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Cambridge Lower Secondary Mathematics Workbook 8 2nd Edition Lynn Byrd, Greg Byrd, Chris Pearce - Solutions

8 Put these fraction cards in order of size, starting with the smallest. 14 A B 5 3 22 C 5 D
7 Write the correct symbol, , between each pair of fractions. a 79 29 b 15 19 C d 8 13 +3 415
6 Write the missing word from each of these sentences.Use either the word 'larger' or 'smaller'.When you compare two fractions with the same denominator, a the larger the numerator the the fraction.b When you compare two fractions with the same numerator, the larger the denominator the the fraction.
5 a Complete the workings to write each fraction as a decimal. Work out the first four decimal places.b. Write the fracti−177, 229, and −2711-\frac{17}{7},\ \frac{22}{9},\ \text{and}\ -\frac{27}{11}−717, 922, and −1127in order of size, starting with the smallest. i --17--22 04 2 7 3
4 Work out which is larger. a 58 b or 212 225 C -72 or 3
3 Write the correct symbol, , between each pair of fractions. They have all been started for you. Use the number lines to help. a -2 b -2 d - 15 - 27 5 17 3 5 15 2--2--2-and-2--2- 6 6 -2 12 4 12 12
2 Write the correct symbol, , between each pair of fractions. They have all been started for you. 20 a b C d 72 33 215 8 23 3 162025 2 3 4 2 8 3 10 10 and 82-8 5 10 15 and 7=7 5 15
1 Write the correct sign, or, between each pair of fractions. They have all been started for you. a 13 b C d 40 13 8 4 4 =3. =3. 8 40 and 4-4 3 9 4-44-4 9 47 47 44 and 4-4 =-4 10 10 10 5 10
15 Read what Arun says. Is Arun correct? -0.006 150 My teacher says and 2-0.013. 150 She must be wrong because is double- 2 150 but double 0.006 is 0.012 not 0.013, 150' Explain your answer.
14Write each length of time, in hours, as:i. a mixed number ii. a decimala. 30 minutesb. 2 hours 45 minutesc. 4 hours 20 minutesd. 9 hours 10 minutese. 11 hours 25 minutes
13Without using a calculator, write each fraction as a decimal.35, 813, 2940, 435\frac{3}{5},\ \frac{8}{13},\ \frac{29}{40},\ \frac{4}{35}53, 138, 4029, 354
12Write these numbers in order of size, starting with the smallest.0.56, 410, 78, 2855, 0.5, 5110.56,\ \frac{4}{10},\ \frac{7}{8},\ \frac{28}{55},\ 0.5,\ \frac{5}{11}0.56, 104, 87, 5528, 0.5, 115
11There are 27 students in a class. 22 of them are right-handed.What fraction of the students are left-handed?Write your answer as a decimal.
10Read what Zara says:“I worked out on my calculator that 7÷9=0.7777777787 \div 9 = 0.7777777787÷9=0.777777778.This means that 7 ninths is not a recurring decimal as the sevens don’t go on forever; there’s an eight on the end.”*Do you think Zara is correct?Explain your answer.
9This is part of Su’s homework.QuestionWrite these fractions as decimals.724,811,1118,539\frac{7}{24}, \frac{8}{11}, \frac{11}{18}, \frac{5}{39}
8Use a calculator to convert these fractions to decimals.a. 67\frac{6}{7}76 811\frac{8}{11}118 513\frac{5}{13}135 521\frac{5}{21}215
7Use a calculator to convert each fraction to a decimal.a. 89\frac{8}{9}98 1720\frac{17}{20}2017 625\frac{6}{25}256 2740\frac{27}{40}4027
6Read what Marcus says:“I know that 16\frac{1}{6}61 and 26\frac{2}{6}62 are recurring decimals. This means that any fraction with a denominator of 6 is also a recurring decimal.”Is Marcus correct? Explain your answer.
5Here are five fraction cards.A 58\frac{5}{8}85 B 13\frac{1}{3}31 C 512\frac{5}{12}125 D 45\frac{4}{5}54 E 815\frac{8}{15}158a. Without doing any calculations, do you think these fractions are terminating or recurring decimals? Explain why.b. Use a written method to convert each fraction to
4 Here are five fraction cards.a Without doing any calculations, do you think these fractions are or recurring decimals? Explain terminating why.b Use a written method to convert each fraction to a decimal.order of size, starting with c Write the fractions in the smallest. A 84 B 45 C 30 D 32 E
3 Use your answers to Question 2 to write these fractions in order of size, starting with the smallest. 73342 10' 5' 8' 9'11
2 Copy and complete the workings to convert each fraction into a decimal. Write if the fraction is a terminating or recurring decimal. The first two have been done for you. 2 a 25 C e 0.666 3 2 20 20 20 3 23 2 = 0.6 recurring decimal 0. 5 3 0 7 2 0 94 30 0 20 0 . 0 5 52 34 50 3 310 25 =0.4 . 4 b 20
1 Match each unit fraction with the correct equivalent decimal.Write if the fraction is a terminating decimal or a recurring decimal.One is done for you: -= 0.16, recurring decimal 12 113 1 1 1 1 3 4 5 6 7 81- 1 1 10 0.16 0.25 0.3 0.5 0.2 0.i 0.1 0.142857 0.125
14 Here are three formula cards. b= 18 a c-bx(2-1)-3(c-11) Work out the value of d when Explain the method you used. 3
13 Here are two calculation cards. A 6+96-9) B (+) (+)Read what Sofia says.Is Sofia correct? Show all your working. The answer to card B divided by the answer to card A is 96.
12 Work out. If you cannot do a calculation mentally, write down some workings to help you. a C 10(-3) 14 13-(-9) 15 b 3+ (1+1) d 12-(+)
11 This is how Arun mentally works out 14+2 107 1 First, I work out 1 which equals 10 2 5 Then I work out 14+1 14 which equals 5 5 5 a Explain the mistake Arun has made.b Work out the correct answer. 7 1 First, I work out which equals 10 2 5 Then I work out 14+, which equals 14-2
10 The diagram shows a rectangle. The area of the rectangle is 15m. The width of the rectangle is 8 m. What is the length of the rectangle? length 58 5. m
9 a Work out. i x4+3= 4 Some working has been shown to help you with the first two. 6+=64+ ii 9+=95+3= 5 !!! iv 8+2 8+ 3 V 12+ vi 20- 20+1 b Use a calculator to check your answers to parta. C Did you get the answers to part a correct? If not, what mistakes did you make?
8 In a bag of mixed fruits, are lemons, 2 are strawberries and the rest are bananas. 8 What fraction of the fruits in the bag are bananas?
7 Work out these additions and subtractions. Use the same method as in Questions 3 and 4. + 3 d 29 1427 + 143579 151525 + 1 -19-12 E 183425 + 132934 b f j 115 112 + 13 Sir g k -
4 Work out each subtraction. Some working has been shown to help you.5 In a tennis club, - of the members are women, 3/2 of the members are men and the rest are children.5 What fraction of the members are children?6 Work out these additions and subtractions. Use the same method as in Questions 1
3 Work out each addition. Some working has been shown to help you. =+ = a 1 1 1x5+1x2 5+2 = b 111x7+1x3 +-= + 25 2x5 10 10 37 2 1 2x4+1x3 + 1 3 1x5+3x6 3x7 21 21 + 3 = d 3 4 3x4 12 12 -+-= 65 6x5
2 Work out each subtraction. Some working has been shown to help you. 9 a U 3 6 2 39 9 9 b d 9 70 - 80 1 10 5 = 8 70 00 8 8 10 10
1 Work out each addition. Some working has been shown to help you. a 11 5 10 1 -0 22 10 10 10 10 8 3. 1 -+ = C + 4 8 B-AM b 9 d + = = 4 12 + 1 = 12 12 12
15 The diagram shows a triangle.a b C Work out the value of y when x=30 Work out the value of y when x=43 Explain why it is not possible for x to be 65. + x +X 1-0 +15
14 A straight line graph has the equation y=x a Copy and complete this table of values. b 0 2 4 6 8 y Draw a coordinate grid going from 0 to 8 on the x-axis and on the y-axis. xf Plot the points from the table above. Draw the line y=x from x=0 to x=8.
13 The answers to these three calculation cards are the first three terms in a sequence. 12 2+ 31 Work out a b C 3+ 11 the first term of the sequence 5+6 7 the term-to-term rule of the sequence the next three terms in the sequence d the 10th term in the sequence.
12 Which of these two calculation cards gives the smaller answer? A 32+ 13 15 B 35+13 15 Explain how you made your decision.
11 Which of these two calculation cards gives the greater answer? A 25+ 7 B 25+5 8 Explain how you made your decision.
10 Jaq uses this formula in a science lesson. s=uxt a b Work out the value of s when u=3 and 1=12. Work out the value of t when s=22 and u=4, 9
9 The area of a rectangle is 18 m. The width of the rectangle is 4m. What is the length of the rectangle? Give your answer as a mixed number in its lowest terms.
8 Work out the answer to each calculation. Give each answer as a mixed number in its lowest terms. a 27 4+ b 3+ 90 10 C 10+ 45 d 814 15
7 Work out the answer to each calculation. Use the reciprocal method. The first two have been started for you. a =8x. 47 C 9+ 3 43 40 12+ 10100 b **-7-8-08 e +9
6 Work out the answer to each calculation. Use the diagrams to help you. a 2+ 23 b 2+1/3 25 C 3+ 3 4
5 This is what Sofia says about dividing an integer by a unit fraction.Use Sofia's method to work out a 11+1 C 12+1 b 20+ The quick way to divide an integer by a unit fraction is to multiply the integer by the denominator of the fraction.
4 Work out the answer to each calculation. Draw diagrams to help if you want to. 4 a 1+1 5 b 3+ 3+ C 2+1
3 a Work out the answer to each calculation. Use the diagrams to help you.b Write the answers to i 1+ ii 2+1
2 a Work out the answer to each calculation. Use the diagrams to help you.b Write the answers to i 1+1 ii 2+1 iv
1 a Work out the answer to each calculation. Use the diagrams to help you.1 ii 2+1 i 1+-2 2 1 iii 3+iv 4+1 2 2 ..b Write the answers to i 2 iii 74 == 9 ii 6+1 iv 8+. 8+ 1212
15 a This is part of Helena's homework.Question x is an integer. Work out the value of x when xx5 = 651 Answer 4 Try x=10 10x5= =10x5 + 10x = 50+40=50 + 4 = 54 9 54651 so try a bigger value for .x 56 Try x = 14 14x5=14x5+ 14x4 = 70 + 50 = 70 + 6 = 762 9 76 > 65 so try a smaller value for x Carry on
14 The diagram shows a cuboid.The length, width and height of the cuboid are shown on the diagram. a Estimate the volume of the cuboid. b Raj works out that the volume of the cuboid is 210 cm. Is Raj correct? Show your working. 12cm 4cm
13 a Work out the value of each of these cards. Write each answer in its simplest form.b Write down the median value. C Work out the range of the values. 6x11 127 15 9x8 6
12 Work out a b an estimate for the area of the grey section of this rectangle the accurate area of the grey section of this rectangle. E 88 m 215 2m
11 Alec works in a factory. His job is to pack boxes. It takes him 3 minutes to pack one box. How long will it take him to pack 60 boxes? Give your answer in hours and minutes.
10 For each of these calculations, work out i an estimate Write each answer in its simplest form. a 2312 b 610 ii the accurate answer. C
9 Write these cards in order of size, starting with the smallest. 9 A 8x43 6 B 123- C 5x7% 5
8 Which is greater, 325 or 421?Show all your working.
7 Rosa buys carpet for her bedroom floor. The floor is a rectangle with length 4m and width 3m. 8 a b Rosa estimates that the area of her bedroom floor is 12 m. Is Rosa correct? Explain your answer. Work out the area of her bedroom floor. Rosa buys carpet that costs $15 per square metre. She can
6 The diagram shows a square joined to a rectangle. Show that the total area of the shape is 131 cm. 7cm 7cm 11 cm
5 Copy and complete each multiplication. a C 32x7=3x7+2x7 -+ -+3 2 80- 62x5=6x+2x5 b 4x9=4x9+x9 =+ *+2D -08 4x8=4x+2x8 5 8.0- -0+08 8+0- -0+08
4 Archie uses this formula in a science lesson. F=mxa a Estimate the value of F when m=21 and a=3 When m=21 and a=32, Archie works out that F=77. bi Use your answer to part a to help you decide if Archie could be correct. ii Work out the value of F to help you decide if Archie is correct.
3 Copy and complete each multiplication.32x12-3x12+2x12 +8 3210=310+210 5 + b 3 2x8-2x8+x8 5 d 1218=118+218
2 This rectangle has a length of 12m and a width of 2 m 2-m.Work out a an estimate for the area of the rectangle b the accurate area of the rectangle. 12m E
1 Copy and complete each multiplication. a 26=26+16 +3 x9 51x9= 59+19 = + 3x8=3x8+x8 + d 415=415+ 115 +
16 The diagram shows four mixed numbers linked by lines. a Work out the total of any two of the linked mixed numbers. C Without working out all the answers, explain how you can decide which two mixed numbers give the greatest total? What is this total? Write your answer in its simplest form. Work
15 Read what Arun says.Use at least two counter-examples to show that Arun's statement is not true. If I add together two mixed numbers, my answer will always be less than the sum of the whole-number parts plus 1.
14 The area of this compound shape is 15 m. The area of one rectangle is 94m. a estimate, then b calculate the area of the other rectangle.
13 The diagram shows two statues. Each statue is made from three parts. The height of each part, in metres, is shown.a Which statue is taller? Show your working.b What is the difference in height between the two statues? A m B 23 E 12 4 m E 34 m 13 m 88 100
12 This is part of Beth's homework. She has made a mistake in her solution.Question Work out 3 4 - 1 3 Answer 3 4 - 3 16 and 1 3 = 1 27 3 16 _127 - 21 36 36 Explain the mistake Beth has made.a bWork out the correct answer.
11 The table shows the distances that Nia drives on Monday to Friday one week.Nia works out that the range of the distances she travels is 9112 km. Is Nia correct? Explain your answer. 20 Show all your working. Day Monday Distance (km) 126 1 Tuesday Wednesday Thursday Friday 1873 2 105- 4 8 957 10
10 Xao is a plumber. He has two pieces of pipe. The first piece is 3 m long; the second is 4m long. He fixes them together, as shown in the diagram. estimate, then a i ii calculate the total length of the two pipes. Xao wants a pipe that is 10 m long.b How much more pipe does he need? 25 3 m 4 m 34
9 Work out these subtractions. Show all the steps in your working. a 71-1-3333 b S 56 522-3399 C 100 4-12 34 d 10. S 22
8 Copy and complete this subtraction. 10 Step 1: Step 3: 33 39 4 10 20 20 Step 2: 33 39 4 10 20 20 20 20 20
7 Silvie has a piece of wood 4m long. She wants to make some shelves. She cuts two pieces of wood, each 1 m long, from the piece she has. How long is the piece of wood Silvie has left? 34 m m 4 up
6 Bim and Yolander have been out for a training run. Bim ran for 8 kilometres. Yolander ran for 10 kilometres. estimate, then 4 b calculate, the answers to these questions. What is the difference between the distances run by Bim and Yolander? a i ii How far in total did Bim and Yolander run?
5 One of these cards gives a different answer to the other two.Which one is it? Show all your working. 19 20 A 4- 2 7 B 10 514-33 C 15 5 54. 7 -3- 21
4 Work out these subtractions. Show all the steps in your working. a 55 55 11 6 12 b 42-1166 10 10 28- d 61-3
3 Copy and complete each subtraction. a += = 92 64 4 b 8 8 8 8448 8 C 5 1 8 10 10 39 2 10 10 =3 10 10 10 d 7 3 6 9
2 Work out these subtractions. Show all the steps in your working. a T 23/3-1/13 35 b 4-2 C d 6-30
1 Copy and complete the steps in each subtraction. 1 a 41-3 14 10 3 3 14 10 3 3 C 3 - 3 711-5334 5 5 3 b 3-1 229 29 16 9 6 69 16 Q.Q d 52-20 7 7 555 55 7 7 7 7 =2 7 a b cd 423-31 193 14 10 3 3 14 10 3 3 3 3 3
14 Arun has three fraction cards. He puts them in order, starting with the smallest.8 29 13 9 36 18 Read what Arun says. a Is Arun correct? Explain your answer.b On a number line, work out which fraction is exactly halfway between -1 and -11
13 In a drugs trial, two different drugs are tested on some patients. 145 patients are given drug A, and it helps 112 of them. 180 patients are given drug B, and it helps 137 of them. Use a calculator to work out which drug helped the greater percentage of patients.
12 One day, a baker sells 87% of his loaves of bread. The following day, he sells 30 out of 34 loaves. Use a calculator to work out on which day he sold the greater percentage of bread loaves.
11 Write these fractions in order of size, starting with the smallest. 61 7 49 6 107 7 8 12
10 Two swimming clubs compare the percentage of girl members. In the Dolphins club, 42 out of 60 members are girls. In the Seals club, 68% of members are girls. Which club has the higher percentage of girl members? Show how you worked out your answer.
9 Three friends sat a Spanish test on the same day. Amina scored 18, Ben scored 37, and Cynthia scored 73%. 25 50 Who had the highest percentage score?
8 Put these fraction cards in order of size, starting with the smallest. 8 A 9 14 B 3 22 C D 5
7 Write the correct symbol, < or >, between each pair of fractions. Write 15+ 10m 719 77 2NIO 4b dC a11 98 813 53
6 Write the missing word from each of these sentences. Use either the word 'larger' or 'smaller'. a When you compare two fractions with the same denominator, the larger the numerator the b ................actio.... When you compare two fractions with the same numerator, the larger the denominator
5 a Complete the workings to write each fraction as a decimal. Work out the first four decimal places. 0.4 2 i -=-22 7 3 30 20 60 0 0 4 9 4 . 40 40 0 0 4 -0.42-2-2.42 -20 0 11 27=-214 11 5 50 60 00 -23= 11 b Write the fractions -17, and in order of size, starting 11 with the smallest.
4 Work out which is larger. 11 a or-25 b 23 8 10 r-2/ 23 C
3 Write the correct symbol, < or>, between each pair of fractions. They have all been started for you. Use the number lines to help. a b - - 20 8 3 3 and -1- 2 -2 -3 C 27 27-51 =-5 5 17 5 15 dand-2--2 -2 12 4 12
2 Write the correct symbol, , between each pair of fractions. They have all been started for you. a 33 7 1 =3=3 2 2 4 b 13 13 4. 3 3 83 83 C 8 and 82-8 10 10 10 d 275 22 m 5 10 and 7--7- 15 5 15
1 Write the correct sign, = or, between each pair of fractions. They have all been started for you. 13 a 3 200 13 =3 =3. 4 8 b 40 4 and 4 4. 9 3 9 C 47 d 44 and 44 10 47 7 =-4 10 10 5 10
15 Read what Arun says.Is Arun correct? Explain your answer.For questions 1 to 4, use the common denominator method. My teacher says 1 -0.006 150 2-0.013. and 150 She must be wrong because 2 1 is double- 150 150' but double 0.006 is 0.012 not 0.013.
14 Write each length of time, in hours, as i a mixed number ii a decimal. a 3 hours 30 minutes b 2 hour 45 minutes C 1 hour 10 minutes d 4 hours 20 minutes e 9 hours 12 minutes f 11 hours 25 minutes
13 Without using a calculator, write each fraction as a decimal. a 5 3 53 b 13 4 29 9 d 88 35
12 Write your answer as a decimal. 12 Write these numbers in order of size, starting with the smallest. 0.56, 4, 0.6, 7, 58.2%, 18, 55%, 0.5 0.56,, 13 15,55%, 27'
11 There are 27 students in a class. 22 of them are right-handed. What fraction of the students are left-handed?

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