Question

Write True (T) or False (F) against each of the following statement
$21:6 = 35:10$
A) True
B) False

Answer 1

Hint: Here we are given two ratios and we are asked to determine whether they are equal or not. When two ratios are equal, they are called proportions. So, we need to prove that the given ratios are proportions. For that first of all, express both the ratios in fraction form and then express them in their simplest form.

Complete step by step solution:
In this question, we are given two ratios and we need to determine whether these ratios are equal to each other or not. First of all, let us see what ratio is.
When a fractional number is represented by a:b form, it is said to be a ratio. And when two ratios are equal, they are called proportions. So, here we need to check whether $21:6 = 35:10$ is a proportion or not.
Now, to check this we need to first convert ratio into fraction. For that, we simply write the first term as numerator and the second term as denominator.
$
   a:b = \dfrac{a}{b} \\
   \Rightarrow 21:6 = \dfrac{{21}}{6} \\
 $
And
$ \Rightarrow 35:10 = \dfrac{{35}}{{10}}$
Now, we can compare them.
$ \Rightarrow \dfrac{{21}}{6} = \dfrac{{35}}{{10}}$
Here, both these fractions can be expressed in simplest form. In LHS, $21 = 3 \times 7$ and $6 = 2 \times 3$ and in RHS $35 = 5 \times 7$ and $10 = 2 \times 5$. Therefore, cancelling out common factors, we get
$
   \Rightarrow \dfrac{{3 \times 7}}{{2 \times 3}} = \dfrac{{5 \times 7}}{{2 \times 5}} \\
   \Rightarrow \dfrac{7}{2} = \dfrac{7}{2} \\
$
Hence, we can say that $21:6 = 35:10$ is a proportion.
Therefore, the given statement is True. And the correct option is option (A).

Note:
> In a given ratio $a:b$, the first term a is called antecedent and the second term b is called consequent.
> In a given proportion $a:b::c:d$, the term $b$ is called the mean term and the term $c$ is called the extreme term.
> The value of a ratio does not get affected when we multiply it or divide it by the same non-zero number.