FIND THE MISSING NUMBER IN PROPORTION

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 2^nd and 3^rd 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 3^rd and 4^th 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