Question

draw the line AB, 12cm long
Mark C on it such that AC is2/3 of AB. Mark D such that AD is 1/4 ofAC. what fraction of AB is AD? ​

Answer 1

Given:

Draw the line AB, 12cm long  

Mark C on it such that AC is 2/3 of AB

Mark D such that AD is 1/4 of AC

To find:

What fraction of AB is AD? ​

Solution:

We have,

AC = $\frac{2}{3} \times AB$

substituting the value of AB = 12 cm

$\implies AC = \frac{2}{3} \times 12$

$\implies AC = 2 \times 4$

$\implies \bold{AC = 8\:cm}$

Also,

AD = $\frac{1}{4} \times AC$

substituting the value of AC = 8 cm

$\implies AD = \frac{1}{4} \times 8$

$\implies AD = 1 \times 2$

$\implies \bold{AD = 2\:cm}$

Therefore, substituting the value of AD = 2 cm & AB = 12 cm, we get

The ratio of AD and AB

i.e., $\frac{AD}{AB} = \frac{2}{12}$

$\implies \frac{AD}{AB} = \frac{1}{6}$

$\implies \bold{AD = \frac{1}{6} \times AB}$

Thus, AD is $\underline{\bold{\frac{1}{6}^t^h }}$ of line AB.

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