Integers — Exercise 1(B)

Divide :

(i) 117 by 9

(ii) (-117) by 9

(iii) 117 by (-9)

(iv) (-117) by (-9)

(v) 225 by (-15)

(vi) (-552) ÷ 24

(vii) (-798) by (-21)

(viii) (-910) ÷ 26

Answer

(i) $117 \div 9 = \dfrac{117}{9} = \dfrac{13 \times 9}{9}$ = 13.

(ii) $(-117) \div 9 = \dfrac{-117}{9} = \dfrac{-13 \times 9}{9}$ = -13.

(iii) $117 \div (-9) = \dfrac{117}{-9} = \dfrac{-117}{9} = \dfrac{-13 \times 9}{9}$ = -13.

(iv) $(-117) \div (-9) = \dfrac{-117}{-9} = \dfrac{117}{9} = \dfrac{13 \times 9}{9}$ = 13.

(v) $225 \div (-15) = \dfrac{225}{-15} = \dfrac{-225}{15} = \dfrac{-15 \times 15}{15}$ = -15.

(vi) $(-552) \div 24 = \dfrac{-552}{24} = \dfrac{-23 \times 24}{24}$ = -23.

(vii) $(-798) \div (-21) = \dfrac{-798}{-21} = \dfrac{798}{21} = \dfrac{38 \times 21}{21}$ = 38.

(viii) $(-910) \div 26 = \dfrac{-910}{26} = \dfrac{-35 \times 26}{26}$ = -35.

Evaluate :

(-234) ÷ 13

Answer

$(-234) \div 13 \\[1em] = \dfrac{-234}{13} \\[1em] = \dfrac{-18 \times 13}{13} \\[1em] = \mathbf{-18}$

Evaluate :

234 ÷ (-13)

Answer

$234 \div (-13) \\[1em] = \dfrac{234}{-13} \\[1em] = \dfrac{-234}{13} \\[1em] = \dfrac{-18 \times 13}{13} \\[1em] = \mathbf{-18}$

Evaluate :

(-234) ÷ (-13)

Answer

$(-234) \div (-13) \\[1em] = \dfrac{-234}{-13} \\[1em] = \dfrac{234}{13} \\[1em] = \dfrac{18 \times 13}{13} \\[1em] = \mathbf{18}$

Evaluate :

374 ÷ (-17)

Answer

$374 \div (-17) \\[1em] = \dfrac{374}{-17} \\[1em] = \dfrac{-374}{17} \\[1em] = \dfrac{-22 \times 17}{17} \\[1em] = \mathbf{-22}$

Evaluate :

(-374) ÷ 17

Answer

$(-374) \div 17 \\[1em] = \dfrac{-374}{17} \\[1em] = \dfrac{-22 \times 17}{17} \\[1em] = \mathbf{-22}$

Evaluate :

(-374) ÷ (-17)

Answer

$(-374) \div (-17) \\[1em] = \dfrac{-374}{-17} \\[1em] = \dfrac{374}{17} \\[1em] = \dfrac{22 \times 17}{17} \\[1em] = \mathbf{22}$

Evaluate :

(-728) ÷ 14

Answer

$(-728) \div 14 \\[1em] = \dfrac{-728}{14} \\[1em] = \dfrac{-52 \times 14}{14} \\[1em] = \mathbf{-52}$

Evaluate :

272 ÷ (-17)

Answer

$272 \div (-17) \\[1em] = \dfrac{272}{-17} \\[1em] = \dfrac{-272}{17} \\[1em] = \dfrac{-16 \times 17}{17} \\[1em] = \mathbf{-16}$

Find the quotient in each of the following divisions :

(i) 299 ÷ 23

(ii) 299 ÷ (-23)

(iii) (-384) ÷ 16

(iv) (-572) ÷ (-22)

(v) 408 ÷ (-17)

Answer

(i) Required quotient = $\dfrac{299}{23} = \dfrac{13 \times 23}{23}$ = 13.

(ii) Required quotient = $\dfrac{299}{-23} = \dfrac{-299}{23} = \dfrac{-13 \times 23}{23}$ = -13.

(iii) Required quotient = $\dfrac{-384}{16} = \dfrac{-24 \times 16}{16}$ = -24.

(iv) Required quotient = $\dfrac{-572}{-22} = \dfrac{572}{22} = \dfrac{26 \times 22}{22}$ = 26.

(v) Required quotient = $\dfrac{408}{-17} = \dfrac{-408}{17} = \dfrac{-24 \times 17}{17}$ = -24.

Divide :

(i) 204 by 17

(ii) 152 by -19

(iii) 0 by 35

(iv) 0 by (-82)

(v) 5490 by 10

(vi) 762800 by 100

Answer

(i) $204 \div 17 = \dfrac{204}{17} = \dfrac{12 \times 17}{17}$ = 12.

(ii) $152 \div (-19) = \dfrac{152}{-19} = \dfrac{-152}{19} = \dfrac{-8 \times 19}{19}$ = -8.

(iii) $0 \div 35 = \dfrac{0}{35}$ = 0.

(iv) $0 \div (-82) = \dfrac{0}{-82}$ = 0.

(v) $5490 \div 10 = \dfrac{5490}{10} = \dfrac{549 \times 10}{10}$ = 549.

(vi) $762800 \div 100 = \dfrac{762800}{100} = \dfrac{7628 \times 100}{100}$ = 7628.

State, true or false :

(i) 0 ÷ 32 = 0

(ii) 0 ÷ (-9) = 0

(iii) (-37) ÷ 0 = 0

(iv) 0 ÷ 0 = 0

Answer

(i) True. Zero divided by any non-zero integer is 0.

(ii) True. Zero divided by any non-zero integer is 0.

(iii) False. Division of any integer by zero is not defined.

(iv) False. Division of zero by zero is not defined.

Evaluate :

(i) 42 ÷ 7 + 4

(ii) 12 + 18 ÷ 3

(iii) 19 - 20 ÷ 4

(iv) 16 - 5 × 3 + 4

(v) 6 - 8 - (-6) ÷ 2

(vi) 13 - 12 ÷ 4 × 2

(vii) 16 + 8 ÷ 4 - 2 × 3

(viii) 16 ÷ 8 + 4 - 2 × 3

(ix) 16 - 8 + 4 ÷ 2 × 3

(x) (-4) + (-12) ÷ (-6)

(xi) (-18) + 6 ÷ 3 + 5

(xii) (-20) × (-1) + 14 ÷ 7

Answer

Solving using the BODMAS rule (Division, Multiplication, Addition, Subtraction) :

(i) Solving,

42 ÷ 7 + 4

= 6 + 4

= 10

∴ 42 ÷ 7 + 4 = 10

(ii) Solving,

12 + 18 ÷ 3

= 12 + 6

= 18

∴ 12 + 18 ÷ 3 = 18

(iii) Solving,

19 - 20 ÷ 4

= 19 - 5

= 14

∴ 19 - 20 ÷ 4 = 14

(iv) Solving,

16 - 5 × 3 + 4

= 16 - 15 + 4

= 20 - 15

= 5

∴ 16 - 5 × 3 + 4 = 5

(v) Solving,

6 - 8 - (-6) ÷ 2

= 6 - 8 - (-3)

= 6 - 8 + 3

= 9 - 8

= 1

∴ 6 - 8 - (-6) ÷ 2 = 1

(vi) Solving,

13 - 12 ÷ 4 × 2

= 13 - 3 × 2

= 13 - 6

= 7

∴ 13 - 12 ÷ 4 × 2 = 7

(vii) Solving,

16 + 8 ÷ 4 - 2 × 3

= 16 + 2 - 6

= 18 - 6

= 12

∴ 16 + 8 ÷ 4 - 2 × 3 = 12

(viii) Solving,

16 ÷ 8 + 4 - 2 × 3

= 2 + 4 - 6

= 6 - 6

= 0

∴ 16 ÷ 8 + 4 - 2 × 3 = 0

(ix) Solving,

16 - 8 + 4 ÷ 2 × 3

= 16 - 8 + 2 × 3

= 16 - 8 + 6

= 22 - 8

= 14

∴ 16 - 8 + 4 ÷ 2 × 3 = 14

(x) Solving,

(-4) + (-12) ÷ (-6)

= (-4) + 2

= -2

∴ (-4) + (-12) ÷ (-6) = -2

(xi) Solving,

(-18) + 6 ÷ 3 + 5

= (-18) + 2 + 5

= -18 + 7

= -11

∴ (-18) + 6 ÷ 3 + 5 = -11

(xii) Solving,

(-20) × (-1) + 14 ÷ 7

= 20 + 2

= 22

∴ (-20) × (-1) + 14 ÷ 7 = 22

The product of two integers is -90. If one of them is 6, find the other integer.

Answer

Let the other integer be x.

6 × x = -90

x = $\dfrac{-90}{6} = \dfrac{-15 \times 6}{6}$

x = -15.

∴ The other integer is -15.

The product of two integers is 210. If one of them is -15, find the other.

Answer

Let the other integer be x.

(-15) × x = 210

x = $\dfrac{210}{-15} = \dfrac{-14 \times 15}{15}$

x = -14

∴ The other integer is -14.