Relative numbers: 4th grade math course download pdf.

This fourth grade math course on relative numbers covers the four operations on relative numbers: addition, subtraction, multiplication and division. The student will need to know the properties of the different operations as well as the sign rule for multiplication and division of two relative numbers. We will end this lesson with problem solving in the fourth grade.

Relative numbers in math are very instructive.

I. Addition and subtraction

1.addition of two relative numbers

  • The sum of two Nbre. Rel. (Nbre. Rel.) having the same sign is a Nbre. Rel. whose sign remains unchanged and whose numerical part is the sum of the numerical parts of these two numbers;
  • The sum of two Nbre. Rel. of opposite signs has for sign that of the number having the greater numerical part and has for numerical part the difference between the two numerical parts.

2. subtraction of two relative numbers


The opposite of a Nbre. Rel. is the number with the same numerical part and a different sign.

The opposite of – 7.2 is + 7.2.

To subtract a relative number is to add its opposite.


II. Multiplication of two relative numbers

1. product of two relative numbers

Property: (sign rule)

The product of two Nbre. Rel. is a Nbre. Rel. having as numerical part the product of the two parts and numerical, and a sign :

  • positive if both Nbre. Rel. have the same sign;
  • negative if both Nbre. Rel. have different signs.


A\,=\,(\,-\,4\,)\,\times  \,(-\,5\,)\,=\,+\,20\\B\,=\,(\,+\,7\,)\,\times  \,(\,-\,6)\,=\,-\,42\\C\,=\,(\,-3\,)\,\times  \,(\,+\,9\,)\,=\,-\,27\\D\,=\,(\,+\,5)\,\times  \,(\,+\,6)\,=\,+\,30

Multiplying a relative nb by – 1 means taking its opposite.

A\,=\,(\,-\,29\,)\,\times  \,(-\,1\,)\,=\,+\,29\\B\,=\,(\,+\,17\,)\,\times  \,(\,-\,1)\,=\,-\,17
this means that for any Nbre. Rel. a x ( – 1 ) = – a.

2. multiplication of several relative numbers

Property: (generality of the sign rule)

The product of several relative numbers is :

  • positive if there is an even number of negative factors;
  • negative if there is an odd number of factors.


This property is the generalization of the sign rule.
A=\,(\,-5\,)\,\times  \,(\,-9)\,\times  \,(\,+\,2)\,\times  \,(-69)\,\times  \,(+\,37)
There are three signs – and 3 is an odd number so the product A has a negative sign.
B=\underbrace{(-1)\times  \,(-1)\times  \,(-1)\times  \,.....\times  \,(-1)}_{158fois}
There are 158 signs – and 158 is an even number so B has a positive sign.

3. Inverse relative number


Two Nbre. Rel. are inverse relative numbers if their product is equal to 1.

Let a and b be two numbers. Rel.

a and b are said to be “inverse” if and only if a\,\times  \,b\,=\,-1.

  • The inverse of 5 is \frac{1}{5} because 5\times  \,\frac{1}{5}=1;
  • The inverse of \frac{7}{3} is \frac{3}{7} because \frac{7}{3}\times  \,\frac{3}{7}=\frac{21}{21}=1.

IV. Division of two relative numbers


The quotient of two relative numbers, if it exists, is a Nbre. Rel. having for numerical part the quotient of the two numerical parts and for sign :

  • positive if the two relative numbers have the same sign;
  • negative if the two relative numbers have different signs.




V. Numerical expressions and sequences of operations


The calculations in the innermost brackets are performed first.

Then, the possible powers are calculated.

Multiplication and division are then performed before addition and subtraction.

If there are several multiplications and divisions which follow one another, the calculations are carried out in the direction of the reading.

If there are several successive additions or subtractions, the calculations are made in the same direction as the reading.


Determine the value of the following expressions:


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