Fractions and indices
Exercices
Fractions and indices 1
Exercise 1: Calculate and give the result as a fraction in its simplest form.
7 +1
7+ 3
a) 5 + 16
12 6
8 10
14 14
b) 125 − 4
22 22
15 − 4
36 3
c) 3× 8
5 11
21× 24
40 49
d) 3 ÷ 5
4 7
8
5
16
15
9+4+2
5 9 6
8 − 16 + 12
7 5 35
−2× −6
9 −5
3× −4
13
17÷ 16
3
9 .
−45
2
Exercise 2: Calculations using powers. Give the results in the form a n (where a and n are whole numbers).
a) 75×73
e)
1
85
b)
89
83
f) 69×6−11
c) 94×34
d) (54)6
5−3
57
h) 1−4 .
7
g)
Exercise 3: Write the following numbers in standard form.
a) 23 000 000
b) 4 007 000
c) -234 500 000
d) 0.002 318
e) -0.023 046
f) 0.000 023 768
.
Exercise 4: Calculate, giving your answer in its simplest form.
a)
2
1 8
+ ×
7
7 3
b)
7
3 11
+ ×
5
5 6
c)
1
1 4
− ×
3
3 7
.
d)
2
5 21
− ×
3
3 15
e)
6
1
1
÷ 
− 
5
5
 15
f)
7  1

÷
− 2 
9  3

Exercise 5: Write the following in standard form
a) 54.2 × 103
b) 120×10−4
c) − 17.4 × 10 −3
Exercise 6: Write the following in standard form
10 7 × 10 −3
4 ×1014 × 12
a) 5 ×
b)
10
3 × 1011
d) 0.007 × 10²
c)
5 × 10 -3 × 12 × 10 4
3 × 10 × 2 ×10 −1
Fractions and indices 2
Exercise 1 Calculate, and give the results in the simplest form.
3
2×
4
6
7
a)
b) − 2 ×
5
5
5
−1
3
7 2 3
d) − − ×
9 9 4
g)
e)
3 4 5
÷ −
7 21 2
5 2
j)  − 
6 3
2
1
3
c)
2
1
 
2
2−
4
13 + 1
− 2×
3
13 − 1
f)
5 7 1 2
− × +
6 6 14 3
2 
4

h)  4 −   2 − 
3 
3

2 1

i)  3 − 4 ×  ÷
3  12

3 7
−
4 8
k)
5 11 23
+ +
2 4 8
7 1
+
l) 3 9
7
−3
3
Exercise 2 Calculate, and give the results in their simplest form (power of a whole number, standard form)
1 
a) 6 − 4  − 1
4 
c)
2
3,2 ×10 −3 × 5 × (10 2 ) 3
4 × 10 − 2
(2 × 5 )
e)
( 4 ×10 )
2
2
−4 2
−3 3
2
4
90

g) 3  2 −  −
7
49

b)
7 × ( 7 −2 ) −4
711
d) −
4 × 10 −2 × (−5) × 10 7
3 × 10 5
5
 5
f) 
− 
3
 12
3
 (63)−2×66 
h) 
4

 6

2
Fractions and indices Brevet Questions
All these exercises are extracts from brevet exam papers.
Exercise 1 : Calculate, giving the result in its simplest form
 2  2
A= 7 − 3× 8
B = 1 −  ÷  1 + 
4 4 9
 3  3
Exercise 2 : Write D first as a decimal, and then in standard form.
7×10−12×6×105
D=
21×10− 4
Exercise 3 : Calculate and give the result as a fraction in its simplest form
E = 2×4+ 7
3
6
F = 2× 3 − 2
5 4 1− 2
7
Exercise 4 : Calculate and give the result in standard form
H =15×(107)2×3×10−5
23 24
G= 2 ÷
3 3