To find missing number in proportions, first we have to know about the following terms.
Proportion :
An proportions is an equation in which two ratios are equal to each other.
For example, a : b and c : d are equal, they will be proportion. We can write it as
a : b = c : d
To simplify it further, we can write ratios as fractions and do cross multiplication.
Equivalent fractions :
A fraction that is the same as another fraction with a different denominator.
Find the missing number in each of the following proportions :
Problem 1 :
3/5 = x/20
Solution :
We can do this problem in two ways.
Method 1 :
Using cross product :
3/5 = x/20
Doing cross multiplication, we get
3 (20) = 5 x
Dividing by 5 on both sides, we get
3(20)/5 = x
x = 3(4)
x = 12
So, the missing value is 12.
Method 2 :
Finding equivalent fraction :
Here the denominator of the first fraction is 5, the second fraction is 20.
By multiplying 5 by what, we will get 20.
So, multiply numerator and denominator of the first fraction should be multiplied by 4 to get 20.
(3/5) ⋅ (4/4) = 12/20
So, the missing value is 12.
Problem 2 :
x/18 = 2/9
Solution :
Doing cross multiplication, we get
x/18 = 2/9
9x = 2(18)
Dividing by 9 on both sides, we get
x = 2(18)/9
x = 36/9
x = 4
Problem 3 :
8/x = 3.2/4
Solution :
Doing cross multiplication, we get
4(8) = 3.2x
Dividing by 3.2 on both sides
32/3.2 = x
320/32 = x
x = 10
Problem 4 :
x/45 = 16/40 = 24/y
Solution :
x/45 = 16/40 = 24/y
Equating the first two fractions, we get
x/45 = 16/40
Multiplying by 45 on both sides, we get
x = (16/40) ⋅ 45
x = 18
Equating the second and third fractions, we get
16/40 = 24/y
Doing cross multiplication, we get
16y = 24(40)
Dividing by 16 on both sides, we get
y = 24(40)/16
y = 60
Problem 5 :
16/36 = x/63 = 36/y = z/117
Solution :
16/36 = x/63 = 36/y = z/117
By equating the first two fractions, we get
16/36 = x/63
Multiplying by 63 on both sides, we get
(16/36) ⋅ 63 = x
x = 28
Equating 2nd and 3rd fraction, we get
x/63 = 36/y
Here x = 28
28/63 = 36/y
Doing cross multiplication, we get
28y = 36(63)
Dividing by 28 on both sides, we get
y = 36(63)/28
y = 81
Equating 3rd and 4th fraction, we get
36/y = z/117
Here y = 81
36/81 = z/117
Doing cross multiplication, we get
(36/81)⋅117 = z
z = 52
Problem 6 :
20m : 70m = $8 : $x
Solution :
20m : 70m = $8 : $x
20/70 = 8/x
Doing cross multiplication, we get
20x = 8(70)
Dividing by 20 on both sides, we get
x = 8(70)/20
x = 28
Problem 7 :
The shadow of a 3m long stick is 4m long. At the same time of the day, if the shadow of a flagstaff is 24 m long, how tall is the flagstaff?
Solution :
Length of flag staff : length of shadow = 3 : 4
Length of shadow of flagstaff = 24 m
Length of flagstaff = x
3 : 4 = x : 24
Doing cross multiplication, we get
3/4 = x/24
Multiplying by 4 on both sides, we get
3(24) = 4x
Dividing by 4 on both sides, we get
3(24) / 4 = x
x = 18 m
So, length of flag staff is 18 m.
Problem 8 :
In a school, the ratio of the number of large classrooms to small classrooms is 3:4. If the number of small rooms is 20, then find the number of large rooms.
Solution :
Solution :
Ratio between larger class rooms to small class rooms = number of class room to small rooms
Let x be the number of large class rooms.
3 : 4 = x : 20
3/4 = x/20
Doing cross multiplication, we get
20(3) = 4x
Dividing by 4, we get
x = 20(3)/4
x = 15
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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