Even and odd numbers

Even and odd numbers exercise

• Determine if 11 is odd or even.

  Hints

  An even number is divisible by 2 and has no remainder.

  An odd number has a remainder when it is divided by 2.

  Solution

  Autumn knows that an even number is divisible by 2, with no remainder. Odd numbers have a remainder when divided by two.

  Therefore, Autumn knows that if she divides 11 by 2 she can figure out if the number, 11, is even or odd. She knows that if she gets a remainder, then 11 must be odd. If she gets no remainder, then 11 must be even.

  Autumn divides 11 by two using long division. You can see her calculations in the image.

  She finds that 11 divided by 2 is 5, with a remainder of 1.

  Since there is a remainder of 1, 11 must be odd.

• Summarize your knowledge about even and odd numbers.

  Hints

  A number is divisible by two, if you get no remainder when you divide that number by two.

  Even numbers are divisible by two.

  Solution

  Even Steven reviews some key facts about even and odd numbers before he starts completing Autumn's statements.

  A number is divisible by two if you get no remainder when you divide that number by two.

  Even numbers are divisible by two. Odd numbers are not divisible by two.

  So Stephen knows that:

  "Odd numbers...are all the numbers that are not evenly divisible by two."

  "All numbers that...are divisible by two are even numbers."

  "Even numbers...are all divisible by two with no remainder."

  "Numbers that give a remainder when divided by two...are odd."

• Determine which numbers are odd and which are even.

  Hints

  If you divide a number by $2$ and get a remainder, that number is odd.

  If you divide a number by $2$ and get no remainder, that number is even.

  A number is even if its last digit is a $0$, $2$, $4$, $6$, or $8$.

  Solution

  If you divide a number by $2$ and get a remainder, that number is odd. If you divide a number by $2$ and get no remainder, that number is even.

  But Even Stephen has a trick: He knows that a number is even if its last digit is a $0$, $2$, $4$, $6$, or $8$. A number is odd if its last digit is $1$, $3$, $5$, $7$, or $9$.

  Using Stephen's trick, we can see that:

  $6$ pears, $14$ walnuts, and $26$ basil leaves are all even numbers.

  $19$ hazelnuts, $7$ apples, and $11$ cherries are all odd numbers.

• Determine which numbers are even and which are odd.

  Hints

  If a number ends in $1$, $3$, $5$, $7$, or $9$, then it's odd.

  If a number ends in $0$, $2$, $4$, $6$, or $8$, then it's even.

  Solution

  If a number ends in $1$, $3$, $5$, $7$, or $9$, then it's odd.

  If a number ends in $0$, $2$, $4$, $6$, or $8$, then it's even.

  So $283$, $8247$, $921$, and $3011$ are odd.

  And we have that $926$, $4822$, $9740$, and $2734$ are even.

• Explain what it means if a number is divisible by another number.

  Hints

  A number is even if its last digit is a $0$, $2$, $4$, $6$, or $8$.

  If a number is divisible by $3$, you get no remainder when you divide that number by $3$.

  Solution

  If you divide a number by $2$ and get a remainder, that number is odd, not even.

  A number is divisible by two if you get no remainder when you divide that number by two. So the third statement is correct.

  A number is even if its last digit is a $0$, $2$, $4$, $6$, or $8$. So the fourth statement is correct.

• Select the even numbers.

  Hints

  If a number ends in $1$, $3$, $5$, $7$, or $9$, then it's odd.

  If a number ends in $0$, $2$, $4$, $6$, or $8$, then it's even.

  Solution

  If a number ends in $1$, $3$, $5$, $7$, or $9$, then it's odd. If a number ends in $0$, $2$, $4$, $6$, or $8$, then it's even. These rules are always true, not matter how many digits a number has.

  So out of the given numbers, only the following numbers are even:

  $134$ - $624$ - $938$ - $836$

  $7298$ - $2084$ - $3942$ - $3094$

  $20932$ - $83584$ - $65692$ - $89264$