Understanding Engineering Mathematics

1.3.3 Highest common factor and lowest common multiple

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38

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A.Express in terms of prime factors

(i) 2 (ii) − 6 (iii) 21

(iv) 24 (v) − 72 (vi) 81

(vii)

27

14

(viii) 143 (ix) 391

(x) 205

B. Determine the highest common factor of each of the following sets of numbers

(i) 11, 88 (ii) 28, 40 (iii) 25, 1001

(iv) 20, 45, 90 (v) 14, 63, 95 (vi) 24, 72, 96

(vii) 36, 42, 54

C.Find the lowest common multiple of each of the following sets of numbers

(i) 2, 4 (ii) 5, 8 (iii) 12, 15

(iv) 6, 9, 27 (v) 12, 42, 60, 70 (vi) 66, 144

1.3.4 Manipulation of numbers

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310

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A.Evaluate

(i) 3− 6 × 7 (ii) 3( 4 − 1 )− 2 (iii) ( 4 − 1 )÷( 6 − 3 )

(iv) 6−( 3 − 6 )× 4 (v) 24÷( 6 ÷ 2 ) (vi) ( 24 ÷ 6 )÷ 2

(vii) ( 2 ×( 3 − 1 ))÷( 7 − 2 ( 3 − 1 ))

B.Evaluate

(i) 10−( 2 − 3 × 42 ) (ii) 100− 3 ( 7 − 10 )^3 (iii) −((−(−((−1)))))

(iv) − 3 ( 2 −( 3 + 1 )(− 4 + 2 )+ 4 × 3 ) (v) 1− 4 (− 2 )

C.Evaluate 4+ 5 × 23 in its conventional meaning. Without these conventions how many
pairs of brackets would be needed to make the meaning of the expression clear?
Now insert one pair of brackets in as many different non-trivial ways as possible
and evaluate the resulting expressions (retaining the other usual conventions). Can any
other results be obtained by the insertion of a second pair of brackets?

1.3.5 Handling fractions

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312

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A.Find in simplest form as a fraction