Math Tests - mathematics practice questions

Division by 2

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Division by 3

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Division by 4

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Division by 5

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Division by 10

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Division by 11

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Remainders after division by 2-4

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Remainder after division

The result of division is not always a nice and round number, e.g. 7÷3. We know that three fits twice into 7. However, 3×2=6. There is 1 still remaining. We call 1 in this case the remainder or left over after dividing (7 is dividend and 3 is divisor).

To calculate it you need to find the greatest multiple of the divisor which is still lower than the dividend and subtract it from dividend.

Example:
44÷5 → 5×8=40 → 44−40=4 (4 is remainder after division by 5: 44=5×8+4).



Remainders after division by 5-7

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Remainder after division

The result of division is not always a nice and round number, e.g. 7÷3. We know that three fits twice into 7. However, 3×2=6. There is 1 still remaining. We call 1 in this case the remainder or left over after dividing (7 is dividend and 3 is divisor).

To calculate it you need to find the greatest multiple of the divisor which is still lower than the dividend and subtract it from dividend.

Example:
44÷5 → 5×8=40 → 44−40=4 (4 is remainder after division by 5: 44=5×8+4).



Long division (easy)

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8 175217÷8=2−1621−161521− 87−1615219− 872(1)8 175215÷8=1(7)8 175272÷8=9


Odd or even? (divisibility by 2)

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Divisibility rules


A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. These numbers are called even numbers. Numbers not divisible by 2 are called odd numbers.

A number is divisible by 3 if the sum of its digits is divisible by 3.

A number is divisible by 4 if the number's last two digits are divisible by 4 or the number ends with 00.

A number is divisible by 5 if it ends in 0 or 5.

A number is divisible by 6 if the sum of its digits is divisible by 3 and 2.

A number is divisible by 8 if the number's last three digits are divisible by 8 or the number ends with 000.

A number is divisible by 9 if the sum of its digits is divisible by 9.

A number is divisible by 10 if it ends with 0.



Divisibility by 3

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Divisibility rules


A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. These numbers are called even numbers. Numbers not divisible by 2 are called odd numbers.

A number is divisible by 3 if the sum of its digits is divisible by 3.

A number is divisible by 4 if the number's last two digits are divisible by 4 or the number ends with 00.

A number is divisible by 5 if it ends in 0 or 5.

A number is divisible by 6 if the sum of its digits is divisible by 3 and 2.

A number is divisible by 8 if the number's last three digits are divisible by 8 or the number ends with 000.

A number is divisible by 9 if the sum of its digits is divisible by 9.

A number is divisible by 10 if it ends with 0.



Multiples and factors

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Multiples

The multiples of a number are the values in that number’s times table. E.g. the multiples of 5 are 5 , 10 , 15 , 20 , 25 and so on.

There is an infinite amount of multiples of any given number.

Factors

Factors of the number are the numbers you multiply together to get this number. A factor is an integer that will divide exactly into another number. E.g. 8 is a factor of 24 because 8 will divide into 24 exactly 3 times with no remainder.

Factor pairs

Factor pairs are two integers which multiply together to make a particular number. For example, the factor pairs of 20 are 1 and 20; 2 and 10; 4 and 5. This means that the factors of 20 are: 1 , 2 , 4 , 5 , 10 and 20. Every integer has a finite number of factors.



   
   

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