Page 56 - Mathematics of Business and Finance

36 Chapter 1 | Review of Basic Arithmetic

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39. It took three consultants 27 hours, 21 hours, and 18 hours, respectively, to design a product. If each of them was
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paid $55 per hour, what was the total amount paid to them?
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40. Three software programmers worked 17 hours, 25 hours, and 11 hours, respectively, to develop an e-commerce
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site. If each of them was paid $18 per hour, how much did they receive in total?
1.4 Order of Operations (BEDMAS)

When arithmetic expressions contain multiple operations with brackets, exponents, divisions,
multiplications, additions, and subtractions, the arithmetic operation is performed in the following
Order of arithmetic sequence:
operations:
Brackets 1. Perform all operations within the brackets. If there is more than one bracket, start with the
Exponents innermost bracket and move outwards to complete all the brackets.
Divisions 2. Perform operations with exponents and roots.
Multiplications
Additions 3. Perform the necessary divisions and multiplications in the order in which they appear from left to right.
Subtractions
4. Complete the operation by performing the necessary additions and subtractions in the order in
which they appear from left to right.
The order of operations - Brackets, Exponents, Divisions, Multiplications, Additions, Subtractions -
can be remembered by the acronym BEDMAS.
Example 1.4(a) Computing Arithmetic Expressions by Following the Order of Operations (BEDMAS)

Compute the following arithmetic expressions:
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(i) (100 – 3 × 24) ÷ 2 + 4 × 3 (ii) 6 + 4 × 50 ÷ (8 – 3) – 1 (iii) 12 + 3 [(8 × 5) ÷ 5] – 7 + 2
Solution (i) (100 – 3 × 24) ÷ 2 + 4 × 3
= (100 – 3 × 24) ÷ 2 + 4 × 3 Perform multiplication within the brackets,
= (100 – 72) ÷ 2 + 4 × 3 Perform subtraction within the brackets,
= 28 ÷ 2 + 4 × 3 Perform division and multiplication from left to right,
= 14 + 4 × 3
= 14 + 12 Perform addition,
= 26
(ii) 6 + 4 × 50 ÷ (8 – 3) – 1
2
= 6 + 4 × 50 ÷ (8 – 3) – 1 Perform the operation within the brackets,
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= 6 + 4 × 50 ÷ (5) – 1 Perform the operation with the exponent,
= 6 + 4 × 50 ÷ 25 – 1 Perform division and multiplication from left to right,
= 6 + 200 ÷ 25 – 1
= 6 + 8 – 1 Perform addition and subtraction from left to right,
= 14 – 1
= 13
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(iii) 12 + 3 [(8 × 5) ÷ 5] – 7 + 2
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= 12 + 3 [(8 × 5) ÷ 5] – 7 + 2 Perform the operation within the inner brackets,
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= 12 + 3 [40 ÷ 5] – 7 + 2 Perform the operation within the outer brackets,
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= 12 + 3 (8) – 7 + 2 Perform the operation with the exponent,
= 12 + 9(8) – 7 + 2 Perform multiplication,
= 12 + 72 – 7 + 2 Perform addition and subtraction from left to right,
= 84 – 7 + 2
= 77 + 2
= 79