3 Marks Question

Question 13 Marks

Write six distinct integers whose sum is $7$.

Answer

Let the six distinct integers be $1, 2, -2, 3, -3$ and $6$.
Now, sum of the above six distinct integers $= 1 + 2 + (-2) + 3 + (-3) + 6.$
We can arrange the numbers, so that the positive integers and negative integers are grouped together.
We have, $1 + 2 + 3 + 6 + (-2) + (-3)$
$= 12 - 2 - 3 = 12 - 5 = 7$
Hence, the required integers are $1, 2, -2, 3, -3$ and $6$.
Note: There are infinite combinations exist.

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Question 23 Marks

Using the number line, write the integer which is: $3$ less than $2$.

Answer

Firstly, we draw a number line. Now, to get the integer $3$ less than $2,$ we start from $2$ and move $3$ steps to the left of $2$ and reach at $-1.$

Flence, $3$ less than $2$ is $-1$.

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Question 33 Marks

Write four pairs of integers which are at the same distance from $2$ on the number line.

Answer

As the pairs of integers should be same distance from $2$ on the number line.
Therefore, the required pairs are:
$(1, 3) \Rightarrow $ both are at a distance of $1$ unit.
$(0, 4) \Rightarrow $ both are at a distance of $2$ units.
$(-1, 5) \Rightarrow $ both are at a distance of $3$ units.
$(-2, 6) \Rightarrow $ both are at a distance of $4$ units.
Note There may be many pairs.

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Question 43 Marks

Using the number line, write the integer which is: $2$ less than $-2$.

Answer

Firstly, we draw a number line. Now, to get integer $2$ less than $-2$, we start from $-2$ and move $2$ steps to the left of $-2$ and reach at $-4$.

Flence, $2$ less than $2$ is $-4$.

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Question 53 Marks

If we are at $8$ on the number line, in which direction should we move to reach the integer:
$a.\ -5$
$b.\ 11$
$c.\ 0?$

Answer

Firstly, we draw a number line and mark some points at equal distance on it.

$a.\ $Clearly, if we move towards $-5$ from $8$, then we are moving in left direction.
$b.\ $Clearly, if we move towards $11$ from $8$, then we are moving in right direction.
$c.\ $Clearly, if we move towards $0$ from $8$, then we are moving in left direction.

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Maths 3 Marks Question

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