Chapter 1, Lesson 1 Arithmetic and Algebra

126 Pages·2003·1.37 MB·English

Name Date Period Workbook Activity
1
Chapter 1,Lesson 1
Arithmetic and Algebra
EXAMPLE 16 + 2 = 22 false
10 ÷5 = 2 true
33 – n= 12 open
Directions Write trueif the statement is true or falseif it is false.Write
openif the statement is neither true nor false.
1. 11 + 5 = 16 ___________________ 16. 50 – 5 = 45 ___________________
18
2. 11 + 3 = 16 ___________________ 17. (cid:2)(cid:2)= 6 ___________________
3
3. 7 – 7 = 0 ___________________ 18. 30 + 30 = 60 ___________________
4. 6 • 6 = 36 ___________________ 19. 22n= 44 ___________________
5. 12 + n= 17 ___________________ 20. 27 ÷9 = 3 ___________________
6. 32 ÷8 = 4 ___________________ 21. 27 – 9 = 18 ___________________
7. 2 • 3 = 5 ___________________ 22. 6 • 6 = 38 ___________________
22
8. (cid:2)(cid:2)= 3 ___________________ 23. 11 + n= 35 ___________________
11
9. 100 + 10 = 120 ___________________ 24. 15 ÷3 = 4 ___________________
10. 7n= 49 ___________________ 25. 18 ÷9 = 2 ___________________
11. 7 • 7 = 49 ___________________ 26. 8n= 112 ___________________
12. 37 – n= 12 ___________________ 27. 4 • 4 = 8 ___________________
n
13. (cid:2)(cid:2)= 6 ___________________ 28. 14 – n= 1 ___________________
2
6
14. 60 – 60 = 10 ___________________ 29. (cid:2)(cid:2)= 3 ___________________
2
15. 17 • 1 = 18 ___________________ 30. 7 + 27 = 35 ___________________
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2
Chapter 1,Lesson 2
Representing Numbers Using Letters
EXAMPLE
Numerical expressions: 33 – 13 (cid:2)36(cid:2)
12
Algebraic expressions: 2m÷5 8d+ 2
Variables: nin 7n+ 7 kin k– 3
Operations: Multiplication and addition in 2y+ 3 Division in (cid:2)14(cid:2)
2
Directions Name the variable in each algebraic expression.
r
1. 4y+ 12 __________ 7. (cid:2)(cid:2) __________
4
2. k– 6 __________ 8. 14k– 10 __________
3. 2x+ 7 __________ 9. x– 100 __________
4. 7n __________ 10. 3 ÷p __________
2m
5. (cid:2)(cid:2) __________ 11. 4 + y __________
4
6. 3(d) __________ 12. 2m÷5 __________
Directions Fill in the table.For each expression,write the expression
type—numericalor algebraic—and list the operation or
operations.
Expression Expression Type Operation(s)
16 ÷2 13. 14.
8d 15. 16.
5 + 11 17. 18.
36
(cid:2)(cid:2) 19. 20.
12
2p– 1 21. 22.
4k+ 4 23. 24.
Directions Solve the problem.
25. Only 17 members of Mr.Ricardo’s class are going on the class trip.
The class has a total of kstudents.Write an algebraic expression
for the number of students who are notgoing on the trip. __________________________
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3
Chapter 1,Lesson 3
Integers on the Number Line
↓ ↓
EXAMPLE
(cid:3)8 (cid:3)7 (cid:3)6 (cid:3)5 (cid:3)4 (cid:3)3 (cid:3)2 (cid:3)1 0 1 2 3 4 5 6 7 8
• All the numbers on this number line are examples of integers.
• An example of a negative integeris –5 (see arrow).
• An example of a positive integeris 5 (see arrow).
• The number 0 is neither negative nor positive.
• |–5| = 5. In other words, –5 is 5 units from 0 (count the units).
• |5| = 5. In other words, 5 is 5 units from 0 (count the units).
Directions Identify each integer as either negative,positive,orzero.
1. 6 ____________ 5. 8 ____________ 9. 20 ____________
2. 13 ____________ 6. –9 ____________ 10. 1 ____________
3. –2 ____________ 7. 0 ____________ 11. 7 ____________
4. 11 ____________ 8. –33 ____________ 12. –1 ____________
Directions Write each absolute value.
13. |–5| __________ 17. |+18| __________ 21. |12| __________
14. |6| __________ 18. |5| __________ 22. |4| __________
15. |–2| __________ 19. |–11| __________ 23. |–9| __________
16. |2| __________ 20. |–12| __________ 24. |9| __________
Directions Solve this problem.
25. On the number line,how could you represent $5 that you earned?
How could you represent $5 that you had to pay? __________________
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Chapter 1,Lesson 4
Adding Integers
EXAMPLE Add 2 + (–5).
Start at 2, move 5 units to the left.The answer is –3.
–5
(cid:3)8 (cid:3)7 (cid:3)6 (cid:3)5 (cid:3)4 (cid:3)3 (cid:3)2 (cid:3)1 0 1 2 3 4 5 6 7
Add –3 + 7.
Start at –3, move 7 units to the right.The answer is 4.
+7
(cid:3)8 (cid:3)7 (cid:3)6 (cid:3)5 (cid:3)4 (cid:3)3 (cid:3)2 (cid:3)1 0 1 2 3 4 5 6 7
Directions Answer the questions.
1. To add a negativenumber,in which direction do you count on the number line? ______________
2. To add a positivenumber,in which direction do you count on the number line? ______________
Directions Write each sum on the blank.
3. –4 + 4 __________ 12. –2 + (–4) __________
4. 1 + (–7) __________ 13. –6 + 6 __________
5. 1 + 5 __________ 14. 6 + (–6) __________
6. 0 + 6 __________ 15. –4 + 8 __________
7. –1 + (–5) __________ 16. –6 + 12 __________
8. 5 + (–11) __________ 17. –2 + 6 __________
9. –5 + 3 __________ 18. –3 + 9 __________
10. –6 + 3 __________ 19. 7 + 7 __________
11. 11 + (–12) __________ 20. 2 + (–8) __________
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Chapter 1,Lesson 5
Subtracting Integers
EXAMPLE Find the difference: 14 – (–15)
Rule To subtract in algebra, add the opposite.
15 is the opposite of –15.
14 + 15 = 29
Directions Rewrite each expression as addition.Solve the new
expression.
1. –4 – (–11) ________________________ 10. –5 – (–5) ________________________
2. 9 – (+3) ________________________ 11. 2 – (+9) ________________________
3. –1 – 13 ________________________ 12. 1 – (+4) ________________________
4. –6 – (+10) ________________________ 13. 6 – 8 ________________________
5. 7 – (–10) ________________________ 14. –8 – (–3) ________________________
6. 4 – (+4) ________________________ 15. –3 – (+7) ________________________
7. 2 – (+8) ________________________ 16. 8 – (–7) ________________________
8. –11 – (–1) ________________________ 17. 10 – (+5) ________________________
9. 6 – (+2) ________________________ 18. 5 – 6 ________________________
Directions Solve these problems.Write an expression and the answer.
19. Dara’s kite is flying 67 feet high.Jill’s is flying
40 feet high.What is the difference between
the heights of these two kites?
________________________________
20. A helicopter hovers 60 m above the ocean’s
surface.A submarine is resting 30 m
underwater,directly below the helicopter.
What is the difference between the positions of
these two objects?
________________________________
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6
Chapter 1,Lesson 6
Multiplying Integers
EXAMPLE Notice the possible combinations for multiplying positive and negative integers.
positive (positive) = positive 4(4) = 16
positive (negative) = negative 4(–4) = –16
negative (positive) = negative –4(4) = –16
negative (negative) = positive –4(–4) = 16
Multiplying any integer, positive or negative, by 0 gives 0 as the product.
Directions Tell whether the product is positive,negative,or zero.
1. (4)(–7) _____________ 6. (5)(–3) _____________ 11. (–3)(–9) _____________
2. (–6)(3) _____________ 7. (–15)(–1) _____________ 12. (4)(6) _____________
3. (–7)(0) _____________ 8. (0)(14) _____________ 13. (11)(–2) _____________
4. (–9)(–9) _____________ 9. (–5)(7) _____________ 14. (2)(9) _____________
5. (2)(–11) _____________ 10. (–8)(–2) _____________ 15. (–6)(4) _____________
Directions Find each product.Write the answer.
16. (2)(9) __________ 25. (–11)(–2) __________
17. (–5)(9) __________ 26. (–4)(8) __________
18. (3)(–9) __________ 27. (–10)(–8) __________
19. (–10)(2) __________ 28. (5)(–5) __________
20. (–9)(–7) __________ 29. (–1)(–1) __________
21. (–5)(10) __________ 30. (7)(10) __________
22. (12)(2) __________
23. (–32)(0) __________
24. (6)(–4) __________
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7
Chapter 1,Lesson 6
Integers
Data from a climbing expedition is shown in this table.
Elevation in Feet
(Compared to Sea Level)
Base Camp –384
Camp 1 +5,027
Camp 2 +7,511
Camp 3 +8,860
Camp 4 +10,103
Camp 5 +10,856
Camp 6 +11,349
Summit +12,015
During the climb,some climbers began at base camp and climbed to the summit.
Other climbers also began at base camp but did not reach the summit—these climbers
moved back and forth between camps carrying supplies and other necessities.
Directions The movements of various climbers in the expedition are shown
below.Find the number of feet climbed by each climber.
1. Climber A:Base Camp to Camp 1 to Base Camp __________________________
2. Climber C:Base Camp to Camp 5 to Base Camp __________________________
3. Climber F:Base Camp to Camp 3 to Base Camp __________________________
4. Climber B:Base Camp to Camp 2 to Base Camp __________________________
5. Climber H:Base Camp to Camp 6 to Base Camp __________________________
6. Climber E:Base Camp to Summit to Base Camp __________________________
7. Climber G:Base Camp to Camp 4 to Base Camp __________________________
8. Climber D:Base Camp to Camp 5 to Camp 3
to Camp 4 to Base Camp _________________________
9. Climber I:Base Camp to Camp 2 to Camp 1
to Camp 6 to Base Camp __________________________
10. How many feet above base camp is the summit? __________________________
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Chapter 1,Lesson 7
Dividing Positive and Negative Integers
EXAMPLE Notice the possible combinations for dividing positive and negative integers.
positive ÷positive = positive 6 ÷2 = 3
positive ÷negative = negative 6 ÷–2 = –3
negative ÷positive = negative –6 ÷2 = –3
negative ÷negative = positive –6 ÷–2 = 3
Dividing 0 by any integer, positive or negative, produces 0 as the quotient.
Directions Tell whether the quotient is positive,negative,or zero.
1. 16 ÷–4 __________________ 9. –27 ÷3 __________________
2. –63 ÷–9 __________________ 10. 0 ÷–4 __________________
3. –10 ÷2 __________________ 11. –81 ÷–9 __________________
4. 33 ÷11 __________________ 12. 19 ÷–1 __________________
5. –12 ÷4 __________________ 13. 56 ÷8 __________________
6. 100 ÷10 __________________ 14. 500 ÷5 __________________
7. 36 ÷–9 __________________ 15. 32 ÷–8 __________________
8. 15 ÷–5 __________________
Directions Find and write each quotient.
16. 36 ÷12 __________ 24. –50 ÷10 __________
17. 21 ÷–7 __________ 25. 27 ÷–9 __________
18. 18 ÷–3 __________ 26. –14 ÷2 __________
19. –35 ÷7 __________ 27. 0 ÷16 __________
20. –24 ÷2 __________ 28. –72 ÷–9 __________
21. –16 ÷–8 __________ 29. –1 ÷–1 __________
22. 45 ÷–9 __________ 30. 9 ÷3 __________
23. –200 ÷–200 __________
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9
Chapter 1,Lesson 8
Simplifying Expressions—One Variable
EXAMPLE
Simplify 2n+ 2 + 4n.
1. Look for like terms. 2nand 4nare like terms, because they have the same variable, n.
2. Combine the terms: 2n+ 4n= 6n
3. Rewrite the whole expression: 6n+ 2
Now you are finished, because 6ncannot combine with 2.
Directions In each expression,underline the like terms.
1. 3k– 8 + 2k 6. –2 + 11c+c
4
2. p+ 12 + p 7. (cid:2)(cid:2)+ 2m+ 3m
7
3. 100 + 4w+ 4w 8. 2y– (–3y) + 7
4. 5m– 3 + 2m 9. 4x– 13 + 5x
5. 7x + 5x– 12 10. 8r + (–3r)
Directions Simplify each expression.
11. 3b+ b ___________________ 21. 2y+ (–2y) + 5 ___________________
12. 11y+ 2y+ y ___________________ 22. –5 + 6n– 4n ___________________
13. 7j+ 3j– 2j ___________________ 23. 2x+ 11x– 13 ___________________
14. 2k– 17 + k ___________________ 24. –h+ 7h ___________________
15. 11x+ x– 14 ___________________ 25. –11 – (–3k) + k ___________________
16. 22 + 2d+ 8d ___________________ 26. 7d– d+ 40 ___________________
17. 9g+ (–2g) + 4 ___________________ 27. 8 + 3m– (–m) ___________________
18. 14h– 3 – 2h ___________________ 28. 3w+ (–5w) ___________________
19. 2m+ (–8m) ___________________ 29. 2 + 5x– 2x ___________________
20. 3 + 4k– 3k ___________________ 30. 8g+ (–5g) – 6 ___________________
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Chapter 1,Lesson 9
Simplifying Expressions—Several Variables
EXAMPLE Simplify 2j + 4 + j– 1 + 3k.
1. Scan for variables. The expression has two: jand k.
2. Combine jterms: 2j + j= 3j
3. Combinekterms: 3k (no combining required)
4. Combine integers: 4 + (–1) = +3
5. Rewrite the whole expression: 3j+ 3k+ 3
Now you are finished, because you cannot combine unlike terms.
Directions Check the column or columns to show which kinds of terms
each expression includes.
Expression x terms yterms Integers
1. 3x+ 2x+ 3 + 6y
2. 3y – 14
3. x+ 2y– 10 + 3y
4. 72 – 68
5. x– 8
Directions Combine like terms.Simplify each expression.
6. 3k– 2k+ 12 + 5r ____________________
7. 2c+ 3b+ 8b+ c ____________________
8. 5k+ 3 + 2j– 2 – k ____________________
9. 7 + 4p– 6 + 2m– 2p ____________________
10. –4n+ 4 – (–2d) + n– 5 ____________________
11. 18 + (–4x) + 1 – 3x+ 8y ____________________
12. 2w+ (–11) + 18y+ 2w– 11 ____________________
13. 6h– 12 – 9h+ 8k+ (–3k) ____________________
14. 3 – 3m– 3m– 8p– 3p ____________________
15. 14x– 7 + 3y– 7x– 7x ____________________
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