Question

A $2m$ rope is divided into 3 parts.
If the first part is $\frac{8}{15}$ m and the second part is $\frac{12}{15}$ m,
then the third part is m long.

• A. $\frac{13}{15}$
• B. $\frac{5}{15}$
• C. $\frac{7}{15}$
• D. $\frac{10}{15}$

Answer 1

The correct option is D $\frac{10}{15}$

Length of the rope = $2m$

Length of the first part of the rope = $\frac{8}{15}m$

Length of the second part of the rope = $\frac{12}{15}m$

Let's calculate the length of the third part of the rope.

So, add the first and second parts of the rope.
$=(\frac{8}{15}+\frac{12}{15})m$ (like fractions)

As the denominators of the fractions are same, the numerators can be added directly and the denominator remains same.

$=\frac{8+12}{15}$

$=\frac{20}{15}m$

To calculate the length of the third part of the rope, subtract $\frac{20}{15}m$ from $2$.

Now, make an equivalent fraction of 2 with denominator 15.

Length of the third part of the rope = $=(\frac{30}{15}-\frac{20}{15})m$ (like fractions)

As the denominators of the fractions are same, the numerators can be subtracted directly and the denominator remains same.

$=\frac{30-20}{15}$

$=\frac{10}{15}m$

Hence, the length of the third part of the rope is $\frac{10}{15}m$.