Q35. - Algebra 1

Question

Find the following quotient.

$-\frac{9}{10}÷3$

Step-by-Step Solution

Answer

The quotient is $-\frac{3}{10}$.

Step 1. Formula Used.

The division of two fractions is given by multiplying the first fraction by the reciprocal of the second fraction.

$\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

Step 2. Definition of reciprocal.

The product of any number and its reciprocal is 1.

Step 3. Find the reciprocal of the given number.

Reciprocal of 3 

$3·\frac{1}{3}=1$

Hence the reciprocal of 3 is $\frac{1}{3}$.

Step 4. Find the quotient of the given numbers.

Now by the definition of quotient of two fractions:

$\begin{array}{c}-\frac{9}{10}÷3=-\frac{9}{10}\times \frac{1}{3}\\ =-\frac{3}{10}\end{array}$