Integers - Class 6 - Mathematics
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Examples - Integers | NCERT | Mathematics | Class 6
By looking at the number line, answer the following questions : Which integers lie between -8 and -2 ? Which is the largest integer and the smallest integer among them?
The integers that lie between -8 and -2 are:
-7, -6, -5, -4, -3.
Among these, the largest integer is -3 and the smallest integer is -7.
(a) One button is kept at - 3. In which direction and how many steps should we move to reach at -9 ?
(b) Which number will we reach if we move 4 steps to the right of -6 .
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Sign up nowUsing the number line, write the integer which is
(a) 4 more than -1
(b) 5 less than 3
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Sign up nowFind the sum of $(-9)+(+4)+(-6)+(+3)$
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Sign up nowFind the value of $(30)+(-23)+(-63)+(+55)$
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Sign up nowFind the sum of $(-10),(92),(84)$ and $(-15)$
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Sign up nowFind the value of $-8-(-10)$ using number line
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Sign up nowSubtract ( -4$)$ from $(-10)$
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Sign up nowSubtract $(+3)$ from $(-3)$
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Sign up nowExercise 6.1 - Integers | NCERT | Mathematics | Class 6
Write opposites of the following:
(a) Increase in weight
(b) $30 \mathrm{~km}$ north
(c) $80 \mathrm{~m}$ east
(d) Loss of Rs 700
(e) $100 \mathrm{~m}$ above sea level
(a) Decrease in weight
(b) $30 \mathrm{~km}$ south
(c) $80 \mathrm{~m}$ west
(d) Gain of Rs 700
(e) $100 \mathrm{~m}$ below sea level
Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height two thousand metre above the ground.
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
(c) A deposit of rupees two hundred.
(d) Withdrawal of rupees seven hundred.
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Sign up nowRepresent the following numbers on a number line:
(a) +5
(b) -10
(c) +8
(d) -1
(e) -6
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Sign up nowOn a vertical number line The number line is oriented vertically with letters marking specific points. It has an origin labelled "O" in the centre, from which it extends in two directions.
(a) If point $\mathrm{D}$ is +8 , then which point is -8 ?
(b) Is point $\mathrm{G}$ a negative integer or a positive integer?
(c) Write integers for points B and E.
(d) Which point marked on this number line has the least value?
(e) Arrange all the points in decreasing order of value.
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Sign up nowFollowing is the list of temperatures of five places in India on a particular day of the year.
Place | Temperature | |
---|---|---|
Siachin | $10^{\circ} \mathrm{C}$ below $0{ }^{\circ} \mathrm{C}$ | |
Shimla | $2^{\circ} \mathrm{C}$ below $0{ }^{\circ} \mathrm{C}$ | |
Ahmedabad | $30^{\circ} \mathrm{C}$ above$0{ }^{\circ} \mathrm{C}$ | |
Delhi | $20^{\circ} \mathrm{C}$ above $0{ }^{\circ} \mathrm{C}$ | |
Srinagar | $5^{\circ} \mathrm{C}$ below $0{ }^{\circ} \mathrm{C}$ |
(a) Write the temperatures of these places in the form of integers in the blank column.
(b) Plot the number line representing the temperature in degree Celsius. Plot the name of the city against its temperature.
(c) Which is the coolest place?
(d) Write the names of the places where temperatures are above $10^{\circ} \mathrm{C}$.
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Sign up nowIn each of the following pairs, which number is to the right of the other on the number line?
(a) 2,9
(b) $-3,-8$
(c) $0,-1$
(d) $-11,10$
(e) $-6,6$
(f) $1,-100$
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Sign up nowWrite all the integers between the given pairs (write them in the increasing order.)
(a) 0 and -7
(b) -4 and 4
(c) -8 and -15
(d) -30 and -23
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Sign up now(a) Write four negative integers greater than -20 .
(b) Write four integers less than -10 .
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Sign up nowFor the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) -8 is to the right of -10 on a number line.
(b) -100 is to the right of -50 on a number line.
(c) Smallest negative integer is -1 .
(d) -26 is greater than -25 .
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Sign up nowDraw a number line and answer the following :
(a) Which number will we reach if we move 4 numbers to the right of -2 .
(b) Which number will we reach if we move 5 numbers to the left of 1.
(c) If we are at -8 on the number line, in which direction should we move to reach -13 ?
(d) If we are at - 6 on the number line, in which direction should we move to reach -1 ?
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Sign up nowExercise 6.2 - Integers | NCERT | Mathematics | Class 6
Using the number line write the integer which is :
(a) 3 more than 5
(b) 5 more than -5
(c) 6 less than 2
(d) 3 less than -2
To find the integers that satisfy each condition, we don't need a number line but can simply perform basic arithmetic. Here's how:
(a) 3 more than 5: $$5 + 3 = 8$$
(b) 5 more than -5: $$-5 + 5 = 0$$
(c) 6 less than 2: $$2 - 6 = -4$$
(d) 3 less than -2: $$-2 - 3 = -5$$
Therefore, the integers that satisfy each condition are:
- (a) 8
- (b) 0
- (c) -4
- (d) -5
Use number line and add the following integers : with steps
(a) $9+(-6)$
(b) $5+(-11)$
(c) $(-1)+(-7)$
(d) $(-5)+10$
(e) $(-1)+(-2)+(-3)$
(f) $(-2)+8+(-4)$
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Sign up nowAdd without using number line : with steps
(a) $11+(-7)$
(b) $(-13)+(+18)$
(c) $(-10)+(+19)$
(d) $(-250)+(+150)$
(e) $(-380)+(-270)$
(f) $(-217)+(-100)$
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Sign up nowFind the sum of : with steps
(a) 137 and - 354
(b) -52 and 52
(c) $-312,39$ and 192
(d) $-50,-200$ and 300
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Sign up nowFind the sum : with steps
(a) $(-7)+(-9)+4+16$
(b) $(37)+(-2)+(-65)+(-8)$
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Sign up nowExercise 6.3 - Integers | NCERT | Mathematics | Class 6
Find with steps
(a) $35-(20)$
(b) $72-(90)$
(c) $(-15)-(-18)$
(d) $(-20)-(13)$
(e) $23-(-12)$
(f) $(-32)-(-40)$
To solve each subtraction problem, we apply the basic rules of arithmetic and the properties of negative numbers.
(a) $35-(20)$:
- Subtract 20 from 35. The result is simply the difference of the two numbers because both are positive.
(b) $72-(90)$:
- Subtract 90 from 72. Because the subtrahend is larger, the result will be negative, representing the notion that 72 is less than 90.
(c) $(-15)-(-18)$:
- Subtracting a negative is equivalent to adding its positive counterpart. So, this becomes
-15 + 18
. You start from -15 and move 18 units to the right on the number line, ending in positive territory if 18 is larger than 15.
(d) $(-20)-(13)$:
- Subtract 13 from -20. Since both numbers have different signs, you effectively increase the numerical value of the negative result, moving further left on the number line.
(e) $23-(-12)$:
- Similar to (c), subtracting a negative number is like adding its positive equivalent. Thus, this becomes
23 + 12
. From 23, you move 12 units to the right on the number line.
(f) $(-32)-(-40)$:
- Again, subtracting a negative number translates to adding its positive equivalent. Therefore, this converts to
-32 + 40
. You start from -32 and move 40 units to the right on the number line, likely ending in positive territory because 40 is larger than 32.
Let's calculate the specific results:
(a) $35-(20) = 15$
(b) $72-(90) = -18$
(c) $(-15) - (-18) = -15 + 18 = 3$
(d) $(-20) - (13) = -20 - 13 = -33$
(e) $23 - (-12) = 23 + 12 = 35$
(f) $(-32) - (-40) = -32 + 40 = 8$
These operations show how subtraction can lead to both positive and negative results, depending on the signs and relative magnitudes of the numbers involved.
Fill in the blanks with $>,<$ or $=$ sign. with steps
(a) $(-3)+(-6)$ $(-3)-(-6)$
(b) $(-21)-(-10)$ $(-31)+(-11)$
(c) $45-(-11)$ $57+(-4)$
(d) $(-25)-(-42)$ $(-42)-(-25)$
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Sign up nowFill in the blanks. with steps
(a) $(-8)+\square=0$
(b) $13+\square=0$
(c) $12+(-12)=$
(d) $(-4)+\square=-12$
(e) $-15=-10$
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Sign up nowFind with steps
(a) $(-7)-8-(-25)$
(b) $(-13)+32-8-1$
(c) $(-7)+(-8)+(-90)$
(d) $50-(-40)-(-2)$
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Sign up nowExtra Questions - Integers | NCERT | Mathematics | Class 6
Evaluate: $-3 - (-6) - 5 - (-8)$
A) 6
B) 8
C) -6
D) -8
The correct option is A
$$ 6 $$
Given expression: $$ -3 - (-6) - 5 - (-8) $$ To simplify, we change the signs where we have a minus before a parenthesis: $$ -3 + 6 - 5 + 8 $$ Now, combine like terms: $$ (-3 - 5) + (6 + 8) $$ Simplify further: $$ -8 + 14 $$ Resulting in: $$ 6 $$