Question

Tell whether the ratios form a proportion. Help me on 6, 8, and 12.

Answer 1

It is extremely simple and relatively easy.

To find whether a ratio forms a proportion or not determine the total product by cross multiplication of products in a diagonal way or even more simpler, the diagonals are the opposite fractions to be multiplied and then compared with a equivalence factor, to check the proportionate to be equal for their values.

We can do this by two ways. One is by directly calculating in the form of fraction to decimal conversion to check the proportion. Second is the cross multiplication of the given products on opposite sides.

So, let us say the one sum given in your textbook, we are said to find and determine if they are equal or in a direct proportion in any provided ways.

Do it by the decimal conversion from a fraction form.

$\mathbf{6) \quad \dfrac{1}{5}, \: \: \dfrac{6}{30}}$

$\bf{\dfrac{6}{30}}$ is having a common factor of the numbered value 6. So, 6 can be simplified on numerator to get 1 that is $\bf{\dfrac{6}{6} = 1}$ and the denominator can be simplified and is definitely divisible for their values.

According to the tables of 6. 6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18, 6 × 4 = 24, 6 × 5 = 30. We can see the multiplication of 5 times of 6 gives the value of 30. So, we can divide it and take a common factor of 6 to simplify it and get the same value, equivalent to $\bf{\dfrac{1}{5}}$.

$\mathbf{\therefore \quad 0.2 = 0.2}$

Similarly, all the sums can be solved like this, or we can chose the second easier method if division is not in use or it is more difficult for you in those ways, by converting fraction to decimal.

Second method is cross multiplication, we simply multiply the numerator with the denominator of an opposite side, that is:

$\mathbf{\dfrac{1}{5} \searrow \dfrac{6}{30}}$

$\mathbf{\dfrac{1}{5} \swarrow \dfrac{6}{30}}$

We are getting the cross multiplied product value and producing them in a order to determine the equivalence of the given values. Are they equal or not; So:

$\mathbf{1 \times 30 = 5 \times 6}$

$\mathbf{30 = 30; \quad They \: \: are \: \: equal.}$

Now solving all other sums with cross multiplication method.

$\mathbf{7) \quad \dfrac{3}{4}, \: \: \dfrac{24}{18}}$

$\mathbf{3 \times 18 = 4 \times 24}$

$\mathbf{54 \neq 96}$

$\mathbf{8) \quad \dfrac{2}{5}, \: \: \dfrac{40}{16}}$

$\mathbf{2 \times 16 = 5 \times 40}$

$\mathbf{32 \neq 200}$

$\mathbf{10) \quad \dfrac{18}{27}, \: \: \dfrac{33}{44}}$

For this, simplify the fractions for a easier solution. Here we can see that $\bf{\dfrac{18}{27}}$ is divisible by the numbered value of 3. We can deduce, like this:

$\mathbf{\dfrac{\overbrace{\cancel{18}}^6}{\underbrace{\cancel{27}}_9}}$

$\mathbf{\dfrac{\overbrace{\cancel{6}}^2}{\underbrace{\cancel{9}}_3}}$

Now just do one thing; Cross Multiply them for a easier solution via a simplified fraction of $\bf{\dfrac{2}{3}}$.

$\mathbf{10) \quad \dfrac{2}{3}, \: \: \dfrac{33}{44}}$

$\mathbf{2 \times 44 = 3 \times 33}$

$\mathbf{88 \neq 99}$

$\mathbf{11) \quad \dfrac{7}{2}, \: \: \dfrac{16}{6}}$

Common factor is the numbered value 2 in $\mathbf{\dfrac{16}{6}}$.

$\mathbf{11) \quad \dfrac{7}{2}, \: \: \dfrac{8}{3}}$

$\mathbf{7 \times 3 = 2 \times 8}$

$\mathbf{21 \neq 16}$

$\mathbf{12) \quad \dfrac{12}{10}, \: \: \dfrac{14}{12}}$

Common factor is 2 in both the fractional values.

$\mathbf{12) \quad \dfrac{6}{5}, \: \: \dfrac{7}{6}}$

$\mathbf{6 \times 6 = 5 \times 7}$

$\mathbf{36 \neq 35}$

Hope it helps.