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#### Question O1:

Name the smallest whole number.

#### Answer:

 0 [The whole numbers are 0, 1, 2, 3, ….]

#### Question O2:

Which is greater (−4) or (+3)?

#### Answer:

+3 is greater than −4.

[On the number line, −4 lies on the left and +3 lies on the right of zero.]

#### Question O3:

How many whole numbers are there from (0) to (+3) on number line

#### Answer:

There are two whole numbers from 0 to 3.

[The whole numbers from 0 to 3 are 0, 1, 2, 3.]

#### Question W1:

Answer the following

(1) Write the set of Natural numbers.

(2) Write the symbol of denote Whole numbers.

(3) Which is the least Natural number?

(4) What are the two main features of the number line?

#### Answer:

(1)

(2) ‘W’ denotes the set of whole numbers.

(3) 0 is the least whole number. 1 is the least natural number.

(4) Features of number line are:

The positive numbers are indicated to the right of zero and the negative numbers are indicated to the left of zero.

On a number line, the numbers are at equal distances.

#### Question W2:

Draw a number line and indicate the following integers on it:

(1) +4, −2, + 5, −3, + 3

(2)

(a) +2, − 2

(b) +3, 0

(c) +5, −4

(d) +6, + 5

(e) −1, −2

(3)

(a) −4 to + 2

(b) +1 to + 5

(c) −6 to + 1

(1)

(2)

(a)

(b)

(c)

(d)

(e)

(3)

(a)

(b)

(c)

#### Question W3:

Fill in the blanks

(1) +4 one the number line will be to ……… of zero.

(2) Total number of integers from −2 to +5 is …….

(3) ……. is the only number which has no positive or negative sign.

(4) {−1, −2, −3,……} are …….integers.

(5) …….is the next number greater than −5

#### Answer:

(1) +4 on the number line will be to the right of zero.

(2) Total number of integers from −2 to +5 is 8 .

(3) 0 is the only number which has no positive or negative sign.

(4) {−1, −2, −3,……} are negative integers.

(5) −4 is the next number greater than −5.

#### Question O1:

What is the sign given to the sum of negative integers?

#### Answer:

The sign given to the sum of negative integers is ‘−‘.

#### Question W1:

Add using number line:

(1) 5 and 3

(2) 6 and 2

(3) (−3) and (+5)

(4) 8 and (−12)

(5) (−7) and 5

(6) 10 and (−14)

(7) (−5) and (−2)

(8) (+6) and (−9)

(9) (−4) and (−1)

(10) 1 and (−5)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

#### Question W2:

Add the following:

(1)

(2)

(3)

(4)

(5)

(1)

(2)

(3)

(4)

(5)

#### Question O2:

What is the sum of (+4) and (−10)?

6

#### Question W3:

Add:

(1) −354 and + 564

(2) +10, −8 and +6

(3) 530, −410 and −20

(4) + 680 and −680

(5) −5778 and −4222

(1)

(2)

(3)

(4)

(5)

#### Question W4:

Observe the number line, find their sum

#### Question W5:

Complete the following table:

 + −1 +3 −5 +7 −9 +1 −2 +3 −4 +5 −6

#### Answer:

 + −1 +3 −5 +7 −9 +1 0 +4 −4 +8 −8 −2 −3 +1 −7 +5 −11 +3 +2 +6 −2 +10 −6 −4 −5 −1 −9 +3 −13 +5 +4 +8 0 +12 −4 −6 −7 −3 −11 +1 −15

#### Question O1:

Subtract 8 from 6.

#### Answer:

The subtraction of 8 from 6 is.

#### Question W1:

Subtract by using number line:

(1) 6 from 8

(2) 9 from 6

(3) +5 from −7

(4) −4 from +5

(5) −2 from −5

(1) 8 6 =2

(2) 6 9 = 3

(3)

(4)

(5)

#### Question O2:

What do you get when (−4) is subtracted from 3?

#### Answer:

On subtracting −4 from 3, we get.

#### Question W2:

Subtract without using number line:

(1) 40 from 50

(2) −20 from + 30

(3) −25 from −40

(4) +20 from −50

(5) +25 from −25

(6) −25 from + 25

(7) +40 − (−10) − (+20)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

#### Question O3:

What come when (−3) is subtracted from (−7)?

#### Answer:

On subtracting −3 from −7, we get.

#### Question W3:

Simplify the following:

(1) Subtract (−5) from 5.

(2) How much should be subtracted from (+5) to get −7?

(3) By how much (−10) exceeds (−20).

(4) From what number should (+10) be subtracted to get −15?

(5) What must be added to +7 to get −10?

(6) What should be added to +10 to get −4?

(7) If then, fill up the gap.

(8) If then fill up the gap.

(9) . Find the difference and show the operation by drawing a number line.

(10) Subtract −100 from the sum of −30 and +30.

#### Answer:

(1)

(2) Let the number subtracted be .

Thus, 12 should be subtracted from (+5) to get −7.

(3)

Thus, (−10) exceeds (−20) by 10.

(4) Let the number subtracted be .

(5) Let the number added be .

(6) Let the number added be .

(7)

(8)

(9)

The difference is 2.

(10)

#### Question W4:

Complete the following table using subtraction rule:

 +6 −7 +10 −2 +8 −5 +8 −5 +6 +4 −4 +10 −15

#### Answer:

 +6 −7 +10 −2 +8 −5 +8 −2 −15 +2 −10 0 −13 −5 +11 −2 +15 +3 +13 0 +6 0 −13 +4 −8 +2 −11 −4 +10 −3 +14 2 +12 −1 +10 −4 −17 0 −12 −2 −15

#### Question W5:

Simplify:

(1) 2 + (−4) − (+3)

(2) −5 + 4 − (−2)

(3) 10 + (−5) − (−4)

(4) 12 − (+6) + (−3)

(5) −15 + (−4) − (+3)

(1)

(2)

(3)

(4)

(5)

#### Question O1:

What is the sign given to the product of two integers having like signs?

#### Answer:

The sign given to the product of two integers having like signs is ‘+’.

#### Question O2:

What is the product of (+8) and (−3)?

#### Answer:

The product of +8 and −3 is.

#### Question O3:

By which number should (+3) be multiplied to get (−9)?

#### Answer:

The required number is

#### Question W1:

Find the product of:

(1) 15 × 6

(2) 16 × (−8)

(3) 20 × (−5)

(4) (−35) × (10)

(5) (−25) × (−5)

(1)

(2)

(3)

(4)

(5)

#### Question W2:

Multiply:

(1) (−10) by (−15)

(2) (+35) by (−5)

(3) (−15) by (+8)

(4) (+10) by (−10)

(5) (+100) by (−10)

(1)

(2)

(3)

(4)

(5)

#### Question W3:

Fill in the blanks:

(1) Product of two negative integers will have ……..sign.

(2) Product of two integers with unlike signs will have …….. sign.

(3) (+4) × (−5) = ……

(4) (+5) × (+3) = …...

(5)

#### Answer:

(1) Product of two negative integers will have positive sign.

(2) Product of two integers with unlike signs will have negative sign.

(3)

(4)

(5)

#### Question W4:

Solve the following:

(1) What number should be multiplied by (−6) to get (+30) as product?

(2) If then, find the missing term.

(3) What number is multiplied by (−15) to get the product as (+90)

(4) If then, find the missing integer.

(5) If then, find the missing integer.

#### Answer:

(1) Let the number be .

Thus, (5) should be multiplied by (6) to get (+30) as product.

(2) Let the missing term be .

(3) Let the number be .

Thus, (6) should be multiplied by (15) to get (+90) as product.

(4) Let the missing integer be .

(5)

The missing integer is 3.

#### Question W5:

Observe the number line and write the mathematical statement.

#### Answer:

The mathematical statement is .

#### Question W6:

Complete the multiplication table:

 × +3 −5 +7 −11 +13 −17 +2 −4 +44 +6 +8 −136 −10

#### Answer:

 × +3 −5 +7 −11 +13 −17 +2 +6 −10 +14 −22 +26 −34 −4 −12 +20 −28 +44 −52 +68 +6 +18 −30 +42 −66 +78 −102 +8 +24 −40 +56 −88 +104 −136 −10 −30 +50 −70 +110 −130 +170

#### Question O1:

Give the quotient when (−8) is divided by (+4).

#### Answer:

On dividing −8 by +4, we get the quotient .

#### Question W1:

Find the quotient of:

(1) 26 ÷ 2

(2) 54 ÷ 3

(3) 68 ÷ (−4)

(4) 108 ÷ (−9)

(5) (−56) ÷ 7

(6) (−168) ÷ 4

(7) (−96) ÷ (−8)

(8) (−209) ÷ (−11)

(9)

(10)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

#### Question O2:

What is the quotient when (+10) is divided by (−2)?

#### Answer:

On dividing +10 by −2, we get the quotient .

#### Question W2:

Do the following sums:

(1) Divide (+20) by (−2)

(2) Divide (−24) by (−6)

(3) Divide (−48) by (+16)

(4) Find the quotient of

(5) Find the Quotient of

(1)

(2)

(3)

(4)

(5)

#### Question O3:

What is the quotient you get when (−20) is divided by (−5)?

#### Answer:

On dividing −20 by −5, we get the quotient .

Fill in the gap:

(1)

(2)

(3)

(4)

(5)

(1)

(2)

(3)

(4)

(5)

#### Question W4:

Solve the following:

(1) Which number must be divided by 5 to get the quotient 6?

(2) By how much is 20 divided to get (−5)?

(3) If , then find the missing integer.

(4) If the fill the gap

(5) −10 ÷ 2 = −5 write this by using multiplication sign.

#### Answer:

(1) Let the number be .

Thus, 30 must be divided by 5 to get the quotient 6.

(2) Let the number be .

Thus, 20 is divided by to get .

(3) Let the missing integer be .

(4) Let the missing integer be .

(5)

or

#### Question W5:

Complete the following division table:

 +20 −40 +50 −80 +100 −30 +2 +10 −5 +10

#### Answer:

 +20 −40 +50 −80 +100 −30 +2 +10 −20 +25 −40 +50 −15 −5 −4 +8 −10 +16 −20 +6 +10 +2 −4 +5 −8 +10 −3

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