator, they should reduce the fraction as follows: = You might start by giving your student hints. You might say, for instance, The numerator and denominator of this fraction either divide by or by. Check which one works. Here are some sample questions you can use during this lesson: Division: = 1 = 8 = 1 = 1 = = 10 = 0 =

14 page 1 Reducing fractions (easier): = = = = = = Reducing fractions (harder): = = 8 = 8 = = 9 = Note: If your student has just learned to multiply, only ask them to reduce fractions where the numerator and denominator divide by, or. You should give them the same questions repeatedly for homework as it may take them some time to get used to reducing. Section F-9: Finding the Lowest Common Denominator (This section should only be taught to second year JUMP students or to very advanced first years.) The lowest common multiple (LCM) of two numbers is the lowest number that both divide into evenly. For instance, the lowest common multiple of and is 1. Notice that the lowest common multiple of and is lower than their product ( x = ). But with other numbers, say and, the lowest common multiple is the product. To find the lowest common multiple of a pair of numbers, simply count up by the larger number and keep checking if the smaller divides into the result. Example: and. Count up by sixes. does not go into. Keep counting up. 1 goes into 1. Therefore, LCM = 1 Example: and. Count up by threes. does not go into. Keep counting up. goes into. Therefore, LCM = Example: and 10. Count up by tens. 10 goes into 10. Therefore, LCM = 10 By counting up, have your student find the LCM of the following pairs. Also have them say whether the LCM is equal to the product, or less than the product. and and 8 and

15 page 1 and 10 and 10 and 9 and 10 and and and 8 8 and 10 and 7 The method of adding fractions we taught in sections F- to F- doesn t always yield a final denominator that is the LCM of the two denominators; by our method the student would add 1 both fractions as follows: and x x + 10 x x 10 can be reduced (see Section F-8) to 1 by changing If the student thinks that the LCM of a pair of denominators may be lower than the product, then (to avoid having to reduce the answer) they should proceed as follows: To find the LCM, count up by the larger denominator (in this case ) until you reach a number that the smaller denominator divides into. Counting by sixes you get 1, and you can stop counting there because divides into 1, so the student can use 1 as the denominator: x x + x x Make sure your student knows the LCM is also called the lowest common denominator. Your student should try these questions: This method will also work for triple fractions Tell the student to count up by the larger denominator, and at each stage check if the smaller denominators divide the number you have reached. For instance: two 10s are 0, but does not divide 0, so the student should keep counting by tens. Three 10s are 0, and and both divide 0, so the student should use 0 as the denominator. Here are some sample (Grade 8 level) questions you can use during this lesson: (1) () ()

16 page 1 Section F-10: Mixed and Improper If the numerator of a fraction is bigger than the denominator, the fraction is called an improper fraction. Any improper fraction can also be written as a mixed fraction, that is, as a combination of a whole number and a fraction. For instance: = 1 1 You can explain these two ways of writing a fraction with a picture. or 1 1 Three half-size pieces of a pie are the same as one whole pie, plus an extra half. How to write a fraction as an improper fraction: Example: 7 Step 1: How many pieces are shaded? Answer: 7. Put this number in the numerator. Step : How many pieces is each pie cut into? Answer:. Put this number in the denominator. (Even though you have more than one pie, the piece size doesn t change you still have third-size pieces in each pie 7 altogether.) How to write a fraction as a mixed fraction: Example: 1

17 page 17 Step 1: How many whole pies are there? Answer:. Write this down as a whole number. Step : Write down what fraction of a pie you have in the last pie. Give your student lots of practice in the two ways of writing a fraction. Here are some examples you might use: 11 or or or 1 Your student should be able to draw simple, mixed fractions like 1 1, 1, 1 1, 1, 1 1, 1. Your student should also be able to decide, in simple cases, which of two mixed fractions is larger. For instance: 1 or or 1 1 or 1 1 Your student should be able to explain how they can tell when a fraction represents more than a whole pie: i.e. they should be able to say when the top (or numerator) is larger than the bottom (or denominator) you have more than one pie. As a test, write out several fractions and ask your student to identify the fractions that represent more than one whole pie. For instance, 7 1

18 page 18 IMPORTANT NOTE: GRADE & TEACHERS STOP HERE!! If you are a Grade - classroom teacher participating in the JUMP In-Class program, you are only expected to teach up to section F-10. When you are sure your students understand the material in Sections F-1 to F10 you can give them the Pre-Test for Workbooks and, and then the Test for Workbooks and. Grade - teachers should complete the entire unit and give the Pre and Actual Tests for Workbooks and. (All tests are included at the end of this Manual) Section F-11: Converting (Without Pictures) Converting mixed fractions into improper fractions: Example: Step : + 1 = 7 1 = 7 Step Step x Step 1: Multiply the whole number by the denominator (i.e. x = ). To explain this step, point out that in the two whole pies (each cut into three pieces), there are six pieces. Step : Add the number you got in the last step to the numerator. Put the sum in the numerator of your improper fraction. (To explain this step, point out that in the one-third pie you have one piece which has to be added to the six pieces in the two whole pies, giving seven pieces altogether.) Step : Write the denominator of the mixed fraction in the denominator of the improper fraction. (The two fractions have the same denominator because the piece size is still one-third.) Here are some sample questions you can use during this lesson: 1 = 1 = 1 = 1 = = 1 1 = 1 = = = = = 1 = Section F-1: Converting Converting improper fractions into mixed fractions. First, you may have to teach your student how to divide when the divisor doesn t go evenly into the number being divided:

19 page 19 Example: 9 Step 1: Count up on your fingers by the divisor (i.e., ) until you reach a number just below the number being divided (i.e., 9). 8 Stop here If the student has trouble knowing when they should stop counting up, practise this step with various examples: If your student is really struggling with this step, write the numbers from 1 to 10 and circle the numbers divisible by. This will help your student see when to stop counting. Repeat this with the numbers between 1 and 1 (for counting by threes) and 1 and (for counting by fives). Step : Write the number of fingers you have up on top of the division sign: 9 Step : Write the number you reached on your fingers below the number being divided: 9 8 Step : Subtract to find the remainder: R Explain that the answer on top means that fits into 9 four times with 1 left over. You might draw a picture to illustrate this: remainder 1 How to convert an improper fraction into a mixed fraction: Step 1: Rewrite the fraction as a division statement: 9 9

20 page 0 Have the student practise putting the right number in the right place. Step : Do the long division. Your student should know how to do this from the previous section: R Step : Use the answer to the division problem to write the mixed fraction: 9 = R 1 After your student has learned to convert improper fractions to mixed fractions, teach them to estimate how many whole pies an improper fraction represents. For instance 7 is at least two whole pies because divides into 7 two times (the remainder, 1, is the number of fractional pieces in the last pie plate). Your student should be able to say, in simple cases, which of two improper fractions is larger. For instance, 7 11 is larger than because in the first case you have at least three whole pies, and in the latter, two. They should also be able to say when an improper fraction is bigger than a whole number. For instance, 7 is bigger than. Finally, your student should know that an improper fraction is always bigger than a proper fraction. You might write out several pairs and have them identify the larger; for instance, / and 7 /. Here are some sample questions you can use during this lesson: = 7 = 7 = 9 = 11 = 9 = 1 = 1 = = 17 = 11 = 17 = Note: Maggie Licata (JUMP s former Executive Director) suggested a method for converting improper fractions to mixed fractions which I think is easier than the one I give above (her method also enables students to do the conversions in their heads). If you use the following method, you should still, at some point, teach your student how to do long division by the method above.

21 page 1 Change 9 to a mixed fraction: Step 1: Count by the denominator until you reach a number just below the number being divided. (This is just step 1, as outlined above) Step : Write the number of fingers you have raised (i.e. four fingers) as a whole number: 9 = Step : Write the numerator of the original fraction beside the whole number: 9 = Step : Multiply the whole number by the denominator: x = 8 Step : Subtract the result of step from the denominator of the improper fraction: 9-8 = 1 Step : The answer from step is the numerator of the mixed fraction: 9 = 1 If your student has trouble with step, teach them to subtract as follows (see also the Appendix): 17-1 =? Step 1: Say the second number ("1") with your fist closed. Step : Raising one finger at a time, count until you reach the first number (i.e. the student raises one finger when they say "1" and another when they say "17"). The number of fingers you have up is the answer. Give your student lots of practice at this. (Eventually you can use fairly large numbers like to boost your student's confidence. Make sure the numbers you pick aren't too widely separated: for numbers that have a difference greater than 10, it is better to subtract by lining the numbers up in the traditional way.)

24 page Section F-1: Word Problems Here are some word problems from a Grade 7 book you could try: 1. Ken ate 8 of a pizza and Nola ate 1. What fraction of the pizza was eaten?. On Monday Mike ran for 1 hour in the morning and 1 hour in the afternoon. What fraction of an hour did Mike run on Monday?. Over one supper hour Carl used 1 of a container of tomatoes, and 1 of a container of olives. How many containers of toppings did he use? Give your students other questions of this sort. NOTE: Your student may now write the Fraction Test. Please use Pre-Test for Workbooks & (page ) as practice and Test for Workbooks & (page 8) as a final test. The Pre-Test & Test for Workbooks & are intended for students in grade or. If your student scores 80% or higher, they can move on. If they don t score 80% or higher, review the material they had trouble with and let them write the test again. (Make sure you let your student know, before you give them the test, that they can write it as many times as they need to.) Let your student know that the material in the test goes up to a Grade -7 level.

25 Name: Date: page F- HW: Adding and Subtracting 1. Name these fractions. Add a) b) + c) d) e) + f) Subtract a) - 1 b) - c) BONUS:

26 Name: Date: page F- HW: Adding and Subtracting 1. Name these fractions a) b) c). Add or Subtract a) b) + c) d) - 1 e) 9 - f) Add or Subtract a) b) c) d) + 1 e) + 1 f) 1 + g) - 1 h) 1-1 I) - 1

27 Name: Date: page 7 F- HW: Adding and Subtracting 1. Add or Subtract (Don t change the denominators) a) 1 + b) + c) d) 7 - e) 11-9 f) Add or Subtract (Change both denominators) a) + 1 b) + 1 c) 1 + d) 1-1 e) + f) - 1. Add or Subtract (Change one denominator) a) b) c) d) + 1 e) + 1 f)

28 Name: Date: F- HW: page 8 1. a) Cut the pie into pieces. b) Cut the pie into pieces. Shade 1/ Shade 1/ Which piece of pie is bigger: 1/ or 1/? Why?. Add or Subtract a) - b) + + c) Add or Subtract (change both the denominators). a) b) + 1 c) 1-1. Add or Subtract (change one denominator). a) b) c) d) + 1 e) - f) Advanced: Add or Subtract (change one denominator or change both ** for each question you have to decide what to do**) a) b) + 1 c)

29 Name: Date: F-8 HW: page 9 1. Add or Subtract: Change one denominator, change both or don t change either. a) 1-1 b) c) d) 1 + e) f) g) h) + i) Reduce a) b) c) d) e) f) g) h) Advanced: Reduce a) b) c) 10 d) e) f) 1 g) 1 h) Add a) b) BONUS: c) d)

30 Name: Date: F-1 HW: Mixed and Improper page 0 1. Add or Subtract: Change one denominator, change both or don t change either. a) b) - 1 c) d) + 1 e) f) Add a) b) =. Change to an improper fraction. a) 1 = b) 1 = c) = d) = e) 1 = f) 1 =. Divide a) 7 b) 9 c) 11 d) 7 e) 8 f). Change to a mixed fraction a) 7 = b) 11 = c) 17 = d) 1 =

31 Name: Date: page 1 PRE-TEST (for Workbooks & ): 1. Name these fractions:. Add or Subtract: Reduce: = = 1 = 0 = 9

32 Name: Date: page PRE-TEST continued (for Workbooks & ):. Name these fractions as mixed fractions:. Name these fractions as improper fractions:. Draw these mixed fractions: Draw these improper fractions: 7

33 Name: Date: page TEST (for Workbooks & ): 1. Name these fractions:. Add or Subtract: Reduce: = = 1 = 0 = 9

34 Name: Date: page TEST continued (for Workbooks & ):. Name these fractions as mixed fractions:. Name these fractions as improper fractions:. Draw these mixed fractions: Draw these improper fractions: 7

35 Name: Date: page PRE-TEST (for Workbooks & ): 1. Name these fractions:. Add or Subtract: BONUS: Reduce: 1 0 9

36 Name: Date: page PRE-TEST continued (for Workbooks & ):. Convert to an improper fraction: 1 1. Convert to a mixed fraction: 7 8. Add: Circle the bigger fraction in each pair (make the denominators the same first): Jane ate 8 of a pizza and Tom ate 1. What fraction of the pizza did they eat?

37 Name: Date: page 7 TEST (for Workbooks & ): 1. Name these fractions:. Add or Subtract: BONUS: Reduce:

38 Name: Date: page 8 TEST continued (for Workbooks & ):. Convert to an improper fraction: 1. Convert to a mixed fraction: 7 9. Add: Circle the bigger fraction in each pair (make the denominators the same first): Jane ate of a pizza and Tom ate. What fraction of the pizza did they eat?

39 page 9 TEST (for Workbooks & ): (Marking Scheme) Points Question 1: parts pts each - pts numerator correct 8 - pts denominator correct Question : 7 parts pts each - 1 pt correct method 8 - pts correct conversion to same denom. - 1 pt correct add/sub answer BONUS 8 pts - pt correct method 8 - pts correct conversion to same denom. - pt correct add/sub answer Question : parts pts each - pts correct divisor 1-1 pt numerator correct (based on divisor chosen) - 1 pt denominator correct (based on divisor chosen) Question : parts pts each - pts correct whole number 10 - pt correct fraction Question : parts pts each - pts numerator correct 10 - pts denominator correct Question : parts pts each - pts correct number of pies 10 - pts correct # of subdivisions in each piece - 1 pt correct fractional pie on end Question 7: parts pts each - pts correct number of pies 10 - pts correct # of subdivisions in each piece - 1 pt correct fractional pie on end Total: 100 pts

40 page 0 TEST (for Workbooks & ): (Marking Scheme) Points Question 1: parts pts each - pts numerator correct 8 - pts denominator correct Question : 7 parts pts each - 1 pt correct method 8 - pts correct conversion to same denom. - 1 pt correct add/sub answer BONUS pts - 1 pt correct method - pts correct conversion to same denom. - 1 pt correct add/sub answer Question : parts pts each - pts correct divisor 1-1 pt numerator correct (based on divisor chosen) - 1 pt denominator correct (based on divisor chosen) Question : parts pts each - pts correct numerator 8 (1 pt correct x, 1 pt correct +) - pt correct denominator Question : parts pts each - pts whole number 8-1 pt numerator correct - 1 pt denominator correct Question : parts pts each - pts correct conversion to improper 1 - pts correct conversion to same denom. - pt correct add/sub answer Question 7: parts pts each - 1 pt correct method 8 - pts correct conversion to same denom. - 1 pt correct < or > answer Question 8: 1 part 7 pts - pts correct equation 7-1 pt correct method - pt correct conversion to same denom. - pt correct add/sub answer Total: 100 pts

41 page 1 - Selected Answer Key Worksheet F-. a) b). c) d) e) f) Worksheet F- A 1. a) b) 7 c) 11 d) e) 11. a) b) 1 7 c) 11 d) 8. a) 7 b) 7 c) 8 1 BONUS: 11 Worksheet F- B 1. a) b) 7 c) d) e) 1 19 Worksheet F- A 1. a) b) 7 10 c) 8 1 d) 1 1 e) 7 1 f) 9 0 g) 11 1 h) 9 10 BONUS: a) 1 b) 10 Worksheet F- B 1. a) b) 8 1 c) a) 11 1 b) c) 7 d) 1 1 e) 1 10 f) 1 1 BONUS: a) 1 b) 1 c) 1 10 Worksheet F- C 1. a) 8 1 b) 7 1 c) a) 0 b) 1 1 c) 17 0 d) 1 0 e) 1 0 f) 17 1 BONUS: a) 1 1 b) 11 0 c) 7 0 Worksheet F- D 1. a) 10 1 b) 1 0 c) 1. a) 17 1 b) 8 c) 7 d) 9 8 e) 19 f) BONUS: a) 17 8 b) 8 c) Worksheet F- A 1. a) 10 b) 10 c) 8 d) e) 0 f). a) 11 1 b) 10 c) 11 1 d) 9 1 e) 8 f) 1 g) h) 9 i) 1 1 BONUS: a) 0 b) 1 8 c) 10 Worksheet F- B 1. a) 1 b) 18 c) 8. a) 1 b) 10 1 c) d) 18 e) 0 f) 10 g) 1 7 h) 9 1 i) 9 BONUS: a) 1 1 b) 1 c) 7 8 Worksheet F- A 1. a) 1. a) 1 b) 1 c) 1. a) 7 b) 1 c) 7 17 d) 8 e) 9 17 f) 17. a)

42 page b) 8 1 c) 7 d) 1 0 e) 1 1 f) 10. a) 10 b) 1 c) d) 9 0 e) 1 10 f) 1. Circle b) : = a) b) c) 1 d) 9 0 e) 1 1 f) 9 0 BONUS: a) 19 0 b) 11 1 c) 1 Worksheet F- B 1,The smaller the denominator, the fewer pieces the pie is cut into.. a) 9 b) 1 1 c) 0 d) e) 9 0 f) 10 g) 9 1 h) 8 0 i) 7 1 BONUS: a) 1 b) 17 0 c) 7 d) 7 e) f) 19 0 Worksheet F- C 1. a) 1 b) 7 c) 1 d) e) 1 f) error in some copies of worksheets--q should read 1/ - 1/1= /1 g) 18 h) 1 0 i) 11 j) 11 0 k) 0 1 l) 11 m) 19 n) 1 8 o) 9 1 BONUS: a) 9 b) 1 7 c) 17 Worksheet F-7 A 1. a) 8 1 b) 10 c) 9 0 d) 17 e) 1 f) 1. a) 8 b) 9 1 c) 9 8 d) 1 0 BONUS: a) b) 1 1 c) 11 8 d) 10 0 Worksheet F- 8 A 1. a) 8 b) a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 h) 1 i) 1 j) 1 k) 1 l) 1 m) 1 n) 1 o) 1 p) 1. a) b) c) d) e) f) g) h) i) j) k) l) BONUS: a) b) c) d) Worksheet F- 8 B 1. a) 10 b) 1 1. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 h) 1 i) 1 j) 1 k) 1 l) 1 m) 1 n) 1 o) 1 p) 1. a) b) c)

43 page d) e) f) g) h) Worksheet F- 10 A 1. a) 1 b) 1 1 c) 1 d) 8 e) f) 1 g) 1. Circle the fraction that are bigger than 1 : b) 7, e), f) Worksheet F- 10A (Continued) 1. a) b) c) d) 19 8 e) 1 f) 9 g) 10. Circle the fraction that are bigger than 1: c) 9 11, d), f), g) 7 Worksheet F- 10B 1. a) 1, 7 b), 11 c) 1, 7 d) 1 8, 8 e) 1, 1 f) 1, 9 g) h) 1 1,, 11 i) 1 7 8, 1 8 Worksheet F-10 B(Continued) 1. a), 17 b) 1 8, 8 c) 1, 7 d) 8, 19 8 e) 10, 10 f) 7 10, 7 10 g) 1 9, 1 9 h) 1, 10 i) 1, j) k) Worksheet F-10 C 1. a) b) c) d) e) f) g) h). a) b) c) d) e) f) Worksheet F-11 A 1. a) b) c) 10 d) , 1, 9 e) 11 f) 7 g) 1 h) 17 i) 1 j) 17 k) l) 1 m) 9 n) o) 7 p) 1 q) 1 r) 7 s) 7 t) 19 u) 11 v) 10 w) 17 x) 11 BONUS: a) 11 b) c) 19 d) 1 e). f) 19 g) 1 h) Worksheet F-11 B 1. a) 1 b) 1 c) 7 d) 1 e) 8 f) 7 g) 19 h) i) 7 7 j) 8 9 k) 9 l) 9 8 m) 9 n) 1 o) 7 p) 9 q) 1 r) 19 s) 0 7 t) 1 BONUS: a) 8 b) 7 c) 7 8 d) e) 8 7. f) 9 g) 9 h) Worksheet F-1 B 1. a) R1 b) R1 c) R1 d) R1 e) 1 R f) R1 g) R h) R1 i) R1 j) 9 k) R1 l) R m) R1 n) R o) 1 R1 p) R1 q) R1

44 page r) R1 s) R t) R. a) 1 b) 1 c) 1 d) e) f) g) h) i) 1 j) 1 k) 1 l) 1 m) 1 n) 1 o) 1 p) BONUS: a) 1 b) 1 c) 1 d) 1 Worksheet F-1 A (Cont.d) 1. a) 7 R1 b) 10 R1 c) 7 R1 d) R e) R f) R g) R1 h) 7 R. a) b) c) d) e) f) BONUS: a) 1 b) 1 9 c) 1 7 d) 1 8 Worksheet F-1 A 1. a) 17 or 10 b) or c) 7 10 or 7 10 d) 1 10 or 1 10 e) 17 or f) 7 10 or a) b) 1 or c) 8 or 1 8 BONUS: a) 9 b) 1 10 or 1 10 c) 1 or Worksheet F-1 B 1. a) or or b) 7 9 or 8 9 c) or 7 1 d) or 9 1 e) or 0 or 7 10 f) 78 or 7 g) 8 8 or 10 8 h) or 0 i) or 1 BONUS: a) 7 or 9 or 9 1 b) 7 1 or 9 1 or c) 11 1 or or 7 Worksheet F-1 A 1. a) b) 11 c) 7. a) b) c) d) 1 e) f) 1. a) 7 10 b) c) 1 d) e) f) BONUS: a) (between 1 & ) b) (between 0 & ) c) (between & 1 ) Worksheet F-1 A 1. a) b) 8 1 c) 9 10 d) 8 e) 1 f) 7 1 (typo ate) Worksheet F-1 B 1. a) 9 0 b) 9 c) d) 11 1 BONUS: a) b) 7 8 Worksheet F-1-1 (cont.) 1. a) 10 or 10 or b) 1 or 1 c) 7 or 1 1. a) 7 b) c) 1 d) 11 1 e) f) 11. a) < b) > c) > d) > Worksheet F-1-1 (cont.) 1. a) 7 or 1 1 YES b) 8 or 1 YES BONUS: a) b) APPENDIX: Basic Operations

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