Examples with solutions for Multiplication and Division of Signed Mumbers: Determine the resulting sign from the exercise

Exercise #1

Determine the resulting sign of the following exercise:

1412= \frac{1}{4}\cdot\frac{1}{2}=

Video Solution

Step-by-Step Solution

When there is no minus or plus sign before the numbers, we usually assume that these are positive numbers,

meaning, the expression equals to

(+1/4)*(+1/2)=

The dot in the middle represents multiplication.

So the question in other words is - what happens when we multiply two positive numbers together?

We know that plus times plus equals plus,

therefore the answer is "positive".

Answer

Positive

Exercise #2

What will be the sign of the result of the next exercise?

2(2)= 2\cdot(-2)=

Video Solution

Step-by-Step Solution

To solve the exercise you need to remember an important rule: Multiplying a positive number by a negative number results in a negative number.

()×(+)=() (−)×(+)=(−)
Therefore, if we multiply negative 2 by 2 the result will be negative 4.

That is, the result is negative.

+2×2=4 +2\times-2=-4

Answer

Negative

Exercise #3

What will be the sign of the result of the next exercise?

(2)(4)= (-2)\cdot(-4)=

Video Solution

Step-by-Step Solution

It's important to remember: when we multiply a negative by a negative, the result is positive!

You can use this guide:

Answer

Positive

Exercise #4

What will be the sign of the result of the next exercise?

(2)(12)= (-2)\cdot(-\frac{1}{2})=

Video Solution

Step-by-Step Solution

Let's recall the law:

(x)×(x)=+x (-x)\times(-x)=+x

Therefore, the sign of the exercise result will be positive:

2×12=+1 -2\times-\frac{1}{2}=+1

Answer

Positive

Exercise #5

What will be the sign of the result of the next exercise?

(3)(4)= (-3)\cdot(-4)=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(x)×(x)=+x (-x)\times(-x)=+x

Therefore, the sign of the exercise result will be positive:

3×4=+12 -3\times-4=+12

Answer

Positive

Exercise #6

What will be the sign of the result of the next exercise?

(4)12= (-4)\cdot12=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(x)=x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

4×+12=48 -4\times+12=-48

Answer

Negative

Exercise #7

What will be the sign of the result of the next exercise?

63= 6\cdot3=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(+x)=+x (+x)\times(+x)=+x

Therefore, the sign of the exercise result will be positive:

+6×+3=+18 +6\times+3=+18

Answer

Positive

Exercise #8

What will be the sign of the result of the next exercise?

(6)5= (-6)\cdot5=

Video Solution

Step-by-Step Solution

Remember the law:

(+x)×(x)=x (+x)\times(-x)=-x

For the sum of the angles of a triangle is always:

6×+5=30 -6\times+5=-30

Answer

Negative

Exercise #9

Will the result of the exercise below be positive or negative?

5(12)= 5\cdot(-\frac{1}{2})=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(x)=x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

+5×12=212 +5\times-\frac{1}{2}=-2\frac{1}{2}

Answer

Negative

Exercise #10

What will be the sign of the result of the exercise?

(+314):(+25) (+3\frac{1}{4}):(+\frac{2}{5})

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

+:+= +:+=

Since we are dividing a positive number by a positive number, our result will necessarily be positive.

Answer

+

Exercise #11

What will be the sign of the result of the exercise?

(+7.5):(+3) (+7.5):(+3)

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

+:+= +:+=

Since we are dividing a positive number by a positive number, the result will necessarily be a positive number.

Answer

+

Exercise #12

What will be the sign of the result of the exercise?

0:(18) 0:(-\frac{1}{8})

Video Solution

Step-by-Step Solution

Let's remember the rule that anything we divide by zero will give us a result of zero:

0x=0 \frac{0}{x}=0

0:x=0 0:x=0

Therefore, the answer is zero.

Answer

0

Exercise #13

What will be the sign of the result of the exercise?

(14):(+8) (-14):(+8)

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

:+= -:+=

Since we are dividing a negative number by a positive number, the result will necessarily be a negative number.

Answer

-

Exercise #14

What will be the sign of the result of the exercise?

24:8:12.4 24:-8:12.4

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

+::+= +:-:+=

If we solve the exercise from left to right, we will first divide plus by minus:

+:= +:-=-

Now the remaining exercise is:

:+= -:+=-

Therefore, the sign of the exercise result will be negative.

Answer

-

Exercise #15

What will be the sign of the result of the exercise?

(7):(35) (-7):(-\frac{3}{5})

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

:= -:-=

Since we are dividing a negative number by a negative number, the result will necessarily be a positive number.

Answer

+

Exercise #16

What will be the sign of the result of the exercise?

0.91.1:(4) \frac{-0.9}{1.1}:(-4)

Video Solution

Step-by-Step Solution

Let's see if the number is negative or positive.

As you can see, in the expression the numerator is negative and the denominator is positive.

That is, the division exercise will look like this:

+:= \frac{-}{+}:-=

The result of the expression will be a negative number, since we are dividing a negative number by a positive number.

Therefore, the exercise that will be obtained will look like this:

:=+ -:-=+

Therefore, the sign of the result of the exercise will be negative.

Answer

+

Exercise #17

What will be the sign of the result of the exercise?

40.4:1.7 \frac{-4}{-0.4}:-1.7

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

:= \frac{-}{-}:-=

If we solve the exercise from left to right, we will first divide the numerator of the negative fraction by the denominator of the negative fraction.

Therefore, the resulting fraction will be positive:

=+ \frac{-}{-}=+

Now the remaining exercise will look like this:

+:= +:-=-

Therefore, the sign of the exercise result will be negative.

Answer

-

Exercise #18

What will be the sign of the result of the exercise?

9412103 -\frac{9}{4}\cdot\frac{1}{2}\cdot\frac{10}{3}

Video Solution

Step-by-Step Solution

We will look only at whether the fraction is negative or positive.

In other words, the multiplication exercise looks like this:

×+×+= -\times+\times+=

If we solve the exercise from left to right, we'll first multiply minus by plus:

×+= -\times+=-

Now the remaining exercise is:

×+= -\times+=-

Therefore, the sign of the exercise result will be negative.

Answer

-

Exercise #19

Will the exercise result in a negative or a positive sign:

40.4:1.7 -\frac{4}{-0.4}:-1.7

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the exercise looks like this:

×+:= -\times\frac{+}{-}:-=

If we solve the exercise from left to right, we'll first multiply the fraction:

×+= -\times\frac{+}{-}=

Since the numerator of the fraction is positive and divides by the negative denominator, the resulting fraction will be negative.

Now the remaining exercise is:

×:= -\times-:-=

If we multiply minus by minus, we'll get a positive number:

×=+ -\times-=+

Now the resulting exercise is:

+:= +:-=-

Therefore, the sign of the exercise result will be negative.

Answer

-

Exercise #20

Will the result of the exercise below be positive (+) or negative (-)?

48:0.7 \frac{-4}{-8}:0.7

Video Solution

Step-by-Step Solution

In this question, we only need to work out whether the resulting value is negative or positive.

In other words, the division exercise can be considered as follows:

:+= \frac{-}{-}:+=

If we solve the exercise from left to right, we first divide the numerator of the negative fraction by the denominator of the negative fraction:

=+ \frac{-}{-}=+

This leaves us with:

+:+=+ +:+=+

Therefore, the result of the exercise will be positive.

Answer

+