Answers

Chapter 1: Fractions, Exercise 1.4  (page 14)

 1 3.142  2 3.1416  3 16.2
decimals and  4 0.24  5 14.1  6 14.8
rounding  7 6.2240
10 20
 8 1.90
11 14.3
 9 15.4
12 359 300
Starter 1  (page 1) 13 370 14 10 15 0.0021
 1 100 cm (1 metre)
16 11.0
 2 1}8}
17 a) 1000 b) 1000 c) 20
 3
d) 6 e) 8 f) 20
g) 4 h) 5 i) 6
18 $10 800 or $12 000 19 34.5 cm 20 21 500 mm2
21 Not possible, last week must be at least 24 500, the
week before not more than 24 450, so no overlap is
possible.
 4 One person cuts and the other one chooses.
22 No. The age is only given to the nearest million years
Exercise 1.1  (page 6) so Charlie’s calculation is not valid.
 1 1}4}  2 3}7}  3 }44}1
Exercise 1.5  (page 16)
 4 14}}  5 15}}  6 34}}  1 24.058
 7 3}5}  8 3}5}  9 4}7}  2 24.01
10 }35} 11 7
}} 12
13
7
}}
9  3 5.089 204 26; 5.09
1 11 3 5
13 }2}, }2}0, }5}, }8} 14 2 3 5 7
}}, }}, }}, }} 15
3 4 6 8
2 4 5 13
}}, }}, }}, }}
3 5 6 15
 4 11
7
16 9 17 9 5  5 0.292 279 412; 0.292
16 18
}} } } }}
6
13 3  6 4.929 503 018; 4.93
19 }2}4 20 }}
8 21 TK
 7 2.342 857 143; 2.34
22 }34}78 23 155
}}
252 24 5}14}30  8 1.161 290 323; 1.16
67 15
25 10}7}2 26 2}5}6 27 35}8}  9 17.576
28 2}35} 29 2}34} 30 8}12} 10 5.88
31 3}2}0 3
11 4.301 162 634; 4.30
12 1.16
Exercise 1.2  (page 9) 13 2.150 326 797; 2.15
 1 2}5}  2 5}9}  3 1}21}0 14 5.816 356 248; 5.82
 4 49}}  5 15  6 }115} 15 1.666 666 667; 1.67
 7 }25}8  8 120  9 }185} Exercise 1.6  (page 18)
10 1}2} 11 15
}} 12
16
}}
18
1
 1 a) 50 cm, 46 cm b) 156.25 cm2, 132.25 cm2
13 }17}6 14 1
}} 15
18
3
}}
4
 2 a) 34 cm b) 52.25 cm2
5  3 a) 29.25 cm2 b) 0.538
16 1 17 }} 18
16 2
 4 a) 60 mph b) 56.86 mph  c) 63.27 mph
19 }19}6 20 11}2} 21 TK  5 28.5 cm2
22 205}8} 23 6 24 311}2}
25 12 26 100 27 1
}}
2
Review Exercise 1  (page 18)
 1 1}23}0  2 1}14}5  3 31}21}4
Exercise 1.3  (page 11)  4 4}12}10  5 5  6 23}13}
 1 }26}5  2 1}28}5  3 }13}0  7 33}4}  8 14  9 }17}2, 5}8}, 3}4}, 5}6}
 4 58}}  5 }1901}0  6 }41}0 10 3}5 , 2}3}, 107 , 15
11

 7 14}57}0  8 1}59}0  9 21}8} 11 a) 300 b) 100 c) 8
303 7 29 . 3
10 }
1000 11
} }} 12
9
}}
99
5
12 8, 0.65, 0.6, 4
} } } }
1 1733 43
13 13}} 14 3330 15
}} }}
99 13 a) 7}8} b) 5
}}
11
6 107
16 11 17
} }
333 18
} } 11}313}30 14 a) 0.067, 0.56, 0.6, 0.605, 0.65
. .
19 0.625 20 0.4 28 571~ 21 0. 4 b) 210, 26, 24, 2, 5
22 0.45 23 .. 0.28 . c) 2}5}, 12}}, 2}3}, 3}4}
24 Wrong. 0. 3 5  3 2 5 0.707 070… which is not 0. 7 15 }15}2 16 1
}}
5

1
Answers

17 For example, 13}} and 38}} 33 1.865

18 855.4 kg 34 18
19 a) 3}41}0 b) 21}11}2 35 0.0205
20 a) 69.3 b) 6.93 c) 0.0693
21 a) 100.5 mm b) 101.5 mm Internet Challenge 1  (page 23)
1
22 a) 119.31 b) 119 310 c) 1.23  1 }16}   2 }12}10   3 }14} 1 }1}2   4  }12} 1 13}} 1 }11}2   5 }12} 1 }16} 1 }19}
23 2}9} 99  6 No, but the Erdos–Strauss conjecture claims that
24 41.2 fractions of the form 4}n} may be written as the sum of
25 a) 46.416 376 42 b) 46 three Egyptian fractions. The conjecture has been
26 a) 0.787 965 007 b) 0.79 checked for every individual case up to n 5 1014.
27 a) 17.9867 b) (1.6 + 3.8 × 2.4) × 4.2  7 Emily will write 58}} as 12}} 1 18}}.
28 2.56 For each of the first four sacks, divide the contents
29 a) 19}39} of the sack into two equal piles, giving eight piles of
b) 2}459} 45 1
}} a sack each. For the fifth sack, divide its contents
2
30 a) }14}
1 into eight equal piles, giving }18} of a sack each. Give
b) 2}23}2 each chicken coop one of the }12} sack piles and one of
31 2}115} the 18}} sack piles. The idea is that it is easier to judge
3
32 a) }1}1 splitting a sack into equal piles (1}2} or 1}8}) than to divide
..
b) Let X 5 0.0 x it asymmetrically into 3}8} and 5}8}.
So X 5 0.0x0x0x…
100 X 5 x.0x0x0x…
Subtracting gives:
99 X 5 x
x
So X 5 }}
99