Question

Q-Express each of the following ratios in simplest form:
1) 8ab^2 : 6a^2b



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Answer 1

We have:

8a$b^2$ : 6$a^2$b

We have to express the ratios in simplest form of 8a$b^2$ : 6$a^2$b.

Solution:

∴ 8a$b^2$ : 6$a^2$b

Dividing 2ab, we get

∴ 8a$b^2$ : 6$a^2$b = $\dfrac{8ab^2}{2ab} : \dfrac{6a^2b}{2ab}$

                     = 4b : 3 a

∴ 8a$b^2$ : 6$a^2$b = 4b : 3a

Thus, the simplest form of the ratio is equal to "4b : 3a".

Answer 2

SOLUTION

TO EXPRESS

The following ratios in simplest form:

$\sf{8a {b}^{2} :6 {a}^{2}b }$

EVALUATION

STEP : 1

First write down the given ratio

$\sf{ 8a {b}^{2} :6 {a}^{2}b }$

STEP : 2

Factorise both the terms

$\sf{8a {b}^{2} = 2 \times 2 \times 2 \times a \times b \times b }$

$\sf{6 {a}^{2}b = 2 \times 3 \times a \times a \times b }$

STEP : 3

Find the common factor of both the terms

Here the common factor = 2ab

STEP : 4

Divide both the terms by the common factor to get the final result

$\sf{ 8a {b}^{2} :6 {a}^{2}b }$

$= \displaystyle \sf{ \frac{ 8a {b}^{2}\: }{2ab} : \frac{6 {a}^{2}b}{2ab} }$

$= \sf{4b : 3a \: }$

FINAL ANSWER

Simplest form of

$\sf{ 8a {b}^{2} :6 {a}^{2}b \:}$

$\sf{ = 4b : 3a}$

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