SUBJECT: NUMBER THEORY
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TOPIC : RATIOS
LESSON: Writing down ratios by
comparing two or more quantities or qualities.
PREVIOUS KNOWLEDGE: Students can
evaluate and simplify fractions.
LESSON OBJECTIVES: By the end of the
lesson, students should be able to do the following:
>,,,, down ratios by comparing two or more quantities or qualities.
>apply
ratios to solve problems
TEACHING AIDS: Chalkboard,
TEACHING METHOD: Demonstration, Questioning, Group discussion,
and Assignment Method.
GRADE LEVEL: 7
DURATION: 45 Minutes
DATE:
INTRODUCTION:
>The fraction
2/5 can be read as “2 is to 5”, and written as 2:5
>The
fraction 7/4 can be read as “7 is to 4”, and written as 7:4
The statements
2:5 and 7:4 are called ratios. The position of a number in a ratio is very
important. That is to say 2:5≠5:2. Similarly, 7:4≠4:7. The word ratio is used
to describe a fraction. If the ratio of a boy’s height to his father’s height
is 3:5, the he is 3/5 as tall as his father.
PRESENTATION:
Definition:
A ratio compares two or more quantities or qualities by division. The order in
which the comparison is made is important. For example 2:5≠5:2 or 2/5≠5/2.
Ratios have no units of measurement.
If quantities to be compared or written as
ratio are given indifferent units, they must be converted to the same unit
before the ratio is written correctly.
Example 1: Write each of the following as
ratio; i) 3 m: 6 cm, ii) 450 cm: 3 m
Solution.
i)
3 m:6 cm (change units to cm)
3 m:
6 cm=300 cm: 6 cm
3 m:
6 cm=300 cm/6 cm
3 m:
6 cm=300/6(units cancel out.)
3 m:
6 cm=50/1
3 m:
6 cm=50:1 answer.
ii)
450 cm:3m =450 cm:300cm
450 cm:
3 m=450 cm/ 300 cm
450 cm:
3 m=450/300 (units cancel out)
450 cm:
3 m=45/30
450 cm:
3 m=3/2
450 cm:
3 m=3:2 answer.
Example 2: Express each of the following to
simple ratios, simplifying your answer as far as possible.
i)
90 seconds to 25 minutes
ii)
2 hours to 45 minutes
iii)
4 hours to one day
iv)
4 days to one week
v)
4 days to 4 weeks.
Solution
Always convert all to the smaller unit
of measurement.
i)
90 seconds to 25 minutes= 90 seconds/(25×60)
seconds
90 seconds
to 25 minutes=90/1500(seconds cancel out)
90 seconds
to 25 minutes=9/150
90 seconds
to 25 minutes=3/50
90 seconds
to 25 minutes= 3:50 answer.
ii)
2 hours to 45 minutes=(2×60)minutes/ 45minutes
2 hours
to 45 minutes=120 minutes/ 45 minutes
2 hours
to 45 minutes=120/45 (minutes cancel out)
2 hours
to 45 minutes=8/3
2 hours
to 45 minutes=8:3 answer
iii)
4 hours to one day=4 hours/(1×24)hours
4 hours to
one day=4 hours/24 hours
4 hours
to one day=4/24
4 hours
to one day=1/6
4 hours
to one day=1:6 answer.
iv)
4 days to one week=4 days/(1×7)days
4 days to
one week=4 days/7 days
4 days
to one week=4:7
v)
4 days to 4 weeks=4 days/(4×7)days
4 days
to 4 weeks=4 days/28 days
4 days
to 4 weeks=4/28
4 days
to 4 weeks=1/7
4 days
to 4 weeks=1:7 answer.
Example 3: In a class, there are 30 girls and
40 boys.
a) What is
the ratio of the number boys to the number of girls?.
b) What is
the ratio of the number of girls to the number of boys?
c) What is
the ratio of the number of girls to the total number of students?
Solution
a)
Number of boys/Number of girls=40/30
Number of boys/Number of girls=4/3
Ratio of boys to girls=4:3 answer.
b)
Number of girls/Number of boys =30/40
Number of girls/Number of boys =3/4
Ratio of boys to girls=3:4. Answer.
c)
Total number of students =30+40=70.
Number of girls /Total number of students=30/70
Number of girls/Total number of students=3/7
Ratio of girls to total number of students=3:7 answer.
Example 4: A
man weighs 100 kg and his son weighs 25 kg less than him self. What is the ratio
of the son’s weight to his father’s weight?
Solution
Weight of
man=100 kg
Weight of
son= (100 kg-25 kg) =75 kg
Son’s weight to father’s weight=75 kg/100 kg
Son’s weight
to father’s weight=75/100
Son’s weight
to father’s weight=3/4
Ratio of
son’s weight to father’s weight=3:4 answer.
We can
divide items into given ratios.
Example 1:
Divide 200 kg of meat in the ratio 1:3:4.
Solution
Item to be
shared 200 kg of meat
Ratio; 1:3:4
Sum of
ratio; 1+3+4=8
First part;
1/8 of 200 kg=1/8×200 kg=25 kg
Second part;
3/8 of 200 kg=3/8×200 kg=75 kg
Third
part;4/8 of 200 kg=4/8×200 kg=100 kg.
Example 2:
If $143 is divided in the ratio of 2:4:5.What is the difference between the
largest share and the smallest share.
Solution
Amount to be
shared=$143
Ratio; 2:4:5
Sum of
ratio; 2+4+5=11
First share;
2/11× $143=$26
Second
share; 4/11×$143=$52
Third
share;5/11×$143=$65.
Smallest
share=$26, Largest share=$65
Difference=$65-$26
=$39.
Example 3:
If 5/8 of the children in a school are boys, what is the ratio of boys to
girls?
Solution
Whole=1
Fraction
representing boys=5/8
Fraction left=1─5/8=3/8.
Fraction
representing girls=3/8.
Ratio of
boys to girls = 5/8÷3/8
Ratio of boys to girls =5/8×8/3
Ratio of
boys to girls =5/3 or 5:3.
Example 4:
If x: 3=12:
x .Calculate the positive value of x.
Solution
x: 3=12: x
x/3 =12/x
x2 =12×3
x2=36
x=±6
x=6
EVALUATION
a)
Write down each of the following as a ratio; i)
20 cm to 5 m , ii) 30 minutes to 3 hours , ii) 2 weeks to 1 month.
b)
Divide 180 kg of flour in the ratio 1:2:3:4 and
calculate the difference between the largest share and the smallest share.
c)
A man and a woman share a bingo prize of $1000
between them in the ratio of 1:4.The woman shares her part between her self,
her mother and her daughter in the ratio 2:1:1.How much does her daughter
receive?
d)
A man and his wife share a sum of money in the
ratio 3:2.If the sum of money is doubled, in what ratio should they divide it
so that the man still receives the same amount?
e)
If y: 18=8:y. Calculate the positive value of y.
SUMMARY
Ø
A ratio has no units
Ø
Always change the units of measurement into a
common unit before writing out ratios.
Ø
Ratio can be used to share items or properties.
>The knowledge of ratio can help a family head put order in his family by sharing his property well after he is no more.
>The knowledge of ratio can help a family head put order in his family by sharing his property well after he is no more.
CONCLUSION
Assignment: a) Write each of the following as ratio;
i)1 day to 30 minutes, ii) 1 week to 10 hours
b) $400 is divided
between Ann, Brian and Carol so that Ann has twice as much as Brian, and Brian
has three times as much as Carol.
How much does Brian receive?
c) A cake weighing 550 g
has three ingredients: flour, sugar, and raisins. There is twice as much flour
as sugar and one and the half times as much sugar as raisins. How flour is
there?
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