Addition and subtraction of directed numbers - Examples, Exercises and Solutions

$15-(-4)=$

Let's remember the following law:

$-(-x)=+$

Now let's write the exercise in the appropriate form:

$15+(4)=19$

$19$

$-3+(?)=5$

To find out how much we need to add to the number negative 3 in order to get 5, we will count the number of steps between the two numbers.

Also, we will pay attention to which direction we moved, if we moved to the right then the number is positive, if we moved to the left the number will be negative.

We will start from the number negative 3, and move to the right until we reach the number 5, with each step representing one whole number, as follows:

We discover that the number of steps is 8. Since we moved to the right, the number is positive

$8$

$(+7)-(-6.7)=$

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form and solve it:

$7+6.7=13.7$

$13.7$

$(-\frac{2}{3}x)+(-8\frac{1}{3}x)=$

Let's remember the rule:

$+(-x)=-x$

Now let's write the exercise in the appropriate form and solve it:

$-\frac{2}{3}x-8\frac{1}{3}x=-9x$

$-9x$

a and b are negative numbers.

Therefore, what kind of number is is a-b?

We test using an example:

We define that

a = -1

b = -2

Now we replace in the exercise:

-1-(-2) = -1+2 = 1

In this case, the result is positive!

We test the opposite case, where b is greater than a

We define that

a = -2

b = -1

-2-(-1) = -2+1 = -1

In this case, the result is negative!

Therefore, the correct solution to the whole question is: "It's impossible to know".

Impossible to know.

A and B are positive numbers.

Therefore, A - B results in...?

Let's define the two numbers as 1 and 2.

Now let's place them in an exercise:

2-1=1

The result is positive!

Now let's define the numbers in reverse as 2 and 1.

Let's place an equal exercise and see:

1-2=-1

The result is negative!

We can see that the solution of the exercise depends on the absolute value of the numbers, and which one is greater than the other,

Even if both numbers are positive, the subtraction operation between them can lead to a negative result.

Impossible to know

a is a negative number.

b is a positive number.

Therefore, a - b is....?

We test using an example:

We define that

a = -1

b = 2

Now we replace in the exercise:

-1-(2) = -1-2 = -3

In this case, the result is negative!

We test a case where the value of b is less than a

We define that

a = -2

b = 1

-2-(1) = -2-1 = -3

In this case, the result is again negative.

Since it is not possible to produce a case where a is greater than b (because a negative number is always less than a positive number),

The result will always be the same: "negative", and that's the solution!

Negative

The sum of two numbers is positive.

Therefore, the two numbers are...?

Testing through attempts:

Let's assume both numbers are positive: 1 and 2.

1+2 = 3

Positive result.

Let's assume both numbers are negative -1 and -2

-1+(-2) = -3

Negative result.

Let's assume one number is positive and the other negative: 1 and -2.

1+(-2) = -1

Negative result.

Let's test a situation where the value of the first number is greater than the second: -1 and 2.

2+(-1) = 1

Positive result.

That is, we can see that when both numbers are positive, or in certain types of cases when one number is positive and the other negative, the sum is positive.

Answers a+c are correct.

a is a positive number.

b is a negative number.

The sum of a+b is...?

We will test this through experiments:

Let's assume that the value of the positive number is greater than the value of the negative number 1 and 2.

1+(-2) = -1

The result is negative.

We will try to make the value of the second number greater than the first 2 and 1.

2+(-1)= 1

The result is positive.

That is, we can see that the result depends on the values of the two numbers, so we cannot know from the beginning what the result will be.

It is not possible to know.

a is a positive number.

b is a negative number.

What kind of number is the sum of b and a?

We will illustrate with an example:

Let's assume that a is 1 and b is -2

1+ (-2) = 
1-2 = -1

Answer: Negative

Now we define that a is 2

and b is -1

2+(-1) = 
2-1 = 1

Even though the operation is negative, the number remains positive.

That is, if the absolute value of the positive number (a) is greater than that of the negative (b), the result will still be positive.

As we do not have data on this information, it is impossible to know what the sum of a+b will be.

.Impossible to know.

$-27-(-7)+(-6)+2-11=$

First, we solve the multiplication exercise, that is where there is a plus or minus sign before another sign.

$-27+7-6+2-11=$

Now we solve as a common exercise from left to right:

$-27+7=-20$

$-20-6=-26$

$-26+2=-24$

$-24-11=-35$

$-35$

$-5-(-2)=$

$-3$

$-4+(-2)=$

$-6$

$3+(-4)=$

$-1$

$3-(-2)=$

$5$