1.2 Operations With Rational Numbers
Formulas
5
C  (F  32)
9
How do you use this to convert 350º F?
Page 22
1.2 Operations With Rational Numbers
Discover the Math
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 …………………….
Page 22
1.2 Operations With Rational Numbers
Discover the Math
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
Page 23
1.2 Operations With Rational Numbers
Part B Mental math Strategies
1. Calculate using mental math strategies.
a) 241 +353
1
d) 12  4
2
g) 4  26  250
j) 42 8
b) 7.55 +2.45
c) 3528 ÷ 7
7
1
2
e) 3  1  4
9
2
9
f ) 8 18
h) 2.25  44
1
i) 5  2
3
k) 124  81
2
l) 24  2
8
Page 23
1.2 Operations With Rational Numbers
Part B Mental math Strategies
4. Explain how you can mentally evaluate
in two different ways
1
83
2
Page 23
1.2 Operations With Rational Numbers
Part C Estimation Strategies
4. Estimate. Explain or show how you got your answer.
475
a)
9.97
b) 204  37
d) 3.71  8.99  5.18
c) 458  906  341
2650
e)
99
f ) 3016  2973  3025  2985
Page 23
1.2 Operations With Rational Numbers
 1 
 1 
a)   5.3    4.7
 2 
 2 
 1
 5 8 
b)   12   
 3
 6 9 
Page 24
1.2 Operations With Rational Numbers
c)
1
(3.46  4.59)
4
5(7.87  1.42)
 1
7 
 1  ( ) 
323.6
4
4


d)
 2.41  4.56 
2
(0.5)  0.05 
0.96




Page 24
1.2 Operations With Rational Numbers
Example 2 Apply Rational Numbers (Stock market)
Stock Sales (100’s) High($) Low($) Close($) Net change
Matrix
466
5
9
8
1
9
4
3
9
8
1

4
Page 25
1.2
Communicate the Key Ideas
1. Which mental math strategy would you use?
1
a) 2  4
3
2
1
5
b) 1  4  3
7
4
7
c) 3.25 88
2. Steve’s Problem
4
3 2 
  1  
 
 5
10
3 
 1 8  
 2   

  3 6  

What is the first step?
What could he do next?
Page 26
1.2
Check Your Understanding
# 1 Evaluate. Use mental math as much as possible
A)
[(11)  (7)]  2.5
Page 27
1.2
Check Your Understanding
# 1 Evaluate. Use mental math as much as possible
A)
[(11)  (7)]  2.5
 4  2.5
 1.5
Page 27
1.2
Check Your Understanding
# 1 Evaluate. Use mental math as much as possible
B)
2(8.25  2.75)
1 3 
3  
2 4 
Page 27
1.2
Check Your Understanding
B)
2(8.25  2.75)
1 3 
3  
2 4 
2(5.5)
11
11
= 1 4  = 4  = 12  = 11
3   3   
2
2 3 
6   6 
Page 27
1.2
Check Your Understanding
# 1 Evaluate. Use mental math as much as possible
C)
[(6.5) (2)]  4
Page 27
1.2
Check Your Understanding
# 1 Evaluate. Use mental math as much as possible
C)
[(6.5) (2)]  4
 (8.5)  4
 4.5
Page 27
1.2
Check Your Understanding
# 1 Evaluate. Use mental math as much as possible
D)
 1 4 
   

3
6

2

1
1 1
   
 6  2 
Page 27
1.2
Check Your Understanding
# 1 Evaluate. Use mental math as much as possible
D)
 1 4 
   

3
6

2

1
=



1
1
   
 6  2 
 6 
 
12


2
=  2   1 =


 6 
 1 6 
   

3
4

2

1
1  2 
   
 6 1
1 1 
2   1
2 3
=
Page 27
=
=
=
=
1 1 
2   1
2 3
1 3
2   1
2 1 
3 
2  1
2 
6
1
2
=
3 1
=
4
Page 27
1.2
Check Your Understanding
# 2 Evaluate each expression. Show your work.
2. A
3 5

8 7
3 7 21
 
8 5 40
Page 27
1.2
Check Your Understanding
# 2 Evaluate each expression. Show your work.
B)
11  9 
 2 
12  11
Page 27
1.2
Check Your Understanding
# 2 Evaluate each expression. Show your work.
B)
11  9 
 2 
12  11
11 31
 

12  11 
31 12 12 7



12 12 12 12
7
2
12
Page 27
c)
# 2 Evaluate each expression.
21 15  3
6  
 6 24  4
Show your work.
c)
21 15  3
6  
 6 24  4
Page 27
c)
21 15  3
6  
 6 24  4
7 5 3
 6  
2 8 4
28 5  3
 6  
 8 8  4
33 3
 6  
 8  4
c)
21 15  3
6  
 6 24  4
84 15  3
 6  
24 24  4
99  3
 6 
24  4
594  18
  
 24  24
Page 27
c)
33 3
 6  
 8  4
198 6
  
 8  8
192

8
 24
594  18
  
 24  24
576

24
 24
Page 27
1.2
Check Your Understanding
# 2 Evaluate each expression. Show your work.
d)
 4[0.98  (1.02)]
2
Page 27
1.2
Check Your Understanding
# 2 Evaluate each expression. Show your work.
d)
 4[0.98  (1.02)]
2
 4[2]
2
 4(4)
 16
Page 27
1.2
Check Your Understanding
# 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.
Page 27
1.2
Check Your Understanding
# 4 Costa and the old math book.
1 1 1 1  1 
  1  1  1  1...  1
2 3 4 5  n 
1 
1
  1 
2 
2
1.2
Check Your Understanding
# 4 Costa and the old math book.
1 1 1 1  1 
  1  1  1  1...  1
2 3 4 5  n 
1 
1
  1 
2 
2
1 1   1  2  1
  1  1     
2 3   2  3 3
Page 27
1.2
Check Your Understanding
# 4 iii Costa and the old math book.
1 1 1 
  1  1  1
2 3 4 
 1  2  3 
1
      
 2  3  4 
4
Page 27
1.2
Check Your Understanding
5
  7500
8
1
 937.5
8
5
 4687.5
8
# 5 Daffodil Campaign
937.5
87500
So far $4687.5 has been raised for this daffodil campaign
Page 27
1.2
Check Your Understanding
6. Complete the Magic Square
a)
1

2
1
2
0
1
1
2
Page 28
1.2
Check Your Understanding
6. Complete the Magic Square
b)
0.8
2.0
1.2
0
Page 28
1.2
Check Your Understanding
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?
Page 28
1.2
9.
Check Your Understanding
Celetica Stocks
3
5
11
5 6 3
16  15  15  15  
8
8
8
8 8 4
3
 200  150
4
Tomas would have made $150 if he sold the
200 shares at the highest price of the day.
page 28
1.2
Check Your Understanding
10. Write problems based on question 9 using each expression.
7
a) 150  92
8
1
b) 300(90  96)
4
5
c)  225
8
Page 28
1.2
Check Your Understanding
11. Use decimals for question 11.
Page 29
1.2
Check Your Understanding
12. Use exactly four 4s to get 0-50.
Answers must be exact
Page 29
1.2
Check Your Understanding
13. Formula for the area of a trapezoid is
h
A  (a  b)
2
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?
Page 29
1.2
Check Your Understanding
# 15 Evaluate without a calculator.
2
1
2
1
1
2
2
Page 29
1.2
Check Your Understanding
# 15 Evaluate without a calculator.
2
1
2
1
2
1
2
2
1
1
2
1
2
2
1
5
2
1  2  1  1 
2
2
5
Page 29
1.2 Operations With Rational Numbers
Order of Operations
1.
532
3.
7 53
2.
4.
2
5.
36  4  2
7.
3  4   4
3
6.
8.
832
3
4 32
56  2   3
86 2
Page
Grade 9
Math
October 2007
Order of Operations
9.
12  7  6
11.
14 10  5
3
13.
2  56
15.
3  4   4
3
10.
12.
14.
16.
12  5  6
20  5  3
38  2  6 2
86 2
Grade 9 Math
October 2007
Order of Operations
1.
2  3 4  5
3.
81 • 49  7
2
5
2
2.

4.
32 8  2 • 8• 2
16 • 5 12 • 5  4 • 5
Grade 9 Math
October 2006
Order of Operations
5.
7.
180
• 11• 5
55
6.
54  7  28  7  25  7
11• 180  55 • 5
8.
12
2
4
4 2
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 x8 -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.
14. 3 (12 + 3) - 9 x 4
50 ((41 + 3 ) ÷ 11)
15 3 2 - 2 2 + 1
16. 2 3 - 2 2 + 2
17. ( 11 ) (27 - 5) + 4
18. 32 - 2 (3 + 1)
19. ( )(10 - 1) + ( 5 )(9 - 4)
20. 48 ÷ 6 ÷ 3 -
21. 6 2 - 5 2 + 4 2 - 3 2
22.
3 3
+2 2
+1 2
1.
4 382
2.
52 6
3.
18  5  2
4.
8  3 10
5.
7  3 5 11
6.
11  5  3
8.
7.
3 5  2  1)
9  0 1  8  2  3
9.
6  5  7  2 11 3  4
10.
0.32.5  1.7  3.2 
11.
2.1  4.03.2 1.6
12.
2 
3 
 18  7  1  
3 
2 
13.
14.
15.
16.
1.300.04  2.13 1.07
314  3  9  4
2
2
3
2
1
3  2 1
2  2 2
17.
18.
19.
20.
1
17  5  4
2
32  23 1
2
1
10  1  19  4
3
3
15  3  3  10 
21.
2
2
2
2
2
6  5  4  3  2 1
3
3
3
22.
3  2 1
23.
30  6
42
24.
2
34 56
89
25.
26.
27.
28.
4 23
25
34 682 3
23
4  6  2  3  9  24
23
(24  8)(5  2)(8  7)
52
Order of operation 2
0.4 3  8  (0.02)
2. 25  0.2 • (6)
3.
18  0.05
1.
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.
8.
9.
10.
11.
12.
25000  0.01 (7)
0.1• (75% 44)
6  5  7  2 11 3  4
0.5 • 2.5  10  1.5
(14  0.1) (8.6 1.6)
2 
 48  9  16 
5 
2 5 1
 
3 7 2
Oct 10
2 5 1
 
3 7 2
Oct 10
2. Page 27
2d. Page 27
3. Page 27
4. Page 27
5. Page 27
5
  7500
8
1
 937.5
8
5
 4687.5
8
5. Page 28
937.5
87500
So far $4687.5 has been raised for this daffodil campaign
page 28
page 28
9.a) page 28
15. Find the value of the expression. No calculator.
a)
2
1
2
1
1
2
2
page 28
The End