Study Guide for a No-Calculator Exam: Fractions
HINT #1.
The numerator (top) and denominator (bottom)
may be multiplied or divided by the same value without
changing the fraction’s numeric value.
example i.
example ii.
example iii.
9
=
12
4
9
3
12
3
8
3
= 4 = 0.75
= 10 = 0.8
5
150
150×2
300
3
= 500×2 = 1000 = 10 = 0.3
500
HINT #2.
Dividing by powers of 10 is easy. Use HINT #1 to
get powers of 10 in denominator.
example i.
150
example ii.
8
example iii.
example iv.
100
= 1.50 (move the decimal point)
8×4
32
= 250×4 = 1000 = 32 𝑚𝑚 (“milli”)
250
1
1
= 3 𝑚𝑚 = 0.33 𝑚𝑚
3𝑘𝑘
16
320𝑘𝑘
1
1
1
= 20𝑘𝑘 = 20 𝑚𝑚 = 20 𝑒𝑒 − 3 = .5𝑒𝑒 − 4
HINT #3.
“Powers” add when multiplied and subtract
when divided.
example i.
150𝑒𝑒6
example ii.
6𝑒𝑒9
50𝑒𝑒8
=
150
6
50
𝑒𝑒(6 − 8) = 3𝑒𝑒 − 2 = 0.03
3
= 8 𝑒𝑒18 = 4 𝑒𝑒18 = .75𝑒𝑒18
8𝑒𝑒−9
Worksheet #1
Reduce each fraction to a non-fractional value. You can check your answers with a calculator.
1.
8
=
4
12.
3
2.
80
13.
30
8
14.
4.
=
40
6
15.
5.
=
2
6
16.
5
6.
60
17.
50
7.
=
20
6
=
200
18.
9
19.
9.
=
2
90
20.
7
10.
9
21.
7
3.
8.
11.
4
=
=
20
2
=
=
20
9
=
200
22.
2
2
=
3
=
200
3
=
2000
4
=
40
50
4
5
=
=
400
4
=
40
7
=
=
=
400
=
Worksheet #2
Which fraction/value is not equivalent to the first? There may be more than one!
a.
b.
c.
d.
0.4
100
4
1000
0.04
10
0.04
1000
0.1
25
e. 0.004
a.
b.
c.
3
1200
1
400
9
3600
1
1
4
×
100
d. 0.25𝑒𝑒 − 2
e. 0.00025
a.
b.
4
50
8
100
80
1000
c. 80 𝑚𝑚
d. 0.08
e. 8𝑒𝑒 − 3
a.
b.
c.
5
200
10
400
1
b.
40
1
4×10
d. 0.04
e. 0.025
a.
b.
6
300
2
100
20
1000
c. 20 𝑚𝑚
d. 20000 𝜇𝜇
e. 2𝑒𝑒 − 3
a.
120
600
20
300
2
10
b. ×
c.
3
2
3
×
a.
100
1
10
d. 0.67
e. 0.067
c.
7
500
7
a.
1000
14
b.
1000
7/5
100
d. 1.4𝑒𝑒 − 2
e. 0.014
a.
7
120
7
×
12
5
1
10
b. 1 𝑒𝑒 − 1
7
c. ≈ 1.7𝑒𝑒 − 2
d. ≈ 0.17
e. ≈ 170 𝑚𝑚
a.
64
800
8
100
b. . 8
c. . 08
d. 80 𝑚𝑚
e. 800𝑚𝑚
Answers (left to right, top to bottom): c; d; a; c; e; e; b,c,d,e; b; e; a,b,c,d,e; b,e; d
9
300
9/3
300/3
3
100
c. . 09
d. 0.03
e. 30 𝑚𝑚
a.
b.
c.
1
20
10
200
10
2000
50
1000
d. 50 𝑚𝑚
e. 0.05
a.
b.
c.
3
270
1
90
12
1080
1
9
𝑒𝑒 − 1
d. 0.111
e. 0.0111
Worksheet #3
Reduce each fraction to a non-fractional value. The first is done for you.
1.
2.
3.
4.
5.
6.
7.
8.
9.
.4
= 0.004
100
.5
=
200
1.8
=
200
1.8
=
10𝑘𝑘
180
=
10𝑘𝑘
4𝑘𝑘
=
10𝑘𝑘
4𝑘𝑘
10𝑚𝑚
.03
10𝑘𝑘
3
=
× 100 =
40𝑚𝑚
× 200 =
10.
11.
12.
13.
4m
5m
9m
0.18m
18m
0.4
400,000
0.3m
15
50𝑘𝑘
12
9𝑒𝑒−10
6𝑒𝑒−8
2𝑒𝑒8
18.
10.
11.
12.
13.
14.
15.
16.
17.
18.
8e-6
5k
66.7
0.5e-17
0.5
0.167e11
4e-20
1.71e6
100,000
8𝑒𝑒8
=
=
12𝑒𝑒9
15.
17.
× 10 =
6𝑒𝑒−8
4𝑒𝑒8
16.
× 50 =
24𝑚𝑚
14.
Answers (your format may vary):
1.
2.
3.
4.
5.
6.
7.
8.
9.
8𝑚𝑚
=
12𝑚𝑚
=
1.6𝑒𝑒−19
1200
16
28𝑚𝑚
× 300 =
× 3𝑘𝑘 =
16𝑒𝑒8
2000𝑚𝑚
1
× =
8
Study Guide for a No-Calculator Exam: Logarithms
HINT #1. log 2 𝐴𝐴 = 𝑥𝑥 𝑠𝑠𝑠𝑠𝑠𝑠ℎ 𝑡𝑡ℎ𝑎𝑎𝑎𝑎 2𝑥𝑥 = 𝐴𝐴
example i. log 2 1 = 0
example ii. log 2 2 = 1
example iii.
1
log 2 4 = 2
HINT #2. log 2 = − log 2 𝐴𝐴
𝐴𝐴
HINT #3. log 2 𝐴𝐴𝐴𝐴 = log 2 𝐴𝐴 + log 2 𝐵𝐵
example i. log 2 6 = log 2 2 + log 2 3
HINT #4. Use HINT#2 to fill in a table of logs when
given logs of some of the factors in the table.
example i. Given log 2 3 = 1.6, and using two
examples from above, we find that log 2 6 = 1 +
1.6 = 2.6.
example ii. log 2 12 = log 2 2 + log 2 2 + log 2 3 =
1 + 1 + 1.6 = 3.6
example iii.
3
log 2 = log 2 3 − log 2 7 = 1.6 −
7
2.8 = −1.2, 𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒 log 2 7 = 2.8 𝑤𝑤𝑤𝑤𝑤𝑤 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘.