The document discusses different types of numbers: 1. Natural numbers, whole numbers, integers, fractions, rational numbers, irrational numbers, real numbers, imaginary numbers, prime numbers, and composite numbers. 2. It provides definitions and examples for each type of number, explaining their key properties and relationships. 3. Different types of numbers are distinguished based on their representation in decimal form and whether they can be written as ratios of integers.

1. 1. Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x
A. 4 B. 5 C. 6 D. -4
Solution
6x-27+3x=4+9-x
9x-27=13-x collect like term
9 x + x = 13 + 27
10 x = 40
x = 4
Answer: Option A

2. 2. Solve the equation for x : 19(x + y) + 17 = 19(-x + y) – 21
A. -1 B. -2 C. -3 D. -4
Solution
19x + 19y + 17 = -19x + 19y - 21
38x = -38 =
x = -1
Answer: A

3. 3. The cost of 2 chairs and 3 tables is 1300 Birr. The cost of 3 chairs and 2 tables is 1200
Birr. The cost of each table is more than that of each chair by?
A. 70 Birr B. 75 Birr C. 100 Birr D. 60 Birr
Solution
Chairs=C
Table=T
2C + 3T = 1300 --- (1)
3C + 2T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 100 =>
T - C = 100
T=100 +C
Answer C
Find by your self the cost of each chair is
less than that of each table by?
Write down on comment……………

4. 4. The denominator of a fraction is 1 less than twice the numerator. If the numerator and
denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
 A. 2/3 B. 3/5 C. 4/7 D. 5/9
Solution
Let the numerator =n
denominator =d
d = 2n - 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 1) + 3 => n = 5
d = 2n - 1 => d = 9
Answer D
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COMMENT…………… ADERGU

6. 1. 36men can complete a piece of work in 18 days, in how many days will 27 men
complete the same work?
A. 12 B. 18 C. 22 D. 24
Given
First men =36
First day =18
Second men=27
Required
Second day=?
Solution
Less men, more day(indirect proportion)
27:36=18:X
27/36=18/X
27*X=36*18
X=648/27=24
Answer=D
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7. 2. 39 persons can repair a road in 12 days, working 5 hour per days. In how many
days will 30 persons, working 6 hour per day, complete the work?
A. 12 B. 13 C. 15 D. 17
Given
First persons =39
First day =12
Working hour=5hr/day
Second persons=30
Working hour=6hr/day
Required
Second day=?
Solution
Less person, more day(indirect proportion)
More working hour : less days
30:39=12*5:X*6
30/39=12 day*5 hour/day/X*6hour/day
30*6*X hour/day=39*60 hours
X=2340/180 hour*days/hours
X=2340/180
X=13 Days

8. 3. A person a crosses a 600m long a street in 5 minutes, what is his speed in km/hr.
A. 3.6km/hr. B. 7.2 km/hr. C. 8.4 km/hr D. 10 km/hr.
Given
Distance=600m
Time=5minutes=300sec
Required
speed=?
Solution
Speed=distance/time
V=d/t
V=600m/300s
V=2m/s
Converting m/s to km/hours
V=2 km/1000/hour/3600
V=2*3600/1000 km/hr
V=2*18/5 km/hr
V=36km/5hour
V=7.2 km/hr
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10. 1. A train 360m long is running at the speed of 45 km/hr. in what time will it pass a
bridge 140m long?
A. 40 sec. B. 42sec. C. 45sec D. 48sec
Given
Distance=(360+140)=500m
speed=45km/hr
Required
time=?
Solution
Speed=distance/time
time=distance/speed
Solution
Converting km/hr to m/s
V=(45*5/18)m/s=25/2 m/s
Time=distance/speed
Time=500m*2s/25m
Time=40sec.
Answer A OR
Time=distance/speed
Time=0.5km/45km/hr
Time=5km/10*1/45 hr/km
Time=1/2*1/45 hr
Time=1/90hr
Time=0.0111111111………..hr
Converting hour to secod
1hour=3600second
0.01111111…hr=m
M*1hour=3600sec*0.0111111hr
M=39.999999hour* second/1hour
M=40second

11. 2. What is the number that is one half of one quarter of one tenth of 400?
A. 4. B. 5 C. 6 D. 10
Given
M=400
N=1/10, 1/4/1/2.
Required
N of 400=?
Solution
Of in this context multiplying
Solution
1/10 of 400=400*1/10=40
¼ of 40=40*1/4=10
½ of 10=10*1/2=5
So Answer= B OR
=400*1/10*1/4*1/2
=400*1/80=400/80=5
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12. 3. What is the 7% of 800?
A. 38.4. B. 5.6 C. 56 D. 116.5
Given
M=800
N=7%.
Required
N of 800=?
Solution
Of in this context multiplying
Solution
7% of 800=800*7/100
=8*7
=56
Answer= C
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13. 3. What percentage of 60 is 24?
A. 60%. B. 40% C. 400% D. 25%
Given
M=24
x=60.
Required
N of 60=24?
Solution
Of in this context multiplying
Solution
N of 60= 24
N*60=24
N=24/60
N=0.4
N=0.4*100%
N=40%
Answer= C
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15. Types of Numbers
Numbers are of various types depending upon the patterns of digits that
are used for their creation.

16. Zero is the number that represents no amount or no objects. Another
name for zero in math is thus “null,” as it represents the absence of
any number.

17. Natural Numbers are the range from 1 to infinity.
 These numbers are also called Positive Numbers or Counting
Numbers.
 Natural Numbers are represented by the symbol N.
Example: 1, 2, 3, 4, 5, 6, 7, and so on.

18.  Whole Numbers: Whole Numbers are basically the Natural
Numbers, but they also include ‘zero’.
 Whole numbers are represented by the symbol W.
Example: 0, 1, 2, 3, 4, and so on.

19. Integers: Integers are the collection of Whole Numbers plus the
negative values of the Natural Numbers.
 The range of Integers is from the Infinity at the Negative end and
Infinity at the Positive end, including zero.
 Integers do not include fraction numbers i.e. they can’t be written in
a/b form.
 Integers are represented by the symbol Z.
Example: ...,-4, -3, -2, -1, 0, 1, 2, 3, 4,...

21. Fractions: Fractions are the numbers that are written in the form of a/b,
where, a belongs to Whole numbers and b belongs to Natural Numbers,
 b can never be 0.
 The upper part of the fraction a is termed as a Numerator whereas
the lower part b is called Denominator.
Example: 1/2, 3/7, 8/3, etc.

22. Rational Numbers: Rational numbers are the numbers that can be
represented in the fraction form i.e. a/b. Here, a and b both are integers
and b≠0.
 All the fractions are rational numbers but not all the rational
numbers are fractions.
Example: -2/5, 0.54, 1/5, 13/4, ...
 Terminating decimal፡ የሚቆም አስርዮሽ
 Recurring decimal፣ የሚደጋገም አስርዮሽ

23. Irrational Numbers: Irrational numbers are the numbers that can’t be
represented in the form of fractions i.e. they can not be written as a/b.
Example: √2, √3, √.434343, e, π...
 Non-terminating decimal ፡ የማያቋርጥ አስርዮሽ
 Non-recurring or non- repeating decimal:የማይደጋገም
አስርዮሽ

25. Real and Imaginary Numbers: Real numbers are the numbers that
can be represented in the decimal form.
 numbers include whole numbers, integers, fractions,
 All the integers belong to Real numbers but all the real numbers do
not belong to the integers.

26. Complex Numbers
Complex Numbers are combination of Real Number and an Imaginary Number.
1 + i 39 + 3i 0.8 − 2.2i −2 + πi √2 + i/2
Examples:

27. Prime Numbers : are natural number greater than one.
 it has only two factors that is one and the number itself.
Zero is neither prime nor a composite number.
Example: 2, 3, 5, 7……….
The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

28. Composite Numbers
Composite number is natural number which has more than two factors.
There are two types of composite numbers:
1.Even composite numbers
2.Odd composite numbers
Even Composite numbers
The even numbers that are not prime numbers are called even composite numbers.
For example, 4, 10, 16, 28, 56, etc.

29. Odd Composite numbers
The odd positive integers or the odd numbers that are not prime numbers are called odd
composite numbers.
For example, 9, 21, 33, 45, etc.