20 Arithmetic: Fractions, Study notes of Calculus

Download 20 Arithmetic: Fractions and more Study notes Calculus in PDF only on Docsity! 20 20.1 Arithmetic: Fractions Revision: Whole Numbers and Decimals In this section we revise addition, subtraction, multiplication and division of whole numbers and decimals, before starting to work with fractions. Example 1 Calculate: (a) 18+49 (b) 1.6 +0.84 (c) 3.82-1.6 Solution (a) 18 (b) 1.60 (c) 3.82 + 49 + 0.84 — 1.60 67 2.44 2.22 Example 2 Calculate: (a) 18x34 (b) 1.7x 2.6 Solution (a) 18 (b) 17 x 34 x 26 72 102 540 340 612 442 Hence 1.7 x 1.6 = 4.42 Example 3 Calculate: (a) 165+5 (b) 4.26+3 Solution (a) 33 (b) 1.42 5| 165. 3] 426 so 165 +5= 33 so 4.26+3=1.42 119 20.1 Exercises 1. Calculate: (a) 182 + 57 (d) 3.24+4.7 (g) 0.26 + 1.2 G) 38+4.7 2. Calculate: (a) 192 —71 (d) 0.9 —0.2 (g) 0.8 — 0.11 G) 28 -3.7 3. Calculate: (a) 18 x3 (d) 12 x15 (g) 0.7 x5 Gj) 18x 2.9 4. Calculate: (a) 468 +2 (@) 345 +5 (9) 68444 MEP Y7 Practice Book B (b) (e) (h) (k) (b) (e) (h) (k) (b) (e) (h) (k) (b) (e) (h) 32 + 168 18.2 + 1.9 11.4 + 6.21 0.71 + 2.8 486 — 234 1.8 - 0.3 8.9 - 1.12 52-69 42x5 26 x14 1.9 x6 3.5 x 2.6 578 +2 78 +3 14.7+7 (c) (f) () (c) (f) (i) 0) (c) (f) (i) 0) (c) (f) (i) 1807 + 94 3.71 + 4.2 0.09 + 0.123 4.52 + 9.89 620 — 108 2.42 — 1.23 3.7 — 2.15 4.07 — 3.88 63 x7 39 x 23 4.29 x3 1.42 x 1.6 145 +5 981 +3 7.92 +6 5. | There were 52 people on a bus and 17 got off. How many people were still on the bus? 6. — Floppy disks cost 34p each. How much would 6 floppy disks cost? 7. It costs £5.20 for one adult to go into a theme park. How much would it cost in total for 24 adults to go into the theme park? 8. Tickets for a show cost £3 each. To cover the cost of putting on the show, £378 is needed. How many tickets must be sold to cover the cost of the show? 9. An 8 m length of rope is cut into 5 pieces of equal length. How long is each of the 5 pieces? 120 MEP Y7 Practice Book B This is illustrated in the diagram below: Example 3 Calculate: 1,41 3.3 201 a) 1-43- b) 45-12 :) 22412 @) tes 0) 4G © ashy Solution (a) 143 =4 1.1.3.8 113,38 8 3 24° 24 _ 348 ~ 24 ail ~ 24 so ey3tegll 8 93 24 o) 42-13 . 38_7 8 4 8 4 -3_l4 8 8 _ 35-14 8 = 2! 8 =22 8 Note: It is usually easier to convert the mixed numbers into improper fractions. 123 20.2 MEP Y7 Practice Book B w 224t = 843 3 2 32 16, 9 = —+- 6 6 _ 16+9 6 _ 25 - 6 = 41 6 Exercises 1. Calculate: 31 3 a) ot > b) =+ (a) ata (b) 8 3 7 1 d) —+— e) s+ @ 10 10 ©) 5 1 3 5 45 h) =-— (g) 4°4 (h) 8 . 9 7 8 a ko ® 10 10 “) ll 6 3 4 m) —-— n) =- (a) 13 13 ® 7 2. _ Fill in the missing numbers: ? 92 ? (a) Ill? tl? 2 5 10 10 10 ? 9 ? (b) =4+2=—4+—=— 5 15 15 15 1,4 5,24? () =+2==+—=- 6 5 2? ? ? 4 1 ? 2 ? @ S-ys5-SeS 7 3 21 21 21 5 2 5 ?_? () =S=-==+--+=-+ 6 3 6 6 6 ; (c) : oy 2 i) -3 a) 3 (0) 124 + + olu AIR ln Bp COIN AIN wCle MEP Y7 Practice Book B Calculate: re eee wht oe Bw id ( $42 iy F438 @ p+ off omit oft wit whl oi A birthday cake is divided into 12 equal parts. Andrew eats = of the cake and Timothy eats = of the cake. (a) What fraction of the cake is left? (b) How many pieces of cake are left? A garden has an area of : hectare. The owner buys an extra 2 of a hectare of land. (a) What is the area of the garden now? (b) How much more land would the owner need to have a garden with an area of 2 hectares? Steve and Sheila buy a computer. Steve fills 2 of the hard disk with his programs. Sheila fills ; of the hard disk with her programs. (a) What fraction of the hard disk is full? (b) What fraction of the hard disk is empty? (c) Steve deletes one of his programs that takes up = of the hard disk. What fraction of the hard disk do his programs fill now? If = of all men in the UK own cars, and - of all men in the UK own more than one car, what fraction of men in the UK: (a) donot owna car, (b) own only one car? 125 20.3 MEP Y7 Practice Book B Example 3 Calculate: 4 3 3 @ =xXa b) 1=x= 1—x3- (a) a%5 (b) (©) Solution (@) 4y3 _ 4x3 7 5 7x5 _2 ~ 35 1 TZ a . (b) I=x> = — xe (Note: it is usually quicker to cancel down at 24 3 this stage rather than at the end.) _ 7xi 2x3 =! 6 =1- 3 5 141 4 40 (c) 2—x3= = AX 4 3 4 4 _ 3x5 ~ 2x1 15 ~ 2 =71 2 128 Exercises 1. Calculate: (a) : x15 (d) = x 14 () 3x21 Gj) 66x : 2. Calculate: w ded w bd (g) : x : @ = x ; 3. Calculate: (a) 5 x : (d) 3 x ; () 45x2 gq) 1-x 2 4. MEP Y7 Practice Book B (b) =x 32 (e) ox 28 (h) 24 x3 (k) 34 xs o te od w $d (b) 45 xe (e) 4a x= (h) 5 x 5 (k) 3 x 2 Calculate the area of each of these rectangles: (a) 2m (b) [J colw B (c) (6) (i) (c) () (i) a) (c) (6) (i) a) 1 x16 8 — x30 8x2 9 —x57 19 x x [un col RW Wile Alm BlwW Ble x Jn > x wiry e S O [J 3 gm 129 20.3 MEP Y7 Practice Book B A cake recipe requires : kg of flour. How much flour is needed to make: (a) 2 cakes, (b) 6cakes, (c) 10 cakes? Jan buys : kg cheese. She keeps : of it and gives ; to her sister. What is the weight of: (a) _ the cheese Jan keeps, (b) _ the cheese Jan gives to her sister? A large company makes £: million profit. They spend + of this on new equipment. (a) How much does the company spend on new equipment? (b) How much is left? Calculate the area of each of these rectangles: 1 2- = 20 a [J C [J Uy (a) (b) Bp 3 1 3 What is the area of the shaded border? 130 mo. Example 3 Calculate: (a) Blo wie Solution MEP Y7 Practice Book B (c) 3,28 ® 4°10 ln ls w]e we These problems can be tackled using the same approach as when a whole number is divided by a fraction. 3.1. 32.5 a 322i 3,3 OM 57a ib =32 4 5.2 5.3 b) += = =x ®) 3°72 ab 14 = yt ~ 14 wo 329 235, 4°10 A 2 By => 6 We are using the rule: Exercises 1. Calculate: 1 a ~+3 (a) 3 3 d —+4 (d) 4 6 (g) 543 [Note: You can cancel only when the 2nd fraction has been turned upside-down.] a c aid 22 Lay b od b c (b) os () -+2 5 —+3 +2 (e) 3 () 5 th) S29 @ 123 133 20.4 MEP Y7 Practice Book B @) 224 (k) ~ +6 dd) f27 2. Calculate: (a) 65 (b) 934 (c) 834 (d) 224 (e) 22 (f) 423 (g) 84 (h) 5+3 @ 923 @) 65 (k) ei dd) ned 3. Calculate: De ee @ 52 w S58 @ 12 oh wee on be 4. By using improper fractions, calculate: (a) 15332 (b) 3p e14 (c) 1233 (d) ape (e) S545 (f) zt 5. Ahmed has : kg of sweets. He divides these into 3 equal parts so that he can share them with his two brothers. What fraction of a kg does each boy get? 6. Sandra has + litre of orange squash to make 10 drinks. How much orange squash should she put in each drink? 134 10. MEP Y7 Practice Book B A large cake uses 3 times as much flour as a small cake. A large cake needs 1 kg of flour. How much flour does a small cake need? A piece of leather is 20 cm wide and 45 cm long. 45 cm 20cm How many bookmarks, 2 cm wide, can be made if the leather is: (a) cut as shown above, to make bookmarks 20 cm long, (b) cut the other way to make bookmarks 45 cm long? A recipe for a cake requires + kg of sugar. How many cakes can be made with: 1 (a) i kg of sugar., 3 (b) a kg of sugar, 1 (c) 33 kg of sugar? A car uses 4 litres of petrol for every 10 miles it travels. How far can the car travel on: (a) 5 litres of petrol, (b) 15 litres of petrol, (c) 9 litres of petrol? 135,