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Name of Lecturer: Mr. J.Agius Course: HVAC1 Lesson 8 Chapter 2. Fractions Multiplying Fractions When multiplying together two or more fractions, first multiply all the numerators together and all the denominators together. (There is no need to find a common denominator). Mixed numbers cannot be multiplied together unless one changes them into improper fractions first. It would be easier if one cancel factors that are common to the numerator and denominator before multiplication since one can multiply smaller numbers easier. The answer shall be expressed to its lowest term and as a mixed number where possible. Example 1 Simplify Step 1: Change any mixed number into an improper fraction. i.e. Step 2: The whole number 5 is treated as . So Step 3: Cancel factors that are common to the numerator and denominator before multiplication. So 2 Fractions Page 1 Name of Lecturer: Mr. J.Agius Course: HVAC1 Fractions of Quantities Sometimes in calculations with fractions the word ‘of’ appears. It should always be taken as meaning multiply. Thus, to find of the number of tiles on this floor, one need to find how many tiles are there on the floor and then multiply the answer by . There are 12 × 12 tiles = 144 tiles on this floor. 12 tiles So tiles. 12 tiles Example 2 Find three fifths of 95 metres. Three fifths of 95 means So 3 of 95 metres is 57 metres. 5 Reciprocals If the product of two numbers is 1, then each number is called the reciprocal of the other. For example; 1 3 1 so 3 So, to find the reciprocal of Now 4 3 1 3 4 1 1 is the reciprocal of 3 and 3 is the reciprocal of . 3 3 3 3 one needs the number which, when multiplied by , gives 1. 4 4 So 4 3 is the reciprocal of 3 4 In all cases the reciprocal of a fraction is obtained by turning the fraction upside down. Remember that any number can be written as a fraction. i.e. So the reciprocal of 2 Fractions is . or 1 3. Page 2 Name of Lecturer: Mr. J.Agius Course: HVAC1 Example 3 Find the reciprocal of; a) The reciprocal of 14 ( a) 14 ) is b) 3.5 . b) In order to find the reciprocal of 3.5 one needs to change this number into an improper fraction. i.e. 3.5 = . So the reciprocal of is . Dividing Fractions When dividing together two fractions, first find the reciprocal of the divisor (the number after the division sign). Before starting to work, change all the mixed numbers into improper fractions. Now change the division sign into multiplication and work as usual. Remember that the answer shall be expressed to its lowest term and as a mixed number where possible. Example 4 Work out . Before multiplying or dividing, mixed numbers must be changed into improper fractions. So 2 Fractions Page 3 Name of Lecturer: Mr. J.Agius Course: HVAC1 Multiplying Fractions Q1 Multiply the following quantities: a) b) c) d) e) f) Q2 Multiply the following quantities: a) b) c) d) e) f) Q3 Four pieces of wood each inches long are needed to build a cabinet. To get all four pieces from one board, how long must that board be? Q4 In making a chair, feet of oak are used, including waste. How many feet of oak are needed to complete an order of 64 chairs? Q5 Beams are placed m apart on a roof. If there are 6 beams from end to end, find the length of the floor? (First check how many spaces there are). Q6 This picture represents a square thread of a bolt. If each thread has mm pitch, find the total length of 12 threads. Thread pitch 2 Fractions Page 4 Name of Lecturer: Mr. J.Agius Course: HVAC1 Dividing Fractions Q1 Divide the following quantities: a) b) c) d) e) f) g) h) i) Q2 An ironmonger buys 50 kg cement. How many Q3 Determine the number of pieces of Q4 Find how many threads Q5 A bookshelf is a) kg bags can he get from this? inch plywood in a stack 45 inches high. mm pitch there are in a bolt of inches long. inches long. How many books can fit on the shelf if each book is b) inch thick? inch thick? c) inch thick? Q6 What is the height of each riser in a stair with 14 risers and a total rise of Q7 How many treads are needed for a set of stairs with a total run of tread is inches? inches when each inches wide? Height of riser Total rise (floor to top of top tread) Run or width of one thread Total run of stairs 2 Fractions Page 5