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MATHS 3 Marks Question

Integers · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 22 questions.

Questions

3 Marks Question

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22 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
Find $50 – (–40) – (–2)$
Answer
$50 – (–40) – (–2)$
$= 50 +$ (additive inverse of $–40) – (–2)$
$= 50 + (40) – (–2)$
$= 90 – (–2)$
$= 90 +$ (additive inverse of $–2)$
$= 90 + 2 = 92.$
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Question 23 Marks
Find $(–13) + 32 – 8 – 1$
Answer
$(–13) + 32 – 8 – 1$
$= (–13) + 32 – 9$
$= (–13) + 32 +$ (additive inverse of $9)$
$= (–13) + 32 + (–9)$
$= (–13) + 23 + 9 + (–9)$
$= (–13) + 23 + 0$
$= (–13) +23$
$= (–13) + 13 + 10$
$= 0 + 10 = 10$
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Question 33 Marks
Find $(–7) –8 – (–25)$
Answer
$(–7) –8 – (–25)$
$= (–7) +$ (additive inverse of $8) (–25)$
$= (–7) + (–8) – (–25)$
$= –15 – (–25)$
$= –15 +$ (additive inverse of $–25)$
$= -15 + (+25)$
$= -15 + (+15) + (+10)$
$= 0 + (+10) = 10$
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Question 63 Marks
Add without using number line $:(–250) + (+150)$
Answer
$(–250) + (+150)$
$= (–100) + (–150 ) + (+150)$
$= (–100) + 0 = –100$
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Question 73 Marks
Add without using number line $:(–10) + (+19)$
Answer
$(–10) + (+19)$
$= (–10) + (+10 ) + (+9)$
$= 0 + (+9) = 9$
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Question 83 Marks
Add without using number line $:(–13) + (+18)$
Answer
$(–13) + (+18)$
$= (–13) + (+13) + (+5)$
$= 0 + (+5) = 5$
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Question 103 Marks
Adjacent figure is a vertical number line, representing an integer. Observe it and locate the points:
Arrange all the points in decreasing order of value.
Answer
By looking at the given diagram,
We can conclude that,
The given points can be arranged in the decreasing order as shown below:
$D > C > B > A > O > H > G > F > E$
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Question 113 Marks
Adjacent figure is a vertical number line, representing an integer. Observe it and locate the points:
Which point marked on this number line has the least value?
Answer
It is clear from the figure that on the given vertical number line,
E has the least value
Because it corresponds to $-10.$
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Question 123 Marks
Adjacent figure is a vertical number line, representing an integer. Observe it and locate the points:
Write integers for points $B$ and $E.$
Answer
Clearly from the figure we can easily see that
Point B lies above the point $0$ at a distance of $4$ units
Hence, the integer for point $B$ is $4$
Now, point $E$ lies below the point $0$
And, it is at a distance of $10$ units from $0$ on lower side
Hence,
The integer for point $E$ is $-10$
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Question 133 Marks
Adjacent figure is a vertical number line, representing an integer. Observe it and locate the points:
Is point G a negative integer or a positive integer?
Answer
Clearly,
$– 8 – (– 10) = – 8 + 10$ as additive inverse of $–10$ is $10.$
On the number line, from $– 8$ we will move $10$ steps towards right,

And we reach at $2.$ Thus, $–8 – (–10) = 2$
Hence, to subtract an integer from another integer it is equivalent to adding the additive inverse of the integer that is being subtracted, to the other integer.
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Question 143 Marks
Adjacent figure is a vertical number line, representing an integer. Observe it and locate the points:
If point $D$ is $+ 8$, then which point is $– 8?$
Answer
Since $D$ is $+8$ then,
$-8$ will be a mirror image of $D$ through $0$ on the number line.
Hence,
According to the given vertical line,
$-8$ will be the point $F$ on the number line.
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Question 203 Marks
Find the sum of $(– 10), (92), (84)$ and $(– 15)$
Answer
The required sum is obtained as:
$(– 10) + (92) + (84) + (– 15) = (– 10) + (– 15) + 92 + 84$
$= (– 25) + 176 = 151$
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Question 213 Marks
Find the sum of $(– 9) + (+ 4) + (– 6) + (+ 3)$
Answer
We shall re-arrange the numbers, So that the positive integers and the negative integers are grouped together. So, We have
$(– 9) + (+ 4) + (– 6) + (+ 3) = (– 9) + (– 6) + (+ 4) + (+ 3) = (– 15) + (+ 7) = – 8$
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Question 223 Marks
By looking at the number line, answer the question:
Which integers lie between $– 8$ and $– 2?$ Which is the largest integer and the smallest integer among them?
Answer


From the number line, integers between $– 8$ and $– 2$ are $– 7, – 6, – 5, – 4, – 3.$
The integer $– 3$ is the largest and $– 7$ is the smallest.
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