Multiple choice on rational numbers   - Grade 9   

 

For TRAINING: answer to a group of questions, then click on the "+" button to get the right answers, a score and explanations.  

For a TEST: answer to all the groups of questions, then click on the "Result / Result" menu to get a global score, the right answers, and explanations.  

 

Nom Classe
? ?

 

1. Properties of addition and subtraction

 

Let a , b and c be numbers. Click on true if the property is true for all possible values of a , b and c ; otherwise, click on false.

 

☐

a+b=b+a

 

☐

(a+b)+c=a+(b+c)

 

☐

a-b=b-a

 

☐

(a-b)-c=a-(b-c)


 

 

2. Properties of multiplication

 

Let a , b and c be numbers. Click on true if the property is true for all possible values of a , b and c ; otherwise, click on false.

 

☐

a*b=b*a

 

☐

(a*b)*c=a*(b*c)

 

☐

a(b+c)=ab+c

 

☐

  a(b+c)=ab+ac

 

☐

(a+b)(c+d)=ac+ad+bc+bd


 

 

3. Properties of division

 

Let a , b and c be numbers. Click on true if the property is true for all possible values of a , b and c ; otherwise, click on false.

 

☐

a/b=b/a

 

☐

(a/b)/c=a/(b/c)

 

☐

a/b/c=a/b/c

 

☐

(a+b)/c=a/c+b/c

 

☐

a/(b+c)=a/b+a/c


 

 

4.   Properties of Power

 

Let a , b be numbers and m , n integer numbers. Click on true if the property is true for all possible values of a , b , m and n ; otherwise, click on false.

 

☐

(a+b)²=a²+b²

 

☐

(a-b)²=a²-b²

 

☐

a^m*a^n=a^m+n

 

☐

a^m*n=a^m*a^n

 

☐

a^m/a^n=a^m/n

 

☐

a^m/a^n=a^m-n


 

 

5. Prime numbers and coprime numbers (or relatively prime numbers)

 

Let a , b be integer numbers.

 

☐

a and b are coprime if a does not divide b and b does not divide a

 

☐

a and b are coprime if 1 is the only common divisor of a and b

 

☐

The Euclid algorithm allows finding the GCD of 2 positive integers, it processes as follows:

divide a by b , which provide quotient q and remainder r . If r=0 the GCD is b

If r≠0 process again for b and r

 

☐

In order to calculate the GCD of a and b , one can factor a and b with prime factors and take the common factors

with the lower exponent.

 

☐

Fraction a/b with b≠0 is irreducible if a and b are coprime.

 

☐

A number is a prime if it has only 1 as divisor.


 

 

6. Multiple choice on numbers  

 

☐

The GCD of 12 and 36 is 6

 

☐

In 14*5/5*2 one can simplify by 5 to get an irreducible fraction.

 

☐

In 2²*5*7/2³*7*11 one can simplify by 2²*7 to get an irreducible fraction.

 

☐

The 6 first prime numbers are: 1 2 3 5 7 9


 

 

7. Sorts of numbers

 

☐

Any integer is a decimal number and there exists decimal numbers which are not integers.  

 

☐

Any decimal number is a rational number and there exists rational numbers which are not decimal numbers.

 

☐

The scientific notation consists of writing rational numbers as  irreducible  fractions.

 

☐

There exists numbers which are not rational numbers, they are called irrational numbers.  


 

 

8. Multiple choice on numbers

 

☐

10³/10²  is a rational numbers.

 

☐

3*7*11/14*2  is not a decimal number

 

☐

√3/√12  is an irrational number.

 

☐

0,234*10^-5 is a  scientific form.