Chapter 0.5, Problem 35E

To determine

The quotient of the expression $-\frac{9}{10}÷3$ .

Answer to Problem 35E

The quotient of the expression $-\frac{9}{10}÷3$ is $-\frac{3}{10}$ .

Explanation of Solution

Given information:

The expression $-\frac{9}{10}÷3$ .

Formula used:

Product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \text{ or }\cdot$ .

Product of a negative and a positive integer is always negative.

Division in real numbers is multiplication by reciprocal. If $b\ne 0$ , then,

  $\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

Here, $\frac{1}{b}$ is the multiplicative inverse.

Calculation:

Consider the expression $-\frac{9}{10}÷3$ .

Recall that division in real numbers is multiplication by reciprocal. If $b\ne 0$ , then,

  $\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

Here, $\frac{1}{b}$ is the multiplicative inverse.

Apply it,

  $-\frac{9}{10}÷3=-\frac{9}{10}\cdot \left(\frac{1}{3}\right)$

9 can be expressed as product of 3 and 3.

So, $-\frac{9}{10}÷3$ can be further simplified as,

  $-\frac{9}{10}÷3=-\left(\frac{3\cdot 3}{10\cdot 3}\right)$

Recall that product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \text{ or }\cdot$ .

Simplify it,

  $-\frac{9}{10}÷3=-\left(\frac{3\cdot 3}{10\cdot 3}\right)$

Striking off the common terms, we get,

  $-\frac{9}{10}÷3=-\frac{3}{10}$

Thus, the quotient of the expression $-\frac{9}{10}÷3$ is $-\frac{3}{10}$ .