31
Order of Operations Book 2
Step 1: Remember P. E. M. D. A. S., then draw the tree. (first draw the leaf nodes, putting in the original numbers, then make the non-leaf nodes in the order dictated by PEMDAS. Fill these nodes with both an operation and the value you get when you perform that operation.
Step 2: Evaluate:
17 - 4·3
=17 – 12
= 5
Step 3: Describe the expression as a sum, difference, product, quotient or power (answer comes from the bottom node on the tree. It will match the operation in the next-to-last line in your evaluation.)
This expression is a difference.
10 + 3(2 + 6)
100 – 4( 3(2+6))
50 - 10(4 - 2) + 6
2(3 + 4) – 12 · 2 ¸ 3
2·9 - 3(6 - 1) + 1
8 + 24 ÷ 4 · 2
30 - 3·4 + 2
36 ÷ 4(5 - 2) + 6
20 - 4·2 + 3
4 + 6(8 + 2) - 3
100 - 10(2 + 3) + 4
20 + 3(5 - 1)
3 + 22(1+8)
(5 • 4 )24 • 2 ¸ ( 3 + 5 )
2 [13 - (1 + 6)]
3(6+4)(5 - 3)
(5·3 - 8)3
12 + 23 + 34
(24 - 6) ÷2
102 + 2 · 10 + 1
(10 + 1)2
Challenge Problems:
48 · 2 – 24 – 3 · ( 16 – 7 – 1 )
96 – 32(5 – 2 · 2 + 1) + 7 · 12 ÷ 4
((32 + 42 + 122) ¸ 13 + 12) ¸ 25
31
Order of Operations Book 2
Page 4
10 + 3(2 + 6)
= 10 + 3·8
= 10 + 24
=34
The expression is a sum.
Page 5
100 – 4( 3(2 + 6))
=100 – 4(3·8)
= 100 - 4·24
= 100 – 96
= 4
The expression is a difference.
Page 6
50 – 10(4 – 2) + 6
= 50 – 10·2 + 6
= 50 – 20 + 6
= 30 + 6
= 36
The expression is a sum.
Page 7
2(3 + 4) – 12 · 2 ¸ 3
= 2·7 – 12·2 ¸ 3
= 14 – 12·2 ¸ 3
= 14 – 24 ¸ 3
= 14 – 8
= 6
The expression is a difference.
Page 8
2·9 - 3(6 - 1) + 1
= 2·9 - 3·5 + 1
= 18 - 3·5 + 1
= 18 - 15 + 1
= 3 + 1
= 4
The expression is a sum.
Page 9
8 + 24 ÷ 4 · 2
= 8 + 6·2
= 8 + 12
= 20
The expression is a sum.
Page 10
30 - 3·4 + 2
= 30 - 12 + 2
= 18 + 2
= 20
The expression is a sum.
Page 11
36 ÷ 4(5 - 2) + 6
= 36 ÷ 4·3 + 6
= 9·3 + 6
= 27 + 6
= 33
The expression is a sum.
Page 12
20 - 4·2 + 3
= 20 - 8 + 3
= 12 + 3
= 15
The expression is a sum.
Page 13
4 + 6(8 + 2) – 3
= 4 + 6·10 – 3
= 4 + 60 – 3
= 64 – 3
= 61
The expression is a difference.
Page 14
100 - 10(2 + 3) + 4
= 100 - 10·5 + 4
= 100 – 50 + 4
= 50 + 4
= 54
The expression is a sum.
Page 15
20 + 3(5 - 1)
= 20 + 3·4
= 20 + 12
=32
The expression is a sum.
Page 16
3 + 22(1+8)
= 3 + 22·9
= 3 + 4·9
= 3 + 36
= 39
The expression is a sum.
Page 17
(5 • 4 )24 • 2 ¸ ( 3 + 5 )
= 202 • 4 • 2 ¸ ( 3 + 5 )
= 202 • 4 • 2 ¸ 8
= 400 • 4 • 2 ¸ 8
= 1600 • 2 ¸ 8
= 3200 ¸ 8
= 400
= 391
The expression is a quotient.
Page 18
2 [13 - (1 + 6)]
= 2 [13 - 7]
= 2 · 6
= 12
The expression is a product
Page 19
3(6+4)(5 - 3)
= 3·10(5 - 3)
= 3·10·2
= 30·2
= 60
The expression is a product.
Page 20
(5·2 - 8)3
= (10 - 8)3
= 23
= 8
The expression is a power.
Page 21
12 + 23 + 34
= 1 + 23 + 34
= 1 + 8 + 34
= 1 + 8 + 81
= 9 + 81
= 90
The expression is a sum.
Page 22
(24 - 6) ÷ 2
= 18 ÷ 2
= 9
The expression is a quotient.
Page 23
102 + 2 · 10 + 1
= 100 + 2 · 10 + 1
= 100 + 20 + 1
= 120 + 1
= 121
The expression is a sum.
Page 24
(10 + 1)2
= 112
= 121
The expression is a power.
Page 25
48 · 2 – 24 – 3 · ( 16 – 7 – 1 )
= 48 · 2 – 24 – 3 · ( 9 – 1 )
= 48 · 2 – 24 – 3 · 8
= 96 – 24 – 3 · 8
= 96 – 24 – 24
= 72 – 24
= 48
The expression is a difference.
Page 26
96 – 32(5 – 2 · 2 + 1) + 7 · 12 ÷ 4
= 96 – 32(5 – 4 + 1) + 7 · 12 ÷ 4
= 96 – 32(1 + 1) + 7 · 12 ÷ 4
= 96 – 32·2 + 7 · 12 ÷ 4
= 96 – 34 + 7 · 12 ÷ 4
= 96 – 81 + 7 · 12 ÷ 4
= 96 – 81 + 84 ÷ 4
= 96 – 81 + 21
= 15 + 21
= 36
The expression is a sum.
Page 27
((32 + 42 + 122) ¸ 13 + 12) ¸ 25
= ((9 + 42 + 122) ¸ 13 + 12) ¸ 25
= ((9 + 16 + 122) ¸ 13 + 12) ¸ 25
= ((25 + 144) ¸ 13 + 12) ¸ 25
= (169 ¸ 13 + 12) ¸ 25
= (13 + 12) ¸ 25
= 25 ¸ 25
= 1
The expression is a quotient.
31
Order of Operations Book 2
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