Mathematics VIII PDF Exercise 1.1

6 Mathematics - VIII 22 + (-147) -125 LCM of 21 and 22 462 462...

6 Mathematics - VIII 22 + (-147) -125 LCM of 21 and 22 462 462 462 -125 462 EXERCISE 1.1 1. Add the 4 following: -5 7 () and (ii) and 4 7 7 -13 -13 2. Simplify: -4 9 + 22 13 3 Verity commutative property of addition for the following pairs of rational numbers: -4 3 1 9 2 and (i) and (in) and 3 7 3 11 -13 4. Find the additive inverse of the following rational numbers: 2 -7 (1) -3 (ii) -12 (5.) Verify that- (-x) = x for 10 15 (i) x = (ii) x= 13 17 6. Using appropriate properties of addition, find the following: 4 11 -7 2 3 4 -5 2 (i 5 7 5 21 3 -11 4 -5 7) If a = b= and c = then verify that a + (b + c) = (a + b) + c. 27 18 sUBTRACTION OF RATIONAL NUMBERS Subtracting one rational number from another rational number is same as adding the additive inverse (negative) of the rational number that is being subtracted, to the other rational number. If P and are two rational numbers, then E-=L+ additive inverse of= 3 -5 5 XExample 1. Subtract: () 8 from 12 (ii) 24 from 8 -5 3 -5 3 Solution. (i) + additive inverse of 12 8 12 8 -5 (-10+(-9) -19 LCM of 12 and 8 = 24 12 24 24  5.) 4. Subtract What What Sum Subtract:(1. () of rationalrational 23 the two from sum rational numnbernumber 7 -33 of 7 5 numbers and should should (ii) -4 3-8 be be is from subtracted added 5 fromEXERCISE 3 3T 1.2 If the one 8 sumn to of 11 -5 from them of to (i) 2 5 -4 get? is and 4 5 3 8-7 7 -2 -3 5 1 12-11 to the from other. find get -3;? 2 1 -4 7  Rational Numbers9 2 6. If x=andy= 7 5 then verify that : () x-VV-I (i) -(x + y) = (-x) + ). 4 -7 -2. If x = 12 and z = 3 then verify that x-(V-) = (r- y) - z. 8. Which of the following statements is true/false? 2 4 -5 (i) 5 33 5 is not a rational number. Wi) 7 is the additive inverse of 7 (iüi) Ois the additive inverse of its own. (iv) Commutative property holds for subtraction of rational numbers. (v) Associative property does not hold for subtraction of rational numbers. (vi) 0is the identity element for subtraction of rational numbers.  numbers: commutative (i) Verify Multiply (i) and ) -7 6 X 80-60 30 14and 8 express 63-42 -3 property the 4 (i) 61: (i) result 13 3 3 2 of EXERCISE in 1.3 and lowest (-3) (-2) x multiplication 4x3 8 1 form: 122 6 (ii) (m) 1 -20 -7 for 25 ar the 14 Mathematics -Vm 3. Verify the following and name the poperty also 3 () () 4. Find the multiplicative inverse of the following () 12 (n) 2 () () sing the apprpriate properbes of operations oM rational numters following. evalute () -31 7 14 () (n) 3 14 7 15 12 35 -8 -12 6. If p = and r = then verifv that 44 15 ()px(4xr) =(px q) xr () px (e-r)=xq -pxr Fillin the following blanks: ()The reciprocal of 0is () The numbers.. and.. are their own reiprcals (m) lf y is the reciprocal of x, then the reciprocal of y in terms of x will be (7)The product of a non-zero rational number and its recipcal is... () The reciprocal of anegative rational number is.... 8 Using distributivity, ind 7 5 -3 (1) X (i) 16 12 5 5 12 l6 9. Find the sum of additive inverse and multiplicative inverse of 9. 10. Find the product of additive inverse and multiplicative inverse of -E3 DIVISION OF RATIONAL NUMBERS To divide one rational number by another  8\ Associative Property following Observe the 16 N6 5. 4. 3. 2. If By By The and Mathematics p Divide Divide (i) State()4 Find Thus, If In Pr 6 Thus, Thus, = what what product general, 2! 5 -3 the 13 7 whether the we and the rational rational 3 and we in 8 5 sum sum 5) 10 value conclude concude general, of is we 11 twdroe of of two -9 rational a the are have: VII - and = r number number of we and 3 8 and -13 *-7+) rational following number the following: (i) that the three non-zero thatnon-zeo have -7 7 4 should should 5 -4 5) the by 12 5 numbers statements division division then 10 -2 difference. the theirby EXERCISE1.4 7 raional -3 12 -7 rational verify product be be of 15 l6 divided is of multiplied 12 -11 are rational raionalnumbers, that numbers, 7 (p of true 7 If (vi) 15 15428 11 55 3 to one (iv) (ii) or (ii) numbers (q). and get umbers then to of 24 -76 14 -5 13 13 false: 4 9 -3 -8 then -2 15 165 56 ) 14 13 get -9 them + 11 12 11 the 5 is is is 12 11 NOT is product 2, not 713 -5 NOT 14 13 4 associative. find rational a commutative as 14 5 the ? other. number.  Ratlonal Numbers19) Next hihest oe of thr ining Arvondmg to the 151 31 55 24I (Multiplyiny, both sdes hy 10 Hene the total soe of the inning INas 440) ms EXERCISE 1.5 In a bag, there are 20 kg ot truits. I 7 kg ol 6 these fruits are oranges and 8 ke of these ae apples and rest are grapes, then find the mass of the grapes in the bag. 1 2. The population ot a city is 6,63,432. If of the population are adult males and 2 of the population are adult females, then find the number of children in the city. 3. In an 2 examination, 400 students appeared. If of the boys and all 130girls passed in 3 examination, then find how many boys failed in examination. 4. A car is movin, speed of 40 3 km/h. Find how much distance will it cover in 9 10 hours. 7 5. Find the area of a square lawn whose one side is 5 m long. 6. Perimeter of a rectangle is m. If the length is 4 m, find its breadth. 7. Rahul had arope of 3254 mlong. He cut off a 150 mlong piece, then he divided the 5 rest of the rope into 3parts of equal length. Find the length of each part. 8. if 32 litres of petrol costs R340, then find the cost of 4 litres of petrol. 8 1 9. Ramesh earns 80,000 per month. He spends 8 of the income on food, of 1 remaining on LICpremium and then 2 of the remaining on other expenses. Find he much money is left with him. 1 10. A, B, C,Dand Ewent to a restaurant for dinner. Apaid 2 of the bill, Bpaid of the 5 bill and rest of the bill was shared equally by C, Dand E. What fraction of the bill was paid by each? Aese 2 11. 5 of total number of students of a school come by car while 4 of students coy walk on their bus to school. All the other students walk to school of which 3 the rest are escorted by their parents. If 224 students com (d) 21 own, how many students study in that school? 29  20 Mathematics VI 12. A constructed for 6,00,000 mother and her two s s got a room The elder younger son contributed of his mothe scontibuton while the his mother s shan Hols m.h did the thre contribute individually? contributed 2 13 In a dass ot So th of the number of students, the number of boys is girls. Find y to a of his money to a school, 6 th of the remaining 14 A man donatd church and maining money he distributed equally among his three children. If each T 0 hon muh money did the man originally have child g of that number, the result is 15 greater than 15. lt ot a nunber is added to 4 number Find the number. half of ith 4 16. A student was asked to multiply agiven number by 5 By mistake, he divided L 4 gien number by His answer was 36 more than the correct answer. What 5 given number 5 4 [Hint: let the number be x, then -EX= 36.] OBJECTIVE QUESTIONS strip, MENTAL MATHS 1. Fill in the blanks: (i) The product of two rational numbers is a (ii) Subtraction of rational numbers is.... commutative (i1) Division of rational nunbers is..... associative. (ir) Negative of arational number is called its (r) Multiplicative identity of rational numbers is (vi) Multiplication of rational numbers is Over addition. (ii)) Division of arational number by a non-zero rational number is a.... 2. State whether the following statemnents are true (T) or false (F): () is the additive inverse of 5 9 (ii) Every integer is a rational number. (iii) Zero has its multiplicative inverse. (iv) Every rational number is an integer. (v) Division of two rational numbers is always closed. Sol. (vi) All terminating decimal numbers are rational numbers. (vii) O is the multiplicative identity of rational numbers. Th ii) For rational numbers xand y, if x