# 3.5 Multiplication and division of signed numbers

 Page 1 / 1
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.Objectives of this module: be able to multiply and divide signed numbers.

## Overview

• Multiplication of Signed Numbers
• Division of Signed Numbers

## Multiplication of signed numbers

Let us consider first the product of two positive numbers.

Multiply: $3\cdot 5$ .
$3\cdot 5$ means $5+5+5=15$ .

This suggests that

$\left(\text{positive}\text{\hspace{0.17em}}\text{number}\right)\cdot \left(\text{positive}\text{\hspace{0.17em}}\text{number}\right)=\text{positive}\text{\hspace{0.17em}}\text{number}$ .

More briefly, $\left(+\right)\left(+\right)=+$ .

Now consider the product of a positive number and a negative number.

Multiply: $\left(3\right)\left(-5\right)$ .
$\left(3\right)\left(-5\right)$ means $\left(-5\right)+\left(-5\right)+\left(-5\right)=-15$ .

This suggests that

$\left(\text{positive}\text{\hspace{0.17em}}\text{number}\right)\cdot \left(\text{negative}\text{\hspace{0.17em}}\text{number}\right)=\text{negative}\text{\hspace{0.17em}}\text{number}$

More briefly, $\left(+\right)\left(-\right)=-$ .

By the commutative property of multiplication, we get

$\left(\text{negative}\text{\hspace{0.17em}}\text{number}\right)\cdot \left(\text{positive}\text{\hspace{0.17em}}\text{number}\right)=\text{negative}\text{\hspace{0.17em}}\text{number}$

More briefly, $\left(-\right)\left(+\right)=-$ .

The sign of the product of two negative numbers can be determined using the following illustration: Multiply $-2$ by, respectively, $4,\text{\hspace{0.17em}}3,\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}0,\text{\hspace{0.17em}}-1,\text{\hspace{0.17em}}-2,\text{\hspace{0.17em}}-3,\text{\hspace{0.17em}}-4$ . Notice that when the multiplier decreases by 1, the product increases by 2.

$\begin{array}{ll}\begin{array}{l}4\left(-2\right)=-8\\ 3\left(-2\right)=-6\\ 2\left(-2\right)=-4\\ 1\left(-2\right)=-2\end{array}\right\}\to \hfill & \text{As}\text{\hspace{0.17em}}\text{we}\text{\hspace{0.17em}}\text{know},\text{\hspace{0.17em}}\left(+\right)\left(-\right)=-.\hfill \\ 0\left(-2\right)=0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\to \hfill & \text{As}\text{\hspace{0.17em}}\text{we}\text{\hspace{0.17em}}\text{know},0\cdot \left(\text{any}\text{\hspace{0.17em}}\text{number}\right)=0.\hfill \end{array}$

$\begin{array}{ll}\begin{array}{l}-1\left(-2\right)=2\\ -2\left(-2\right)=4\\ -3\left(-2\right)=6\\ -4\left(-2\right)=8\end{array}\right\}\to \hfill & \text{This}\text{\hspace{0.17em}}\text{pattern}\text{\hspace{0.17em}}\text{suggests}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(-\right)\left(-\right)=+.\hfill \end{array}$

We have the following rules for multiplying signed numbers.

## Rules for multiplying signed numbers

To multiply two real numbers that have

1. the same sign , multiply their absolute values. The product is positive.
$\begin{array}{c}\left(+\right)\left(+\right)=+\\ \left(-\right)\left(-\right)=+\end{array}$
2. opposite signs , multiply their absolute values. The product is negative.
$\begin{array}{c}\left(+\right)\left(-\right)=-\\ \left(-\right)\left(+\right)=-\end{array}$

## Sample set a

Find the following products.

$8\cdot 6$

$\begin{array}{ll}\hfill & \text{Multiply}\text{\hspace{0.17em}}\text{these}\text{\hspace{0.17em}}\text{absolute}\text{\hspace{0.17em}}\text{values}\text{.}\hfill \\ \begin{array}{l}|8|=8\\ |6|=6\end{array}\right\}\hfill & 8\cdot 6=48\hfill \\ \hfill & \text{Since}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{have}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{same}\text{\hspace{0.17em}}\text{sign,}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{product}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{positive}\text{.}\hfill \\ 8\cdot 6=+48\hfill & \text{​}\text{​}\text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}8\cdot 6=48\hfill \end{array}$

$\left(-8\right)\left(-6\right)$

$\begin{array}{ll}\hfill & \text{Multiply}\text{\hspace{0.17em}}\text{these}\text{\hspace{0.17em}}\text{absolute}\text{\hspace{0.17em}}\text{values}\text{.}\hfill \\ \begin{array}{l}|-8|=8\\ |-6|=6\end{array}\right\}\hfill & 8\cdot 6=48\hfill \\ \hfill & \text{Since}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{have}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{same}\text{\hspace{0.17em}}\text{sign,}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{product}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{positive}\text{.}\hfill \\ \left(-8\right)\left(-6\right)=+48\hfill & \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(-8\right)\left(-6\right)=48\hfill \end{array}$

$\left(-4\right)\left(7\right)$

$\begin{array}{ll}\hfill & \text{Multiply}\text{\hspace{0.17em}}\text{these}\text{\hspace{0.17em}}\text{absolute}\text{\hspace{0.17em}}\text{values}\text{.}\hfill \\ \begin{array}{cc}|-4|\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}& =4\\ |7|& =7\end{array}\right\}\hfill & 4\cdot 7=28\hfill \\ \hfill & \text{Since}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{have}\text{\hspace{0.17em}}\text{opposite}\text{\hspace{0.17em}}\text{signs,}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{product}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{negative}\text{.}\hfill \\ \left(-4\right)\left(7\right)=-28\hfill & \hfill \end{array}$

$6\left(-3\right)$

$\begin{array}{ll}\hfill & \text{Multiply}\text{\hspace{0.17em}}\text{these}\text{\hspace{0.17em}}\text{absolute}\text{\hspace{0.17em}}\text{values}\text{.}\hfill \\ \begin{array}{rr}\hfill |6|\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}& \hfill =6\\ \hfill |-3|& \hfill =3\end{array}\right\}\hfill & 6\cdot 3=18\hfill \\ \hfill & \text{Since}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{have}\text{\hspace{0.17em}}\text{opposite}\text{\hspace{0.17em}}\text{signs,}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{product}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{negative}\text{.}\hfill \\ 6\left(-3\right)=-18\hfill & \hfill \end{array}$

## Practice set a

Find the following products.

$3\left(-8\right)$

$-24$

$4\left(16\right)$

64

$\left(-6\right)\left(-5\right)$

30

$\left(-7\right)\left(-2\right)$

14

$\left(-1\right)\left(4\right)$

$-4$

$\left(-7\right)7$

$-49$

## Division of signed numbers

We can determine the sign pattern for division by relating division to multiplication. Division is defined in terms of multiplication in the following way.

If $b\cdot c=a$ , then $\frac{a}{b}=c,\text{\hspace{0.17em}}b\ne 0$ .

For example, since $3\cdot 4=12$ , it follows that $\frac{12}{3}=4$ .

Notice the pattern:

Since $\underset{b\cdot c=a}{\underbrace{3\cdot 4}}=12$ , it follows that $\underset{\frac{a}{b}=c}{\underbrace{\frac{12}{3}}}=4$

The sign pattern for division follows from the sign pattern for multiplication.

1. Since $\underset{b\cdot c=a}{\underbrace{\left(+\right)\left(+\right)}}=+$ , it follows that $\underset{\frac{a}{b}=c}{\underbrace{\frac{\left(+\right)}{\left(+\right)}}}=+$ , that is,

$\frac{\left(\text{positive}\text{\hspace{0.17em}}\text{number}\right)}{\left(\text{positive}\text{\hspace{0.17em}}\text{number}\right)}=\text{positive}\text{\hspace{0.17em}}\text{number}$

2. Since $\underset{b\cdot c=a}{\underbrace{\left(-\right)\left(-\right)}}=+$ , it follows that $\underset{\frac{a}{b}=c}{\underbrace{\frac{\left(+\right)}{\left(-\right)}}}=-$ , that is,

$\frac{\left(\text{positive}\text{\hspace{0.17em}}\text{number}\right)}{\left(\text{negative}\text{\hspace{0.17em}}\text{number}\right)}=\text{negative}\text{\hspace{0.17em}}\text{number}$

3. Since $\underset{b\cdot c=a}{\underbrace{\left(+\right)\left(-\right)}}=-$ , it follows that $\underset{\frac{a}{b}=c}{\underbrace{\frac{\left(-\right)}{\left(+\right)}}}=-$ , that is,

$\frac{\left(\text{negative}\text{​}\text{\hspace{0.17em}}\text{number}\right)}{\left(\text{positive}\text{\hspace{0.17em}}\text{number}\right)}=\text{negative}\text{\hspace{0.17em}}\text{number}$

4. Since $\underset{b\cdot c=a}{\underbrace{\left(-\right)\left(+\right)}}=-$ , it follows that $\underset{\frac{a}{b}=c}{\underbrace{\frac{\left(-\right)}{\left(-\right)}}}=+$ , that is

$\frac{\left(\text{negative}\text{\hspace{0.17em}}\text{number}\right)}{\left(\text{negative}\text{\hspace{0.17em}}\text{number}\right)}=\text{positive}\text{\hspace{0.17em}}\text{number}$

We have the following rules for dividing signed numbers.

## Rules for dividing signed numbers

To divide two real numbers that have

1. the same sign , divide their absolute values. The quotient is positive.
$\begin{array}{cc}\frac{\left(+\right)}{\left(+\right)}=+& \frac{\left(-\right)}{\left(-\right)}=+\end{array}$
2. opposite signs , divide their absolute values. The quotient is negative.
$\begin{array}{cc}\frac{\left(-\right)}{\left(+\right)}=-& \frac{\left(+\right)}{\left(-\right)}=-\end{array}$

## Sample set b

Find the following quotients.

$\frac{-10}{2}$

$\begin{array}{ll}\begin{array}{ll}|-10|=\hfill & 10\hfill \\ \hfill |2|=& \hfill 2\end{array}\right\}\hfill & \text{Divide}\text{\hspace{0.17em}}\text{these}\text{\hspace{0.17em}}\text{absolute}\text{\hspace{0.17em}}\text{values}.\hfill \\ \hfill & \frac{10}{2}=5\hfill \\ \frac{-10}{2}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=-5\hfill & \text{Since}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{have}\text{\hspace{0.17em}}\text{opposite}\text{\hspace{0.17em}}\text{signs,}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{quotient}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{negative}\text{.}\hfill \end{array}$

$\frac{-35}{-7}$

$\begin{array}{ll}\begin{array}{ll}|-35|=\hfill & 35\hfill \\ \hfill |-7|=& \hfill 7\end{array}\right\}\hfill & \text{Divide}\text{\hspace{0.17em}}\text{these}\text{\hspace{0.17em}}\text{absolute}\text{\hspace{0.17em}}\text{values}.\hfill \\ \hfill & \frac{35}{7}=5\hfill \\ \frac{-35}{-7}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=5\hfill & \text{Since}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{have}\text{\hspace{0.17em}}\text{same}\text{\hspace{0.17em}}\text{signs,}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{quotient}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{positive}\text{.}\hfill \end{array}$

$\frac{18}{-9}$

$\begin{array}{ll}\begin{array}{ll}|18|=\hfill & 18\hfill \\ |-9|=\hfill & 9\hfill \end{array}\right\}\hfill & \text{Divide}\text{\hspace{0.17em}}\text{these}\text{\hspace{0.17em}}\text{absolute}\text{\hspace{0.17em}}\text{values}.\hfill \\ \hfill & \frac{18}{9}=2\hfill \\ \frac{18}{-9}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=-2\hfill & \text{Since}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{numbers}\text{\hspace{0.17em}}\text{have}\text{\hspace{0.17em}}\text{opposite}\text{\hspace{0.17em}}\text{signs,}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{quotient}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{negative}\text{.}\hfill \end{array}$

## Practice set b

Find the following quotients.

$\frac{-24}{-6}$

4

$\frac{30}{-5}$

$-6$

$\frac{-54}{27}$

$-2$

$\frac{51}{17}$

3

## Sample set c

Find the value of $\frac{-6\left(4-7\right)-2\left(8-9\right)}{-\left(4+1\right)+1}$ .

Using the order of operations and what we know about signed numbers, we get

$\begin{array}{lll}\frac{-6\left(4-7\right)-2\left(8-9\right)}{-\left(4+1\right)+1}\hfill & =\hfill & \frac{-6\left(-3\right)-2\left(-1\right)}{-\left(5\right)+1}\hfill \\ \hfill & =\hfill & \frac{18+2}{-5+1}\hfill \\ \hfill & =\hfill & \frac{20}{-4}\hfill \\ \hfill & =\hfill & -5\hfill \end{array}$

Find the value of $z=\frac{x-u}{s}$ if $x=57,\text{\hspace{0.17em}}u=51,\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}s=2$ .

Substituting these values we get

$z=\frac{57-51}{2}=\frac{6}{2}=3$

## Practice set c

Find the value of $\frac{-7\left(4-8\right)+2\left(1-11\right)}{-5\left(1-6\right)-17}$ .

1

Find the value of $P=\frac{n\left(n-3\right)}{2n}$ , if $n=5$ .

1

## Exercises

Find the value of each of the following expressions.

$\left(-2\right)\left(-8\right)$

16

$\left(-3\right)\left(-9\right)$

$\left(-4\right)\left(-8\right)$

32

$\left(-5\right)\left(-2\right)$

$\left(-6\right)\left(-9\right)$

54

$\left(-3\right)\left(-11\right)$

$\left(-8\right)\left(-4\right)$

32

$\left(-1\right)\left(-6\right)$

$\left(3\right)\left(-12\right)$

$-36$

$\left(4\right)\left(-18\right)$

$8\left(-4\right)$

$-32$

$5\left(-6\right)$

$9\left(-2\right)$

$-18$

$7\left(-8\right)$

$\left(-6\right)4$

$-24$

$\left(-7\right)6$

$\left(-10\right)9$

$-90$

$\left(-4\right)12$

$\left(10\right)\left(-6\right)$

$-60$

$\left(-6\right)\left(4\right)$

$\left(-2\right)\left(6\right)$

$-12$

$\left(-8\right)\left(7\right)$

$\frac{21}{7}$

3

$\frac{42}{6}$

$\frac{-39}{3}$

$-13$

$\frac{-20}{10}$

$\frac{-45}{-5}$

9

$\frac{-16}{-8}$

$\frac{25}{-5}$

$-5$

$\frac{36}{-4}$

$8-\left(-3\right)$

11

$14-\left(-20\right)$

$20-\left(-8\right)$

28

$-4-\left(-1\right)$

$0-4$

$-4$

$0-\left(-1\right)$

$-6+1-7$

$-12$

$15-12-20$

$1-6-7+8$

$-4$

$2+7-10+2$

$3\left(4-6\right)$

$-6$

$8\left(5-12\right)$

$-3\left(1-6\right)$

15

$-8\left(4-12\right)+2$

$-4\left(1-8\right)+3\left(10-3\right)$

49

$-9\left(0-2\right)+4\left(8-9\right)+0\left(-3\right)$

$6\left(-2-9\right)-6\left(2+9\right)+4\left(-1-1\right)$

$-140$

$\frac{3\left(4+1\right)-2\left(5\right)}{-2}$

$\frac{4\left(8+1\right)-3\left(-2\right)}{-4-2}$

$-7$

$\frac{-1\left(3+2\right)+5}{-1}$

$\frac{-3\left(4-2\right)+\left(-3\right)\left(-6\right)}{-4}$

$-3$

$-1\left(4+2\right)$

$-1\left(6-1\right)$

$-5$

$-\left(8+21\right)$

$-\left(8-21\right)$

13

$-\left(10-6\right)$

$-\left(5-2\right)$

$-3$

$-\left(7-11\right)$

$-\left(8-12\right)$

4

$-3\left[\left(-1+6\right)-\left(2-7\right)\right]$

$-2\left[\left(4-8\right)-\left(5-11\right)\right]$

$-4$

$-5\left[\left(-1+5\right)+\left(6-8\right)\right]$

$-\left[\left(4-9\right)+\left(-2-8\right)\right]$

15

$-3\left[-2\left(1-5\right)-3\left(-2+6\right)\right]$

$-2\left[-5\left(-10+11\right)-2\left(5-7\right)\right]$

2

$\begin{array}{cc}P=R-C.& \text{Find}\text{\hspace{0.17em}}P\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}R=2000\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}C=2500.\end{array}$

$\begin{array}{cc}z=\frac{x-u}{s}.& \text{Find}\text{\hspace{0.17em}}z\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}x=23,\text{\hspace{0.17em}}u=25,\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}s=1.\end{array}$

$-2$

$\begin{array}{cc}z=\frac{x-u}{s}.& \text{Find}\text{\hspace{0.17em}}z\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}x=410,\text{\hspace{0.17em}}u=430,\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}s=2.5.\end{array}$

$\begin{array}{cc}m=\frac{2s+1}{T}.& \text{Find}\text{\hspace{0.17em}}m\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}s=-8\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}T=5.\end{array}$

$-3$

$\begin{array}{cc}m=\frac{2s+1}{T}.& \text{Find}\text{\hspace{0.17em}}m\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}s=-10\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}T=-5.\end{array}$

$\begin{array}{cc}F=\left({p}_{1}-{p}_{2}\right){r}^{4}\cdot 9.& \text{Find}\text{\hspace{0.17em}}F\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}{p}_{1}=10,\text{\hspace{0.17em}}\text{\hspace{0.17em}}{p}_{2}=8,r=3.\end{array}$

1458

$\begin{array}{cc}F=\left({p}_{1}-{p}_{2}\right){r}^{4}\cdot 9.& \text{Find}\text{\hspace{0.17em}}F\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}{p}_{1}=12,\text{\hspace{0.17em}}\text{\hspace{0.17em}}{p}_{2}=7,r=2.\end{array}$

$\begin{array}{cc}P=n\left(n-1\right)\left(n-2\right).& \text{Find}\text{\hspace{0.17em}}P\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}n=-4.\end{array}$

$-120$

$\begin{array}{cc}P=n\left(n-1\right)\left(n-2\right)\left(n-3\right).& \text{Find}\text{\hspace{0.17em}}P\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}n=-5.\end{array}$

$\begin{array}{cc}P=\frac{n\left(n-2\right)\left(n-4\right)}{2n}.& \text{Find}\text{\hspace{0.17em}}P\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}n=-6.\end{array}$

40

## Exercises for review

( [link] ) What natural numbers can replace $x$ so that the statement $-4 is true?

( [link] ) Simplify $\frac{{\left(x+2y\right)}^{5}{\left(3x-1\right)}^{7}}{{\left(x+2y\right)}^{3}{\left(3x-1\right)}^{6}}$ .

${\left(x+2y\right)}^{2}\left(3x-1\right)$

( [link] ) Simplify ${\left({x}^{n}{y}^{3t}\right)}^{5}$ .

( [link] ) Find the sum. $-6+\left(-5\right)$ .

$-11$

( [link] ) Find the difference. $-2-\left(-8\right)$ .

#### Questions & Answers

how can chip be made from sand
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Please keep in mind that it's not allowed to promote any social groups (whatsapp, facebook, etc...), exchange phone numbers, email addresses or ask for personal information on QuizOver's platform.