**Selina Concise Mathematics Class 6 ICSE Solutions – Number Line**

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**IMPORTANT POINTS**

**Number Line :**A Number line is used to represent numbers, such as : fractions, whole numbers, integers, etc.**Using A Number Line to Compare Numbers :**Out of any two numbers, marked on a number line, the number which is on the right of the other number is greater and the number which is on the left of the other number is lesser (smaller).

**EXERCISE 7(A)**

**Question 1.**

Fill in the blanks, using the following number line :

(i) An integer, on the given number line, is ………… than every number on its left.

(ii) An integer, on the given number line, is greater than every number to its …………..

(iii) 2 is greater than – 4 implies 2 is to the ………….. of – 4.

(iv) -3 is ………….. than 2 and 3 is ………. than – 2.

(v) – 4 is ………….. than -8 and 4 is …………… than 8.

(vi) 5 is …………. than 2 and -5 is …………… than – 2.

(vii) -6 is …………. than 3 and the opposite of -6 is ………… than opposite of 3.

(viii) 8 is …………. than -5 and -8 is ……….. than -5.

**Solution:**

(i) An integer, on the given number line, is **greater** than every number on its left.

(ii) An integer, on the given number line, is greater than every number to its **left**.

(iii) 2 is **greater** than – 4 implies 2 is on the **right** of – 4.

(iv) – 3 is **less than** 2 and 3 is **greater** than -2.

(v) – 4 is **greater** than -8 and 4 is **less** than 8.

(vi) 5 is **greater** than 2 and – 5 is **less** than – 2.

(vii) -6 is** less** than 3 and the opposite of -6 is **greater** than opposite of 3.

(viii) 8 is **greater** than -5 and -8 is** less** than -5.

**Question 2.**

In each of the following pairs, state which integer is greater :

(i) -15, -23

(ii) -12, 15

(iii) 0, 8

(iv) 0, -3

**Solution:**

(i) -15, -23

-15 is greater than -23 as -15 lies on the right side of-23 on the number line

(ii) -12, 15

15 is greater than than -12 as 15 lies on the right side of -12 on the number line

(iii) 0, 8 8 > 0

(iv) 0, -3 0 > – 3

**Question 3.**

In each of the following pairs, which integer is smaller :

(i) o, -6

(ii) 2, -3

(iii) 15, -51

(iv) 13, 0

**Solution:**

(i) 0, -6

-6 < 0

(ii) 2, -3

-3 < 2

(iii) 15, -51

-51 < 15

(iv) 13, 0

0 < 13

**Question 4.**

In each of the following pairs, replace ***** with < or > to make the statement true:

(i) 3 * 0

(ii) 0 * -8

(iii) -9 * -3

(iv) 3 * 3

(v) 5 * -1

(vi) -13 * 0

(vii) -8 * -18

(viii) 516 * -316

**Solution:**

(i) 3 > 0

(ii) 0 > -8

(iii) -9 < -3

(iv) -3 < 3

(v) 5 > -1

(vi) -13 < 0

(vii) -8 > -18

(viii) 516 > -316

**Question 5.**

In each case, arrange the given integers in ascending order using a number line.

(i) – 8, 0, – 5, 5, 4, – 1

(ii) 3, – 3, 4, – 7, 0, – 6, 2

**Solution:**

(i) – 8, 0, – 5, 5, 4, – 1

Draw a number line and mark the numbers on it. Arranging in ascending order, as shown -8,-5,-1, 0, 4, 5 as on the number line

(ii) 3, -3, 4, -7, 0, -6, 2

Draw the number line and mark the numbers on it. Arranging in ascending order as shown on the number line.

-7, -6, -3, 0, 2, 3, 4

**Question 6.**

In each case, arrange the given integers in descending order using a number line.

(i) -5, -3, 8, 15, 0, -2

(ii) 12, 23, -11, 0, 7, 6

**Solution:**

(i) -5, -3, 8, 15, 0, -2

Draw the number line and mark these numbers on it. Arranging in descending order 15, 8, 0 -2, -3, -5 as shown on the number line

(ii) 12, 23, -11, 0, 7, 6

Draw a number line and mark these numbers on it. Arranging in descending order. 23, 12, 7, 6, 0, -1 as shown on the number line

**Question 7.**

For each of the statements, given below, state whether it is true or false :

(i) The smallest integer is 0.

(ii) The opposite of -17 is 17.

(iii) The opposite of zero is zero.

(iv) Every negative integar is smaller than 0.

(v) 0 is greater than every positive integer.

(vi) Since, zero is neither negative nor positive ; it is not an integer.

**Solution:**

(i) False

(ii) True

(iii) True

(iv) True

(v) False

(vi) False

**EXERCISE 7(B)**

Use a number line to evaluate each of the following :

**Question 1.**

(i) (+ 7) + (+ 4)

(ii) 0 + (+ 6)

(iii) (+ 5) + 0

**Solution:**

**Question 2.**

(i) (-4) + (+5)

(ii) 0 + (-2)

(iii) (-1) + (-4)

**Solution:**

**Question 3.**

(i) (+ 4) + (-2)

(ii) (+3) + (-6)

(iii) 3 + (-7)

**Solution:**

**Question 4.**

(i) (-1) + (-2)

(ii) (-2) + (-5)

(ii) (-3) + (-4)

**Solution:**

**Question 5.**

(i) (+ 10) – (+2)

(ii) (+8)- (-5)

(iii) (-6) – (+2)

(iv) (-7) – (+5)

(v) (+4) – (-2)

(vi) (-8) – (-4)

**Solution:**

**Question 6.**

Using a number line, find the integer which is :

(i) 3 more than -1

(ii) 5 less than 2

(iii) 5 more than -9

(iv) 4 less than -4

(v) 7 more than 0

(vi) 7 less than -8

**Solution:**

**REVISION EXERCISE**

**Question 1.**

**Fill in the blanks :**

(i) 5 is …………… than -2 and -5 is ………… than 2.

(ii) -3 is ………… than 0 and 3 is …………. than 0.

(iii) on a number line, if x is to the left of y, then x is ………… than y.

(iv) on a number line if x is to the right of y, then y is …………. than x.

**Solution:**

(i) 5 is** greater** than -2 and -5 is **less** than 2.

(ii) -3 is **less** than 0 and 3 is **greater** than 0.

(iii) On a number line, if x is to the left of y, then x is **less** than y.

(iv) On a number line, x is to the right of y, then y is **less** than x.

**Question 2.**

Using a number line, write the numbers -15, 7, 0, -8 and -3 in ascending order of value.

**Solution:**

On the given number line, we mark the numbers -15, 7, 0, -8 and -3 on it, we see that

We see that -15 < -8 < -3 < 0 < 7

-15, -8, -3, 0, 7 are in ascending order

**Question 3.**

Using a number line, write the numbers 8, -6, 2 -12, 0, 15 and -1 in descending order of value.

**Solution:**

On the given number line, we mark the numbers 8, -6, 2, -12, 0, 15 and -1 on it

We see that

15 > 8 > 2 > 0 > -1 > -6 > -12

15, 8, 2, 0, -1, -6, -12 are in descending order

**Question 4.**

Using a number line, evaluate :

(i) (+5) + (+4)

(ii) (+6) + (+8)

(iii) (-3) + (+5)

(iv) (-3) + (+7)

(v) (+6) + (-2)

(vi) (-3) + (+3)

(vii) (-5) + (-5)

(viii) (-7) + (-1)

(ix) (+6) – (+2)

(x) (+5) – (-3)

(xi) (+4) – (-1)

(xii) (-7) – (-2)

**Solution:**

(i) (+5) + (+4)

First of all, we move 5 units to the right of zero then for (+4), move 4 units right of 5, then we reach at 9, then

(+5) + (+4) = +9

(ii) (+6) + (+8)

First of all, we move 6 units to the right of zero then for (+8), we move 8 units to the right of (+6)

Then we reach at +14, then

(+6) + (+8) = +14

(iii) (-3) + (+5)

First of all for (-3) we move, 3 units to the left of zero, then move (+5) units to the right of 5, then we reach at (+2), then

(-3) + (+5) = -3 + 5 = 2

(iv) (-3) + (+7)

First of all, we move for (-3) 3 unit to the left of zero and then for (+7), we move 7 units to the right of (-3) reaching +4 Then (-3) + (+7) = +4

(v) (+6) + (-2)

First of all, we move for (+6), 6 units to the right of zero and then for (-2), move 2 units to the left of 6, then we reach 4 Then (+6) + (-2) = 6 – 2 = 4

(vi) (-3) + (+3)

First of all for (-3), we move 3 units left of zero and then for (+3) we move 3 unit right of (-3) reaching at 0

So, (-3) + (+3) = 0

(vii) (-5) + (-5)

First of all for -5, we move 5 units to left of zero and then for (-5), we move 5 units to left of (-5) reaching at -10

(-5) +(-5) = -10

(viii) (-7) + (-1)

First of all for -7, we move 7 units left of zero and then for (-1) we move 1 unit left of -7 reaching -8

(-7) + (-1) = -8

(ix) (+6) – (+2)

First of all for (+6) we move 6 units right of 0 and then for (+2), we move 2 units left of 6 reaching 4

(+6)-(+2) = 6 – 2 = 4

(x) (+5) – (-3)

Mark the points (+5) and (-3) on the same number line. We see that the position of (-3) is 8 units from (+5) to its right 3.

(+5) – (-3) = 5 + 3 = 8

(xi) (+4) – (-1)

Mark the points (+4) and (-1) on the same number line, we see that the position of (-1) is 5 units from (+4) to its right

(+4) – (-1) = 4 + 1 = 5

(xii) (-7) – (-2)

Mark the points (-7) and (-2) on the same number line, we see that (-2) is 5 units on the left (-2)

-7 – (-2) = -7 + 2 = -5

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