(a) Work out \(48\div 3-5\times 2\).
(b) Insert one pair of brackets to make this statement correct.
3 + 2 × 12 – 4 = 19
(c) Write the following in order, starting with the smallest.
\(\frac{3}{4}\) 0.749 76%
(d) Find the value of: [1 each]
(i) \(\sqrt{265.69}\)
(ii) 83
(e) Write down the smallest prime number.
(f) Write down all the factors of 18.
(g) Write down a common factor of 16 and 72 that is greater than 2.
(h) Write \(\frac{28}{140}\) as a fraction in its simplest form.
(i) Jeff and his friends win a prize. Jeff’s share is \$160 which is \(\frac{5}{11}\) of the prize.
Work out the value of the prize.
▶️ Answer/Explanation
(a) Ans: 6
Using order of operations (BIDMAS):
\(48 ÷ 3 = 16\)
\(5 × 2 = 10\)
\(16 – 10 = 6\)
(b) Ans: 3 + 2 × (12 – 4) = 19
Brackets make the calculation:
\(12 – 4 = 8\)
\(2 × 8 = 16\)
\(3 + 16 = 19\)
(c) Ans: 0.749, \(\frac{3}{4}\), 76%
Convert all to decimals:
\(\frac{3}{4} = 0.75\)
76% = 0.76
Order: 0.749, 0.75, 0.76
(d)(i) Ans: 16.3
\(\sqrt{265.69} = 16.3\) (since \(16.3 × 16.3 = 265.69\))
(d)(ii) Ans: 512
\(8^3 = 8 × 8 × 8 = 512\)
(e) Ans: 2
2 is the smallest number with exactly two distinct factors (1 and itself).
(f) Ans: 1, 2, 3, 6, 9, 18
Numbers that divide 18 exactly: 1 × 18, 2 × 9, 3 × 6.
(g) Ans: 4 or 8
Common factors of 16 (1,2,4,8,16) and 72 (1,2,3,4,6,8,9,12,18,24,36,72) >2: 4, 8.
(h) Ans: \(\frac{1}{5}\)
Simplify \(\frac{28}{140}\): divide numerator and denominator by 28.
(i) Ans: \$352
Let total prize be \(x\):
\(\frac{5}{11}x = 160\)
\(x = 160 × \frac{11}{5} = 352\)
(a) Write down
(i) the number twenty seven million, three hundred and sixty thousand and forty five in figures,
(ii) the six factors of 20,
(iii) a fraction that is equivalent to \(\frac{7}{9}\),
(iv) a prime number between 30 and 40.
(b) For each statement, insert one pair of brackets to make it correct.
(i) \(17-3\times 5-3=11\)
(ii) \(3+2^{2}-4=21\)
(c) Find \(\sqrt[3]{4913}\)
▶️ Answer/Explanation
(a)(i) Ans: 27,360,045
Breakdown:
– Twenty seven million → 27,000,000
– Three hundred sixty thousand → 360,000
– Forty five → 45
Combined: 27,000,000 + 360,000 + 45 = 27,360,045
(a)(ii) Ans: 1, 2, 4, 5, 10, 20
Factor pairs of 20:
1 × 20 = 20
2 × 10 = 20
4 × 5 = 20
(a)(iii) Ans: \(\frac{14}{18}\) (or any \(\frac{7k}{9k}\) where k ≠ 0)
Equivalent fractions can be found by multiplying numerator and denominator by the same number (e.g., 2: \(\frac{7×2}{9×2} = \frac{14}{18}\))
(a)(iv) Ans: 31 or 37
Prime numbers between 30-40:
31 (factors: 1,31)
37 (factors: 1,37)
(b)(i) Ans: 17 – 3 × (5 – 3) = 11
Calculation steps:
5 – 3 = 2
3 × 2 = 6
17 – 6 = 11
(b)(ii) Ans: (3 + 2)² – 4 = 21
Calculation steps:
3 + 2 = 5
5² = 25
25 – 4 = 21
(c) Ans: 17
Since 17 × 17 × 17 = 4913, \(\sqrt[3]{4913} = 17\)