Question

How do we find the missing number in the following proportion: \[\_\_:8::12:32?\]

Answer 1

Hint:We can solve this question by using the rule or property of proportion.The rule says that the product of means is equal to the product of extremes.

Complete step by step answer:
The question is:
\[\_\_:8::12:32\]
We can also write this expression as:
\[\_\_:8 = 12:32\]
Here we have to assign a variable to the missing number first. So, let’s say that the missing number is \[x\].
Now, the mathematical expression looks like:
\[x:8 = 12:32\]

Now, we will use the rule of product of means and extremes. This rule says that the product of means is equal to the product or extremes: If \[a:b = c:d\] then, the product of means is \[a \times d\] and the product of extremes is \[b \times c\]. When we equal them according to the rule, then we get:
\[ \Rightarrow a \times d = b \times c\]
Here, according to the rule:
\[a = x\,;\,b = 8\,;\,c = 12\,;\,d = 32\]
Now, when we put all the values according to the formula then we get:
\[ \Rightarrow x \times 32 = 8 \times 12\]

Now, we will divide both the terms by \[32\]. This is done to make \[x\] alone so that we get our missing number:
\[ \Rightarrow \dfrac{{x \times 32}}{{32}} = \dfrac{{8 \times 12}}{{32}}\]
Now, we will cancel all the like terms:
\[ \Rightarrow x = \dfrac{{8 \times 12}}{{32}}\]
Now, we will cancel out all the numbers that are divisible from both the numerator and the denominator, and then we will get:
\[ \therefore x = 3\]
So, we got our final answer as \[3\]. This tells us that our missing number is \[3\].

Therefore, our proportion is: \[3:8 = 12:32\] or \[3:8::12:32\].

Note:The above method is very easy when we use the rule of proportion which says that the product of means is equal to the product of extremes. But there is another method through which we can solve it. We can easily take the proportion as \[\dfrac{x}{8} = \dfrac{{12}}{{32}}\] by using the properties of ratio. Then, we can solve for \[x\] and find the missing number.