Algebra Infrastructure Flashcards
ACT/SAT/College Math Infrastructure
6 ÷ 3 =
2
-15 ÷ -5 =
3
-35 ÷ 7 =
-5
-55 ÷ -11 =
5
77 ÷ 11 =
7
91 ÷ -13 =
-7
8 ÷ 4 =
2
-10 ÷ -5 =
2
-14 ÷ 7 =
-2
-16 ÷ -8 =
2
24 ÷ 12 =
2
34 ÷ -17 =
-2
36 ÷ 18 =
2
-38 ÷ -19 =
2
-9 ÷ 3 =
-3
-15 ÷ -5 =
3
18 ÷ 6 =
3
21 ÷ -7 =
-3
24 ÷ 8 =
3
-33 ÷ -11 =
3
-39 ÷ 13 =
-3
-45 ÷ -15 =
3
51 ÷ 17 =
3
32 ÷ -8 =
-4
64 ÷ 16 =
4
-52 ÷ -13 =
4
-44 ÷ 11 =
-4
-6 ÷ -3 =
2
8 ÷ 4 =
2
10 ÷ -5 =
-2
12 ÷ 6 =
2
-14 ÷ -7 =
2
-16 ÷ 8 =
-2
-18 ÷ -9 =
2
20 ÷ 10 =
2
22 ÷ -11 =
-2
24 ÷ 12 =
2
-26 ÷ -13 =
2
-28 ÷ 14 =
-2
-30 ÷ -15 =
2
32 ÷ 16 =
2
34 ÷ -17 =
-2
36 ÷ 18 =
2
-38 ÷ -19 =
2
-12 ÷ 4 =
-3
-15 ÷ -5 =
3
18 ÷ 6 =
3
21 ÷ -7 =
-3
24 ÷ 8 =
3
-27 ÷ -9 =
3
-30 ÷ 10 =
-3
-33 ÷ -11 =
3
36 ÷ 12 =
3
39 ÷ -13 =
-3
42 ÷ 14 =
3
-45 ÷ -15 =
3
-48 ÷ 16 =
-3
-51 ÷ -17 =
3
54 ÷ 18 =
3
20 ÷ -5 =
-4
24 ÷ 6 =
4
-28 ÷ -7 =
4
-32 ÷ 8 =
-4
-36 ÷ -9 =
4
40 ÷ 10 =
4
44 ÷ -11 =
-4
48 ÷ 12 =
4
-52 ÷ -13 =
4
-56 ÷ 14 =
-4
-60 ÷ -15 =
4
64 ÷ 16 =
4
68 ÷ -17 =
-4
30 ÷ 6 =
5
-35 ÷ -7 =
5
-40 ÷ 8 =
-5
-45 ÷ -9 =
5
50 ÷ 10 =
5
55 ÷ -11 =
-5
60 ÷ 12 =
5
-65 ÷ -13 =
5
-70 ÷ 14 =
-5
-75 ÷ -15 =
5
80 ÷ 16 =
5
42 ÷ -7 =
-6
48 ÷ 8 =
6
-54 ÷ -9 =
6
-60 ÷ 10 =
-6
-66 ÷ -11 =
6
72 ÷ 12 =
6
78 ÷ -13 =
-6
84 ÷ 14 =
6
-90 ÷ -15 =
6
-56 ÷ 8 =
-7
-63 ÷ -9 =
7
70 ÷ 10 =
7
77 ÷ -11 =
-7
84 ÷ 12 =
7
-91 ÷ -13 =
7
-98 ÷ 14 =
-7
-72 ÷ -9 =
8
80 ÷ 10 =
8
88 ÷ -11 =
-8
96 ÷ 12 =
8
-104 ÷ -13 =
8
-90 ÷ 10 =
-9
-99 ÷ -11 =
9
108 ÷ 12 =
9
110 ÷ -11 =
-10
2 ^ 2 =
4
-2 ^ 3 =
-8
2 ^ 4 =
16
-2 ^ 5 =
-32
2 ^ 6 =
64
-2 ^ 7 =
-128
2 ^ 8 =
256
-2 ^ 9 =
-512
2 ^ 10 =
1024
-3 ^ 2 =
9
3 ^ 3 =
27
-4 ^ 2 =
16
5 ^ 2 =
25
-6 ^ 2 =
36
7 ^ 2 =
49
-8 ^ 2 =
64
9 ^ 2 =
81
-10 ^ 2 =
100
11 ^ 2 =
121
-12 ^ 2 =
144
13 ^ 2 =
169
-14 ^ 2 =
196
15 ^ 2 =
225
2 ^ -1 =
0.5
2 ^ -2 =
0.25
3 ^ -1 =
0.33
3 ^ -2 =
0.11
3 √ 8 =
2
3 √ 27 =
3
4 √ 16 =
2
4 √ 81 =
3
5 √ 32 =
2
6 √ 64 =
2
7 √ 128 =
2
8 √ 256 =
2
9 √ 512 =
2
10 √ 1024 =
2
2 √ 9 =
3
2 √ 16 =
4
2 √ 25 =
5
2 √ 36 =
6
2 √ 49 =
7
2 √ 64 =
8
2 √ 81 =
9
2 √ 100 =
10
2 √ 121 =
11
2 √ 144 =
12
2 √ 169 =
13
2 √ 196 =
14
2 √ 225 =
15
3 √ -8 =
-2
3 √ -27 =
-3
3 √ -125 =
-5
4 ^ 3 =
64
5 ^ 3 =
125
Convert to decimal 1/2 =
0.50
Convert to decimal 1/3 =
0.33
Convert to decimal 1/4 =
0.25
Convert to decimal 1/5 =
0.20
Convert to decimal 1/6 =
0.17
Convert to decimal 1/7 =
0.14
Convert to decimal 1/8 =
0.13
Convert to decimal 1/9 =
0.11
Convert to decimal 1/10 =
0.10
2 ^ -1 =
1/2
3 ^ -1 =
1/3
4 ^ -1 =
1/4
5 ^ -1 =
1/5
6 ^ -1 =
1/6
7 ^ -1 =
1/7
8 ^ -1 =
1/8
9 ^ -1 =
1/9
10 ^ -1 =
1/10
a+b =
a+b (given the information cannot be simplified further)
a x b =
ab
a divided by b =
a/b
a over b =
a/b
a/b reciprocal =
b/a
2 reciprocal =
1/2 or .5
3 reciprocal =
1/3 or .33
4 reciprocal =
1/4 or .25
5 reciprocal =
1/5 or .20
6 reciprocal =
1/6 .or .167
7 reciprocal =
1/7 or .142
8 reciprocal =
1/8 or .125
9 reciprocal =
1/9 or .111
10 reciprocal =
1/10 or .1
Simplify .10 =
.1
Simplify .100 =
.1
Simplify .1000 =
.1
Simplify .10000 =
.1
1 * 10 =
10
2 * 100 =
200
3 * 10 =
30
10 * 100 =
1000
100 * 10 =
1000
20 * 1000 =
20000
a * 10 =
10a
b * 100 =
100b
c * 1000 =
1000c
d * 10 =
10d
100a ÷ 10 =
10a
10b ÷ 100 =
b/10
c ÷ -10 =
-c/10
1000d ÷ -1000 =
-d
10000e ÷ -10000 =
-e
10abc ÷ 10 =
abc
-100def ÷ -100 =
def
10a ÷ a =
10
37b ÷ b =
37
-.2de ÷ d =
-.2e
-.56abc ÷ a =
-.56bc
(a+b) ÷ a =
1+b/a
(-a-b) ÷ -a =
1+b/a
(2a+a) ÷ a =
2+1 = 3
(-3a-2a-a) ÷ -a =
3+2+1 = 6
(ab+ac+ad) ÷ -a =
b+c+d
2a+a + a =
4a
-3a-2a-a + a =
-5a
ab+ac+ad + ab =
2ab+ac+ad
-a ÷ -1 =
a
-a * -1 =
a
-c * -1 =
c
-3 ÷ -1 =
3
-1000 * -1 =
1000
3 ÷ 10 =
0.3
4 ÷ 100 =
0.04
5 ÷ 1000 =
0.005
6 ÷ -10 =
-0.6
7 ÷ -100 =
-0.07
2 ÷ 2 =
1
-78 ÷ -78 =
1
-b ÷ -b =
1
c ÷ -c =
-1
-d ÷ d =
-1
4 ÷ -4 =
-1
a * a =
a^2
a^2 * a^3 =
a^5
a^2 * b =
(a^2)b
b^-3 * b^-1 =
b^-4
b^-4 * b^-2 =
b^-6
a^-1 * a =
1
a^-2 * a^2 =
1
1 * -1 =
-1
3 * 1 =
3
12 * 0 =
0
a * -1 =
-a
ab * 1 =
ab
b * 0 =
0
1 ÷ -1 =
-1
3 ÷ 1 =
3
12 ÷ 0 =
undefined
a ÷ -1 =
-a
ab ÷ 1 =
ab
b ÷ 0 =
undefined
1 ^ -1 =
0.1
3 ^ 1 =
3
12 ^ 0 =
1
a ^ -1 =
1/a
ab ^ 1 =
ab
b ^ 0 =
b
1 + -1 =
0
3 + 1 =
4
12 + 0 =
12
a + -1 =
a-1
ab + 1 =
ab+1
b + 0 =
b
1 - (-1) =
2
3 - 1 =
2
12 - 0 =
12
a - (-1) =
a+1
ab - 1 =
ab-1
b - 0 =
b
a ÷ 0 =
undefined
-a ÷ 0 =
undefined
a * 0 =
0
a - a =
0
-a + a =
0
-a * 0 =
0
-a ^ 0 =
1
-a ÷ -a =
1
a ^ 0 =
1
a ÷ a =
1
-a ÷ a =
-1
-a * -1 =
a
-a ÷ -1 =
a
a ^ 1 =
a
a * 1 =
a
a + 0 =
a
a ÷ 1 =
a
a - 0 =
a
a ÷ -1 =
-a
a * -1 =
-a
-a * 1 =
-a
-a ÷ 1 =
-a
-a + 0 =
-a
-a ^ 1 =
-a
-a - 0 =
-a
a + a =
2a
a + -1 =
a-1
a - 1 =
a-1
a + 1 =
a+1
a - (-1) =
a+1
a * a =
a^2
a ^ -1 =
1/a
a ^ a =
a^a (this is NOT a^2)
-a * a =
-(a^2)
-a + -1 =
-a-1
-a + 1 =
-a+1
-a - (-1) =
-a+1
-a - 1 =
-a-1
-a - a =
-2a
-a ^ -1 =
1/-a
-a ^ a =
-a^a (this is NOT -a^2)
