Math 6th
Unit 1 and 2
By
‫محمد عبد اللطيف‬
The ratio
The ratio is Comparing between two quantities of the same type or the same
unit.
:‫و نقدر نقول‬
.‫أوها مقاروت بيه عدد األجزاء التى صيحصل عليها كل حد مه حدود الىضبت‬
 If Omar has 6 pounds and Hany has 9 pounds.
So, the number of all parts are ( 6 + 9) = 15 parts
This 15 parts will contribute between omar and Hany.
Omar will take 6 parts , Hany will take 9 parts
Then we can express the ratio as:
Omar : Hany = 6: 9
.‫الىضبت يمكه أن تكىن بيه حديه أو اكثر‬
 The ratio between the length of Ali and Hany is
Ratio between the length of Ali , Hany and Ahmmed is

2:3
2:3:5
‫ و لها خىاص الكضىر مه‬fraction ‫الىضبت بيه عدديه يمكه أن تكتب على شكل كضر‬

.‫حيث االختصار و التبضيط والمقاروت‬
2 :3
First term
Second term
2
3
2 to 3
.‫الىضبت يجب فيها الترتيب‬

.‫الىضبت بيه االرقام الكبيرة البد مه اختصارها‬

. units ‫الىضبت ليش لها تمييز‬

‫يجب تىحيد وحداث القياس بيه حدود الىضبت‬

2:3‡ 3:2
Adel saves : ahmed saves : Hany saves
180
:
144
:
108
15
:
12
:
9
5
:
4
:
3
Dad’s tall
1.8 m
1.8
: mum’s tall
: son’s tall
:
:
:
:
1.6 m
1.6
1.2m
1.2


decimal number ‫ ) و ال تكىن كضر عشري‬whole number ( ‫الىضبت يجب أن تكىن عدد صحيح‬

. fraction ‫و ال كضر اعتيادي‬
1
Excercises
[1] complete the following:
 The first term in the ratio 4 : 7 is ………….
 If the first term of a ratio is 7 and the second term is 3 then this ratio is ……..
 If x = half y , then
x
= …………
y
 If a equals third of b , then a : b = …………
 If Ali's weight : Sayed's weight = 2 : 5 ,then Ali =
...
Sayed
...
[2] complete using the opposite figure:
i) AB : BC = ………
ii) BC : AC = ………
iii) AB : AC = ………
iv) AC =
5 cm
...
AB
...
A
...
v) AC = ... BC
...
AB
vi)
= ...
perimeter
BC
...
vii) perimeter =
...
BC  AC
...
iix) perimeter =
...
4 cm
[3] Find the ratio in simplest form:
30 : 40
150 : 450
200 : 150
1.25 : 1.5
0.25 : 2.5
L.E 6 : L.E 30
1.5 kg : 125 gm
1
metre : 150 cm
4
1.5 : 0.3
p.t 500 : L.E 2
1250 ml : 4.5 L
12 , 60
4500 , 6000
250 cm , 3m
7 feddans , 336 kirats
2 week : 35 days
3 cm
B
C
630 piastres , 9 pounds
2.5 dm2 , 11250 cm2
2
[4] In one of the classes of the first primary grade the number of boys is 15 pupils and the
number of girls is 20 pupils. Calculate :
(a) The ratio between the number of boys to the number of girls.
(b) The ratio between the number of girls to the number of all pupils in the class.
(c) The ratio between the number of boys to the number of all pupils in the class.
3
[5] An accountant in a bank earn LE 2000 as a monthly salary. He spends 4 his salary and
saves the remainder. Find :
(a) The ratio between what the accountant spends to his monthly salary.
(b) The ratio between what he saves to his salary.
(c) The ratio between what he spends to what he saves.
[6] The length of a rectangle is 80 cm and its width is 0.6 m. find out:
a) The perimeter.
b) the ratio of length to the width.
c) The ratio of its length to its perimeter.
d) The ratio of its width to its perimeter.
[7] a square of side length 4cm and a rectangle whose dimensions are 6 cm and 3cm Find:
(a) The ratio between the perimeter of the square and the perimeter of the rectangle.
(b) The ratio between the area of the square and the area of the rectangle.
(c) The ratio between the length of the rectangle and its perimeter.
[8] The total number of boys and girls in a school is 480 and the
number of boys in this school is 320 . find
a) The ratio between the number of boys and that of girls
b) The ratio between the number of boys and the total number of pupils .
c) The ratio between the number of boys and the total number of pupils .
[9] complete:
a)
The ratio between the length of two sides of a square is …………: …………
b)
The ratio between the side length of a square and its perimeter is …………:
…………
c)
The ratio between the length of two sides of an
equilateral triangle is …………: …………
[10] The ratio between side length of a square and its perimeter = …… : ……
The ratio between side length of equilateral triangle and its perimeter = …… : ……
The ratio of circumference of a circle to its diameter = ….. : ……. Or
...
...
3
[11] Find in the simplest form the ratio between each of the following:
(a) 250 p.t and 7 ½ pounds.
(b) 2 ½ hours and 75 minutes.
(c) 12 kirats and 1.25 feddan.
(d) 75 kirats and 16 sahms
[12] Write the ratio between the two numbers in each of the following cases
[13] Put in simplest form
Put in simplest form
[14] Hoda, Mona and Thanaa participated in a commerce. Hoda paid LE 1500, Mona paid LE
2000 and Thanaa paid LE 2500. At the end of the year the loss of the company was LE 1200 Find
the share of each of them from loss.
4
The value of the part = ‫قيمة أي كمية فً انىسبة‬
‫انىسبة انخاصة بها‬
.......‫قيمة أي كمية ممكه أن تكىن‬
) first term or second term or third term ( ‫) قيمة أي حذ مه حذود انىسبة‬1
)‫) قيمة انفزق بيه حذيه مه حذود انىسبة ( انفزق بيه بيه انثاوي وانثانث‬2
.‫) قيمة مجمىع كم انىسب‬3
‫ نطلعوا من قيمة حد من حدود النسبة‬each part ‫ قيمة‬
 If the ratio among the heights of three buildings is 3 : 4 : 5 and if the height of the first
building is 12 metres . Calculate the heights of the second and the third building.
------------------------------------- solution -------------------------------------------Ratio
metres
first
second
3
:
4 :
12 :
? :
third
5
?
The value of each part = 12 = 4 m ‫قيمة الحد االول‬
‫نسبة الحد االول‬
3
The height of second = 4 x 4 = 16 m
The height of third = 4 x 5 = 20 m
----------------------------------------------------------------------------------------- The ratio between the number of boys and that of girls in a school is 9 : 7 . If the
number of boys is 378 . Find the number of girls .
------------------------------------- solution --------------------------------------------Ratio
numbers
boys girls
9
:
7
378 :
?
The value of each part = 378 = 42 kids
9
The number of girls = 42 x 7 = 294 girls
----------------------------------------------------------------------------------------- If the ratio between the weight of Hani and the weight of Ahmed is 5 : 6 and if the
weight of Ahmed is 60 kilogrames. Calculate the weight of Hani.
----------------------------------------------------------------------------------------- The ratio of the sides of a certain triangle is 2:7:8. If the longest side of the
triangle is 40 cm, how long are the other two sides?
----------------------------------------------------------------------------------------- If the ratio among the share of Hani and the share of Sherif and the share of Khalid is 3
: 5 : 7 and if the share of Hani is LE 24 caluclate the share of each of Sherif and Khalid.
----------------------------------------------------------------------------------------- If the ratio among the heights of three buildings is 3 : 4 : 5 and if the hight of the first
building is 12 metres calculate the heights of the second and the third building.
difference
5
‫ نطلعوا من الفرق‬each part ‫ قيمة‬
 The ratio between the height of two buildings in a town is 4:7 , if the difference
between the heights is 9 metres . find the height of each of them.
------------------------------------- solution --------------------------------------------Ratio
metres
first
second
4
:
7
? :
?
difference
7–4=3
9 metres
The value of each part = 9 = ‫ = قيمة الفرق‬3 m
3
‫نسبة الفرق‬
The height of the first building = 3 x 4 = 12 m
The height of the second building = 3 x 7 = 21 m
----------------------------------------------------------------------------------------- A rectangular shaped piece of land the ratio between its length and its width is 9 : 7 . If
the difference between the length and the width is 18 metres. Calculate each of the
length , the width and the perimeter of the land.
----------------------------------------------------------------------------------------- If the ratio among the ages of Hoda, Mona and Ola is 2 : 4 : 5 and if the difference
between the age of Hoda and that of Mona is 8 years. Calculate the age of each of Hoda,
Mona and Ola.
sum total ‫ نطلعوا من المجموع‬each part ‫ قيمة‬
 Two wire pieces , the ratio between their length is 5 : 9 . if the sum of their lengthes is
126 metres. Calculate the length of each piece.
------------------------------------- solution --------------------------------------------Ratio
metres
first
second
5
:
9
? :
?
sum
5+9 = 14
126 metres
The value of each part = 621 = ‫ = قيمة المجموع‬9 m
61
‫نسبة المجموع‬
The length of the first wire = 9 x 5 = 45 m.
The length of the second wire = 9 x 9 = 81 m.
----------------------------------------------------------------------------------------- A primary school has 540 pupils. If the ratio between the number of boys to the
number of girls is 4 : 5 , calculate the number of each boys and girls.
----------------------------------------------------------------------------------------- If the ratio among the measures of the angles of a triangle is 5 : 6 : 7 and the measure
of the first angle is 50° . Find the measure of each of the other two angles.
----------------------------------------------------------------------------------------- The ratio between the length and the width of a rectangle is 9 : 5 . If the perimeter of
the rectangle is 56 meters, find out the length and the width of the rectangle, then
calculate its area.
----------------------------------------------------------------------------------------------------- Three persons participated in a commercial (project) with capital LE 60000.
The first paid LE 15000, The second paid LE 25000 and the third paid LE 20000 At the end
6
of the year, the profit was LE 5520 Calculate the share of each of them.
 Find the ratio among the tallness’s of Sahar, Noha and Ola if
The tallness of Sahar : The tallness of Noha
The tallness of Sahar : The tallness of Noha = 2: 3
The tallness of Noha : The tallness of Ola = 6 : 5
------------------------------------- solution --------------------------------------------Saher
2 :
? :
Ratio (6)
Ratio (2)
Noha
3 :
6 :
Ola
?
5
New ratio
12 :
18 :
15
(L.C.M)
Simplest ratio
4:
6:
5
the ratio among the tallness’s of Sahar, Noha and Ola is ( 4 : 6 : 5 )
---------------------------------------------------------------------------------------
 a load of apple fruit weights 280 kg. is distributed among three marchants. The share of
the first = 2/3 the share of the second. The share of the second = 4/5 the share of the
third. Calculate the share of each of them .
------------------------------------- solution --------------------------------------------.‫ وعهيىا أن وكتبها بانطزيقة انعادية و وكمم انبياوات‬، ‫فً هذي انمسأنة انىسبة مكتىبة بطزيقة انكسىر‬
Ratio (6)
Ratio (2)
first
2 :
? :
New ratio (L.C.M)
Kgs
8 :
? :
second third
?
3 :
5
4 :
12 :
?:
15
?:
sum
8+12+ 15=35
280
The value of each part = 280 = ‫ = قيمة المجموع‬8 kg.
35
‫نسبة المجموع‬
The share of the first = 8 x 8 = 64 kg.
The share of the second = 8 x 12 = 96 kg.
The share of the third = 8 x 15 = 120 kg.
----------------------------------------------------------------------------------------- The number of pupils in the grades four, five, and six) in a primary school is 399 pupils
If the number of the pupils of the fourth grade .Equals
grade and the number of pupils of the fifth grade equals
sixth grade calculate the number of pupils of each grade.
the number of pupils of the fifth
the number of pupils of the
----------------------------------------------------------------------------------------- A fruit seller has three kinds of fruit (banana, grapes and Guava)
If the ratio between the weight of banana to the weight of grapes is 2 : 3 and the ratio
between the weight of grapes to that of guava is 2 : 4 . Find the ratio among the weights
of banana, grapes and guava.
-----------------------------------------------------------------------------------------7
 The number of pupils in the grades four, five, and six) in a primary school is 399 pupils
If the number of the pupils of the fourth grade .Equals
grade and the number of pupils of the fifth grade equals
the number of pupils of the fifth
the number of pupils of the
sixth grade calculate the number of pupils of each grade.
----------------------------------------------------------------------------------------- The ratio between the weight of Alaa and Eman is 5 : 6 and The ratio between the
weight of Mona and Eman is 3 : 4 . If the weight of Alaa is 40 kg .Find the weight of Eman
and Mona .
----------------------------------------------------------------------------------------- Aly, Hamed and Salah paid LE 3500 , LE 4500 and LE 6000 to set up a trade, at the end of
the year the Salah profited LE 150 more than Hamed .
Find out the share of each of them in the profit.
----------------------------------------------------------------------------------------- Samy and Basem set up a trade, Samy paid as much as Basem paid . At the end of the
year the profit was LE 7900 ,If Samy took LE 700 from the profit for management and the
rest of the profit was divided with respect to the capital . Find the share of each in the net
profit.
------------------------------------------------------------------------------------------
8
The proportion
Proportion is ratio = ratio
1 = 2 =3 = -- = -2 4 6 -- -- First proportion
second proportion
third proportion
2 = 3
6 = 9
fourth proportion
 Find the missed term denoted by x in the following proportion
=
------------------------------------- solution --------------------------------------------We will make across multiply:
2 x = 6 x 10
X=
X = 30
----------------------------------------------------------------------------------------- If the numbers 4 , x , 12 , 18 are proportional find the value of x .
----------------------------------------------------------------------------------------- in a shop for selling juice . 2 kgs of ornges have been squeezed to get 6 glasses of
orange juice to clients. If 5 kgs of oranges have been squeezed , how many glasses of juice
will be be gotten to offer to clients and how many kilograms of oranges are needed to get
27 glasses of orange juice to the clients?
------------------------------------- solution --------------------------------------------Rule : when we have two ratios , one of them is completed we to make a proportion.
1) We have two ratios:
first :
Second :
2) make a proportion :
2 = 5
6
y
3) Make across multiply
2y=6x5
2y = 30
Y = 15 glasses
kgs of oranges
= 2
Number of glasses
6
5 kgs oranges
y glasses
9
Exercises
[1] Find x in each of the following proportions
(a)
(b)
[2] Find the missed number (x) for the following numbers to be proportional 6, 8 , 3 , x
[3] Ali bought 5 kg of orange, he paid LE 15 . How much money does he pay to buy 8 kg?
[4] A car consumms 20 litre of Benzin for covering 210 km, How many litre of Benzin
does the car consumm to cover 630 km.
[5] The ratio between Hany's weight to the weight of his father = 3 : 5 what is Hany’s
weight if the weight of his father is 90kg.
[6] A primary school, its building height is 14 metre and the shade of this building at a
certian moment is 5m length. What is the height of a tree in the same moment if its shade
length is 3 metres ?
Exercise (2 - 4)
[7] A piece of building land is distributed between two brothers in the ratio 7:5 . If the
share of the first one exceeds the share of the second by 80 square metre. Find the area of
the land and the share of each of the first and the second.
[8] The number of pupils of a primary school in the 1st, the 2 nd and the 3rd grades is 240
pupils. If the ratio among the three grades is 5 : 4 : 3. Calculate the number of pupils in
each grade.
[9] A father distribute LE 225 among his three sons. The share of the first was third of the
sum and the ratio between the share of the second and the share of the third was 2:3. Find
the share of each them.
[10] for solving the illiteracy problem at a village 3 classes have been opened for solving
this problem, the number of learners was 92.Person. If the number of learner in the 1st class
= the number of learners in the 2nd class .and the number of learners in the 2nd class . =
the number of learners in the 3rd class. Find the number of learners in each class.
[11] In one of our schools, there are 560 students, if the number of girls =
the number of
boys find each of the number of looys and girls?
[12] A Fruit seller sells one kilogram of apple for L.E 10
If the ratio between the price of apple to the price of banana is 5 : 2 ,
find the price of 5 kilograms of banana.
[13] A man died and left a piece of lend for building, its area is 17 kirats. We
recommended for building on orphan house on area equals 5 kirats. The remainder is
distributed between his son and his daughter in the ratio 2:1. Calculate the share of each of
them from the land.
[14] A 30 pound moonling weighs 180 pounds on the earth. How much does a 300
pound Earthling weigh on the moon?
10
Drawing scale
It is the length of drawing : the length in reality.
So it’s a ratio , we will solve these problems like ratios and proportion.
( two ratios , proportion , across multiply)
 an engineering design for a villa is made . if the height of the fence of the villa in the
design is 5 cm and its real height is 3 metres find the drawing scale.
------------------------------------- solution --------------------------------------------Drawing scale = length in drawing = 5 = 1
Length in reality
300
60
----------------------------------------------------------------------------------------- if the drawing scale which is registered on a map of some in habitant’s cities is 1 :
500000 . and if the distance between two cities on this map is 3 cm . find the real distance
between them.
------------------------------------- solution --------------------------------------------Drawing scale = length in drawing
Length in reality
1) We have two ratios
The first one , Drawing scale = length in drawing =
1___
Length in reality
500000
The second , _3_
y
2) make a proportion :
__ 1____ = _3_
500000
x
3) Make across multiply
1 x = 3 x 500000
X = 1500000 cm.
------------------------------------------------------------------------------------------
Exercise (2 - 3)
[1] A picture of me of habitation edifices is taken with a drawing scale 1 : 1000. If the
height of the edifice in the picture is 3 cm. What is its real height?
[2] Ahmed draw a picture to his brother Osama with a drawing scale 1 : 40. If the real
length of Osama is 160 cm, What is his length in the picture?
[3 ] A magnified picture of an insect was taken with enlargement ratio100:1 If the length of
the insect on the picture is 2.5 cm.What is the real length of the insect?
[4 ] If the distance between two cities on a map is 3 cm, and the real distance between
them is 9 km. Find the drawing scale of the map and what does it mean? Then If the
11
distance between two cities on the same map is 5 cm. calculate the real distance between
the two cities.
[5 ] Complete the following table.
[6] On a map, one inch represents 150 miles. If Las Vegas and Reno are five inches
apart on the map, what is the actual distance between them?
The rate
It is the ratio between two quantities of different kinds and the unit of rate is the unit of
the first quantity per each unit of the second quantity .
‫ ووحدة قياسى تساوى‬، ‫هو النسبة بين كميتين مختلفتين فى وحدة القياس‬
 A car covered 180km at 3 hours , so the speed (rate) =
= 60 km./ hour.
 A car consumes 20 liter of fuel to cover a distance of 270 km. Calculate the average
distance per one liter of fuel .
------------------------------------- solution --------------------------------------------1) We have two ratios
20 : 270 ,
1 : Y
2) make a proportion :
=
3) Make across multiply
20 Y = 270 x 1
2 Y = 27
Y=
= 13.5 km.
----------------------------------------------------------------------------------------- Hassan spends LE 45 within three days what is the rate of what Hassan spends per day?
A plough for agricultural land, ploughs 6 feddans within 3 hours.Find the rate of work of
this plough. If another plough, ploughs 10 fedan within 4 hours. Which of them is better
than the other.
12
A computer colour printer prints 12 paper each 4 minutes. Find the rate of work of this
printer.
David read 40 pages of a book in 5 minutes. How many pages will he read in 80
minutes if he reads at a constant rate?
If there should be three calculators for every 4 students in an elementary school, how
many calculators should be in a classroom that has 44 students? If a new school is
scheduled to open with 600 students, how many calculators should be ordered?
 If your car can go 350 miles on 20 gallons of gas, at that rate, how much gas would
you have to purchase to take a cross country trip that was 3000 miles long?
The percentage
It is a ratio , its first term is a number of parts and its second term is 100 parts.
.‫ جزء‬111 ‫ وحذها انثاوي‬، ‫هً وسبة حذها األول عذد مه األجزاء‬
Examples
Number of L.E profits : 100 L.E
Number of L.E losses : 100 L.E
Number of girls pupil : 100 pupils
Number of apples : 100 fruits
Number of red balls : 100 balls
--------------------------------------------------------------------------------------------- In a class the number of boys was 35% from the total number of pupils .
- What is the percentage of girls?
- Convert each of the previous percentage into a common fraction then to a decimal.
------------------------------------- solution --------------------------------------------- The percentage of girls = 100% - 35% = 65%
- Converting the percentage into to a common fraction
The percentage of boys is 35% =
The percentage of girls is 65% =
- Converting the percentage into a decimal
The percentage of boys is 35% =
The percentage of girls is 65% =
--------------------------------------------------------------------------------------------- A shopkeeper of cars bought a car for LE 45000. Then he spent LE 3000 for repairing it.
Then he sold it for 50000 pounds Calculate the percentage of profit.
------------------------------------- solution --------------------------------------------- All costs of the car = 45000 + 3000 = 48000 L.E
- The profit of the car = 50000 – 48000 = 2000 L.E
1) two ratios:
( 48000 : 2000 ,
100 : Y )
2) make a proportion :
=
3) Make across multiply: 48000 y = 2000 x 100
48y = 200
y=
= 4.16
Exercise (2 - 5)
13
[1] In a school trip, 12 pupils from 35 pupils in a class have participated find the
percentage of the participant pupils.
[2] Complete the following table as in the example
[3 ] Magid bought a T- shirt, labelled on a small card on it (made of cotton and synthetic).
The percentage of the synthetic 40 % only calculate the percentage of cotton then find the
equivalent fraction to each percentage.
[4] If the percentage of the number of girls in a class whish is mixed is 67% find the
percentage of the number of boys in this class.
[5 ] In a conditioned carriage in a train the number of occupied seats is 46 seats if the
number of seats of the carriage is 60 seats . calculate.
a) The percentage of the occupied seats.
b) The percentage of the empty seats related to the number of occupied seats.
[6] A man died and left a piece of land whose area is 48 kirat. He recommended, the half
of this area is for building a school, the remained is distributes as follows.
the remainder is for his wife, the remainder after That is distributed among his two sons
and his three daughters such that the share of the boy is twice the share of the girl.
Calculate the share of each of them.
[7] Bob had 21 problems correct on a math test that had a total of 25 questions, what
percent grade did he earn? (In other words, how many questions would we expect
him to get correct if there were 100 questions on the test?)
14
more exercises
1) On last week’s math test Carol had 21 correct out of 25 problems. What percent
grade did she receive.
2) Bob received an 85% on his history exam. If there were 20 questions, how many
did he have correct?
3) John receives a 5% commission on his sales. If he received $30. How much did
he sell?
4) Bob received an 84% on his history exam. If there were 50 questions, how many
did he have wrong?
5) If you receive 20% off on a pair of pants that cost $25, how much would you pay?
6) Jessie earns $25 per week. If 8% is deducted for social security, what is the amount
Jessie receives?
7) A radio costs $20, Harold buys it for $16. What percent off did he receive?
8) A quarterback completed 18 of 25 passes in a football game. What percent of the
passes did he complete?
9) Mrs. Freeze bought a watch for $45, she was charged 10% federal tax and 4%
sales tax. How much did she have to pay altogether?
Exercise (2 - 6)
[1 ] If the percentage of the succeeded pupils in an exam. In Arabic in sixth grade in a
school is 85%. Calculate the percentage of failures then write each of the percentage of
succeeded pupils and failures in the form of a common fraction in its simplest form
[2 ] In an European city, the percentage of ill people by flue is 0.12% writ this percentage
in the form of a common fraction in its simplest form.
[3 ] Write in the form of a common fraction in the simplest form each of the following
percentages 28%, 8.5%, 20.4%
[4 ] Hassan ate 3 pieces of gateaux from a box contains 24 pieces of gateavx in a party of
his birthday. And he distributed 6 pieces on his family. Calculate the percentage of the
number of pieces that Hassan ate and the percentage of the number of pieces eaten by his
family.
[5] Hani did not go to his school for 8 days within the school year. If the number of days
of the school year is 214 days .Calculate the percentage of the number of days in which
Hani was absent.
[6] In a day 12 pupils were absentees from a primary school whose number of pupils is
350 pupils. Calculate the percentage of the present pupils and that for the absentees in
that day.
[7] Khaled bought a flat for L.E 150 000, After selling it he found that the percentage of
his loss was 5% .Calculate the selling price of the flat.
15
General exercises
[1] Write the ratio between the two numbers in each of the following cases in the simplest
form :
(a) 16 and 64
(b) 15 and 105
(c) 128 and 16
[2] Write in the simplest form each of the following ratios :
(a) 2.7 : 18.9
(b) 5 : 14.5
[3] Express in two different ways the ratio between each two numbers:
(a) 14 , 128
(b) 2.4 , 18
(c) 185 , 370
[4] Write in the simplest form each of the following cases :
(a) half km : 250 metres (b) 125 piasters : 5 pounds
(c) 150 grammes : aquarter of kilogram
(d) 2,25 feddans:16 kirats
[5]Calculate : using the opposite two figures :
- The ratio between the number of circles in figure. (A) to the number of
circles in figure (B)
- the ratio between the number of circles in figure (B) to the number of
all circles in the two figures (A) and (B) .
[6] An accountant in a bank earn LE 2000 as a monthly salary. He spends
his salary and saves the remainder. Find :
(a) The ratio between what the accountant spends to his monthly salary.
(b) The ratio between what he saves to his salary.
(c) The ratio between what he spends to what he saves.
[7] Afactory produces 5000 juice cans in 8 hours find the production rate pre hour.
Awater tap is leaking 20 litres of water in 5 hours. find the leaking rate of water pre hour.
please advise them:
More excercises
(1) In an exam of mathematics in one class the ratio among the weaked pupils to those
who succeeded to the excellent pupils was 1 : 4 : 1 , If the number of all pupils in the class
was 30 pupils . Calculate the number of succeeded pupils and the number of weaked
pupils.
(2) The ratio among the lengths of the sides of a triangle is 2 : 3 : 4 . If the perimeter of the
triangle is 54 cm, find the length of each side of the triangle.
(3) A ship for transporting goods among the countries. Consumms 25 litres of fuel to
cover a distance 15km. Calculate the rate of consumption of fuel.
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(4) If the ratio between the tallness of Khalid to the tallness of Ahmed is 2 : 3 and the ratio
between the tallness of Ahmed to the tallness of Hani is 4 : 5. Calculate the ratio between
the tallness of Khalid to that of Hani.
(5) On a trip across the country Joe used 20 gallons of gas to go 300 miles. At this
rate, how much gas must he use to go 3500 miles?
(6) On a map 3 inches represents 10 miles. How many miles do 16 inchesrepresent?
(7) If our class is representative of the university and there are 2 males for every 12
females. How many men attend the university if the female population totals 15,000?
(8) The ratio of length to width of a rectangle is 8:3. Find the dimensions of the rectangle
if the perimeter is 88dm.
(9) Snow is falling at a rate of one inch every 3.5 hours. At this rate how long will it take
for 6.5 inches of snow to fall?
(10) The ratio of width to length in a rectangle is 3:8. If the length of the rectangle is 20
inches, what is the width?
(11) There were 5 boys for every 3 girls in the class. Out of the 56 students in the class,
how many were girls?
(13) Fred paid $72 last week in gas for his car. If he used 56 gallons of gas, how much
did he pay per gallon?
(14) A store sells bars of soap at 4 for $3.56 or 3 for $2.97. What is the unit price of the
soap that is the better buy?
(15) Bob drove 320 miles in 5 hours. At this rate, how far could he travel in three hours?
(16) 1_ cups of sugar will serve 6 people, how many people will 2 _ cups serve?
(17) A 15 pound ham is enough to serve 20 people. How much ham do you need to
serve 50 people?
(18) The ratio length to width of a rectangle is 8:3. Find the dimensions of the rectangle if
the perimeter is 88 inches.
(19) The ratio of men to women in a class is 2:7. Of the 36 students in the class, how
many were women?
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[1] Complete the following table for the corresponding numbers in the two rows of the
table are proportional. Then write some form of this proportion.
[2 ] Find the number x in each of the following cases
a) =
b ) If the numbers 9, 21, 3 and x are proportional
c)
= 15 %
d)
=8
[3 ] If the distance between two cities on a map is 10 cm, the real distance between them
is 120 km, Find the drawing scale of the map. And if the distance between two other cities
on the same map is 6 cm calculate the real distance between them.
[4 ] A picture was take to an artificial scene with a drawing scale 1:100.
If the real length of a tree is 8 meter find its length in the picture.
[5] two persons started a commercial business the first paid LE 5000 and the second paid
LE 8000, At the end of the year the profit was lE 3000. Calculate the share of each of them
from the profit .
[6 ] A company for selling the electric sets It shows T.V for LE 2100. If the percentage of
the profit is 12 % find the buying price of t.v
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Test
(1) In an exam of mathematics in one class the ratio among the weaked pupils to those
who succeeded to the excellent pupils was 1 : 4 : 1 , If the number of all pupils in the class
was 30 pupils. Calculate the number of succeeded pupils and the number of weaked
pupils.
(2) The ratio among the lengths of the sides of a triangle is 2 : 3 : 4 . If the perimeter of the
triangle is 54 cm, find the length of each side of the triangle.
(3) A ship for transporting goods among the countries. Consumms 25
litres of fuel to cover a distance 15km. Calculate the rate of consumption of fuel.
(4) Complete try getting the ratio in each of the following cases :
* 250 gm : kg = ………. : ………
* 16 kirat : 1 feedan = ……….. : ………..
* 2 m : 125 cm = ………. : ……….
* 8 hours : 3 days = …….. : ……….
(5) If the ratio between the tallness of Khalid to the tallness of Ahmed is 2 : 3 and the ratio
between the tallness of Ahmed to the tallness of Hani is 4 : 5. Calculate the ratio between
the tallness of Khalid to that of Hani.
Test
1- Find the missed number (x) if the numbers 3, 4, 9, x are proportional
2- Write in the form of a common fraction in its simplest form each of the following.
33% , 10.5 %
, 75 %
3- The number of pupils of grades first, second and third in a primary school is 475 pupils
If the ratio among the number of pupils in the first grade to those of second grade to
those of the third garde is 6 : 5 : 4 Calculate the number of pupils in each grade.
4- Nahed bought an automatic washing machine for LE 3400 and the discount was 10%
Calculate the original price of the washing marching. Before discount .
5- An edifice of height 12 meters. It's shade at a momoment was 4 meters. What is the
height of a tree neighboured to the edifice if its shade = 2 meter long at the same
moment.
6- Hani, khaled and fady shared a commercial business, Hani, paid LE 30000, Khaled paid
LE 40000 and fady paid LE 5000.At the end of the year the loss was 5000 pounds find the
share of them from the loss.
7- A shop keeper for electric sets sold a refrigerator for LE 3200 If the percentage of his
profit is 6% .find the baying price.
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