Question

How do you know if the pair $\dfrac{3}{2}$ and $\dfrac{{18}}{8}$ forms a proportion ?

Answer 1

Hint: When we have to check whether the fraction pair forms proportion or not , we have to apply a simple rule that is if we multiply the numerator of the first number to the denominator of the second number and when we multiply the denominator of the first number to the numerator of the second number. If we get the same result , then we consider it in proportion.

Complete step by step solution:
We have given the pair $\dfrac{3}{2}$ and $\dfrac{{18}}{8}$ ,
We have to find whether this pair forms a proportion or not.
We know that if we have $\dfrac{a}{b}$ and $\dfrac{c}{d}$ pair then for proportion $a \times d = c \times b$ .Only then , we can say that the pair forms a proportion.
Now , multiply the numerator of the first number to the denominator of the second number ,
We will get ,
$3 \times 8 = 24............(1)$
Now , multiply the denominator of the first number to the numerator of the second number ,
We will get ,
$2 \times 18 = 36...........(2)$
Here , $(1)$ is not equals to $(2)$ ,

Therefore, we can say that the pair $\dfrac{a}{b}$ and $\dfrac{c}{d}$ does not form any proportion .

Note: When we have ratio instead of fraction like $a:b$ and $c:d$ then for checking whether it is in proportion or not. The first term that is $a$ and the fourth term that is $d$ are known as extremes and the second term that is $b$ and the third term that is $c$ are known as means. Then the product of extremes is equal to the product of means.