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1.2 Operations With Rational Numbers
Formulas
Page 22
C 5
9(F 32)
How do you use this to convert 350º F?
1.2 Operations With Rational Numbers
Discover the Math
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1 a) Evaluate
i) -2 x 4 ii) -9 ÷ 3 iii) -18 ÷ (-6) iv) 10 x (-2)
• When you multiply or divide two integers with the same sign the result is …………………….
• When you multiply or divide two integers with different signs the result is …………………….
1.2 Operations With Rational Numbers
Discover the Math
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2 a) Evaluate. Will the answer be negative or positive?
a) -3.0 x 0.8 b) -3.6 ÷ 0.9
c) -3.0 ÷ (-0.5) d) 2.0 x (-0.25)
3. Rewrite each expression in question 2 using fractions and evaluate
1.2 Operations With Rational Numbers
Part B Mental math Strategies
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1. Calculate using mental math strategies.
a) 241 +353 b) 7.55 +2.45 c) 3528 ÷ 7
d) 12 41
2e) 3
7
9 1
1
2 4
2
9f ) 8 18
j) 42 8
g) 4 26 250 h) 2.25 44 i) 5 21
3
k) 124 81 l) 24 22
8
1.2 Operations With Rational Numbers
Part B Mental math Strategies
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4. Explain how you can mentally evaluate in two different ways
8 31
2
1.2 Operations With Rational Numbers
Part C Estimation Strategies
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4. Estimate. Explain or show how you got your answer.
a)475
9.97
e)2650
99
f ) 3016 2973 3025 2985
d) 3.71 8.99 5.18
b) 204 37 c) 458 906 341
1.2 Operations With Rational Numbers
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a) 1
2
5.3
1
2
4.7
b) 1
312
5
6
8
9
1.2 Operations With Rational Numbers
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c)
1
4(3.46 4.59)
5(7.87 1.42)
d) 1
1
4 (
7
4)
(0.5)2 0.05
2.41 4.56
323.6
0.96
1.2 Operations With Rational Numbers
Example 2 Apply Rational Numbers (Stock market)
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466 95
89
1
49
3
8
1
4
Stock Sales (100’s) High($) Low($) Close($) Net change
Matrix
1.2 Communicate the Key Ideas
1. Which mental math strategy would you use?
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a) 2 41
3b) 1
2
7 4
1
4 3
5
7c) 3.25 88
2. Steve’s Problem
3
4
51
3
10
2
21
3 8
6
What is the first step?What could he do next?
1.2 Check Your Understanding
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A) [( 11) ( 7)] 2.5
# 1 Evaluate. Use mental math as much as possible
1.2 Check Your Understanding
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A) [( 11) ( 7)] 2.5
# 1 Evaluate. Use mental math as much as possible
4 2.5 1.5
1.2 Check Your Understanding
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B) 2( 8.25 2.75)
31
23
4
# 1 Evaluate. Use mental math as much as possible
1.2 Check Your Understanding
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B)
2( 8.25 2.75)
31
23
4
2( 5.5)
31
24
3
11
34
6
= = = 1112
6
11
2=
1.2 Check Your Understanding
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# 1 Evaluate. Use mental math as much as possible
[( 6.5) ( 2)] 4C)
1.2 Check Your Understanding
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# 1 Evaluate. Use mental math as much as possible
[( 6.5) ( 2)] 4
( 8.5) 4
4.5
C)
1.2 Check Your Understanding
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# 1 Evaluate. Use mental math as much as possible
D) 2
1
3
4
61
6 1
2
1
1.2 Check Your Understanding
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# 1 Evaluate. Use mental math as much as possible
D)
2
1
3
4
61
6 1
2
1
= ==
= 2
1
3
6
41
6 2
1
1
2
6
122
6
1 21
2
1
3
1
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= 21
2
1
3
1
21
2
3
1
1=
23
2
1=
6
21
=
=
3 1
4=
1.2 Check Your Understanding
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# 2 Evaluate each expression. Show your work.
3
8
5
7
3
8
7
5
21
40
2. A
1.2 Check Your Understanding
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# 2 Evaluate each expression. Show your work.
11
12 2
9
11
B)
1.2 Check Your Understanding
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# 2 Evaluate each expression. Show your work.
11
12 2
9
11
B)
11
12
31
11
31
12
12
12
12
12
7
122
7
12
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621
6
15
24
3
4
c)
621
6
15
24
3
4c)
# 2 Evaluate each expression. Show your work.
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621
6
15
24
3
4c)
67
2
5
8
3
4
628
8
5
8
3
4
633
8
3
4
621
6
15
24
3
4c)
684
24
15
24
3
4
699
24
3
4
594
24
18
24
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c) 633
8
3
4
198
8
6
8
192
8
594
24
18
24
576
24
24
24
1.2 Check Your Understanding
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# 2 Evaluate each expression. Show your work.
d) 4[0.98 ( 1.02)]2
1.2 Check Your Understanding
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# 2 Evaluate each expression. Show your work.
d)
16
4[0.98 ( 1.02)]2
4[2]2
4(4)
1.2 Check Your Understanding
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# 3 Exact or estimate? Explain
a) An exact number is required in order to compare the two students.
b) An exact number is required in order to compare the two students.
c) An exact number is required in order to compare the two students.
1.2 Check Your Understanding
# 4 Costa and the old math book.
1
2 1
1
3 1
1
4 1
1
5 1
...
1
n 1
1
2 1
1
2
1.2 Check Your Understanding
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# 4 Costa and the old math book.
1
2 1
1
3 1
1
4 1
1
5 1
...
1
n 1
1
2 1
1
2
1
2 1
1
3 1
1
2
2
3
1
3
1.2 Check Your Understanding
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# 4 iii Costa and the old math book.
1
2
2
3
3
4
1
4
1
2 1
1
3 1
1
4 1
1.2 Check Your Understanding
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# 5 Daffodil Campaign
5
87500
8 7500937.5
1
8937.5
5
84687.5
So far $4687.5 has been raised for this daffodil campaign
1.2 Check Your Understanding
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1
2
0
1
2
11
2
6. Complete the Magic Square
a)
1.2 Check Your Understanding
6. Complete the Magic Square
0.8
0
2.0 1.2
b)
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1.2 Check Your Understanding
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8. Skill testing question
“Take 15, multiply it by one-half, add three, and subtract two and one-half.”
Write an expression for this equation. Is this just a trick?
1.2 Check Your Understanding
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163
8 15
5
815
11
8 15
5
8
6
8
3
4
3
4200 150
Tomas would have made $150 if he sold the
200 shares at the highest price of the day.
9. Celetica Stocks
1.2 Check Your Understanding
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10. Write problems based on question 9 using each expression.
a) 150 927
8
b) 300(901
4 96)
c)5
8225
1.2 Check Your Understanding
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11. Use decimals for question 11.
1.2 Check Your Understanding
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12. Use exactly four 4s to get 0-50. Answers must be exact
1.2 Check Your Understanding
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13. Formula for the area of a trapezoid is
Ah
2(a b)
a
h
b
If a = 3.5 units and b = 4.4 units, draw a graph of the area of the trapezoid as the height increase from 1 to 5 units.What pattern do you see?
1.2 Check Your Understanding
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# 15 Evaluate without a calculator.
2 1
2 1
2 12
1.2 Check Your Understanding
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# 15 Evaluate without a calculator.
2 1
2 1
2 12
2 1
2 1
212
1 21
21
5
21
2
5
1.2 Operations With Rational Numbers
Order of Operations
1. 5 3 2 8 3 232.
7 5 33. 4 3 24.
5. 36 4 22 5 6 2 36.
3 4 3 47. 8 6 28.
Page
Grade 9 Math
October 2007
Order of Operations
9. 12 7 6 12 5 610.
14 10 511. 20 5 312.
13. 23 5 6 3 8 2 6214.
3 4 3 415. 8 6 216.
Grade 9 MathOctober 2007
Order of Operations
1. 2 32 4 5 32 8 2 • 8• 22.
815 • 49 72 3. 16 • 5 12 • 5 4 • 54.
Grade 9 MathOctober 2006
Order of Operations
5. 180
55• 11• 5 11• 180 55 • 56.
54 7 28 7 25 77. 12
42 248.
ORDER OF ARITHMETIC OPERATIONS B1/10/12
Evaluate each expression. No calculator.
1. 4 + 3 - 8 + 2 2. 5 + 2 x 6
3. 18 - 5 x 2 4. 8 + 3 x 10
5. 7 + 3 x 5 - 11 6. 9 x 0 + 1 x 8 - 2 x 3
7. (11 - 5) x 3 8. 3 (5 + 2 - 1)
9. 2 x 5 + 7 x 2 - 6 x 3 10. 3 (27 + 2 - 4)
11.2 + 4 (10 - 2) 12. ( 10)(18 ÷ 9 + 1 )
13. 50 ((41 + 3 ) ÷ 11) 14. 3 (12 + 3) - 9 x 4
15 32 - 2 2 + 1 16. 23 - 2 2 + 2
17. ( 11 ) (27 - 5) + 4 18. 32 - 2 (3 + 1)
19.( )(10 - 1) + ( 5 )(9 - 4) 20. 48 ÷ 6 ÷ 3 -
21.62 - 5 2 + 42 - 3 2 22. 3 3 + 22 + 12
23. 30 - 6 24. 2 x 4 x 5 x 6 4 x 2 12 x 2
25. 11 - 2 x 3 26. 3 x 4 + 6 x 8 - 2 x 3 2 x 5 2 x 3
27. 10 x 6 - 2 x 10 + 8 x 5 27. (8 ÷ 8 ) (5 ÷ 5) (18) 3 x 3 20 - 2
1. 4 3 8 2
3. 18 5 2
2. 5 2 6
4. 8 3 10
5. 7 35 11
7. 11 5 3
6.
9 0 1 8 2 38.
3 5 2 1)
9. 6 5 7 2 113 4
11. 2.1 4.0 3.2 1.6
10. 0.3 2.5 1.7 3.2
12.2
3
18 7 1
3
2
13. 1.30 0.04 2.13 1.07
15. 32 22 11
14.
23 22 216.
3 14 3 9 4
17.1
217 5 4
19.
2
310 1
1
319 4
18.
15 3 3 10 20.
32 2 3 1
21. 62 52 42 32 22 12
23.
30 6
4 2
22.
3 4 5 6
8 924.
33 23 13
25.4 2 3
2 5
28.
(24 8)(5 2)(8 7)
5 2
26. 3 4 6 8 2 3
2 3
27.4 6 2 3 9 24
2 3
1. 0.4 3 8 ( 0.02)
3. 18 0.05
2. 25 0.2 • ( 6)
4. ( 8 ( 3)) 0.1
5. 7.5 3 ( 5) 1.1
6. 19 0 2 0.8 2 0.3
Order of operation 2
7. 25000 0.01 ( 7)
9. 6 5 7 2 113 4
8. 0.1• (75% 44)
10. 0.5 • 2.5 10 1.5 11. (14 0.1) ( 8.6 1.6)
12.2
5
48 9 16
Order of operation 2
2
3
5
7
1
2
Oct 10
2
3
5
7
1
2Oct 10
2. Page 27
2d. Page 27
3. Page 27
4. Page 27
5. Page 27
5. Page 28
5
87500
8 7500937.5
1
8937.5
5
84687.5
So far $4687.5 has been raised for this daffodil campaign
page 28
page 28
9.a) page 28
2 1
2 1
2 12
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15. Find the value of the expression. No calculator.
a)
The End