Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Large numbers wikipedia , lookup
Vincent's theorem wikipedia , lookup
Location arithmetic wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Collatz conjecture wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Positional notation wikipedia , lookup
Name of Lecturer: Mr. J.Agius Course: HVAC1 Lesson 5 Chapter 2. Fractions Equivalent Fractions A fraction is a part of a whole. If one divides a piece of plywood into 2 equal parts, each part can be written as of the original size. Furthermore, if one divides the same piece of plywood into four parts and takes two, one can see that is equivalent to . One can say that , , , etc all mean the same thing. These are called equivalent fractions. They can all be written as . is the simplest form because it has the smallest numbers. To find equivalent fractions, multiply (or divide) the top and bottom by the same number. ×4 ÷3 = = ×4 ÷3 The top number of a fraction is called the numerator. To note: 9 The bottom number of a fraction is called the denominator. Reducing a Fraction to its Lowest Terms Fractions like , , , and are said to be in their lowest terms because it is impossible to find a number which will divide exactly into both the numerator and denominator. There exists other fractions like , , , which are not in their lowest terms because they can be reduced further by dividing both numerator and denominator by a number which divides exactly into both of them. So 2 Fractions Page 1 Name of Lecturer: Mr. J.Agius Course: HVAC1 ÷2 ÷4 = = ÷2 ÷4 ÷ 30 ÷ 11 = = ÷ 30 ÷11 Sometimes one can divide the numerator and the denominator several times before one reaches the lowest terms. Example 1 Reduce to its lowest terms. ÷5 ÷3 = ÷5 ÷3 = ÷3 9 = 9 ÷3 Types of Fractions If the numerator of a fraction is less than its denominator the fraction is called a proper fraction. , , , and are all proper fractions. Note that a proper fraction has a value which is less than 1. If the numerator of a fraction is greater than its denominator then the fraction is called an improper fraction. , , , and are all improper fractions. Note that an improper fraction has a value which is greater than 1. Every improper fraction can be expressed as a whole number and a proper fraction together. These are called mixed numbers. , , , and are all mixed numbers. Consider these two sheets of plywood. One can say that there is 1 whole sheet and 4 parts out of seven from another sheet. The total number of sheets can be expressed as sheets. But if one divides the first sheet into 7 equal parts, the total becomes 2 Fractions sheets, which is an improper fraction. So and are equal. Page 2 Name of Lecturer: Mr. J.Agius Course: HVAC1 Example 2 How many pieces of plywood are there if there are be divided into 9 pieces. sheets of plywood and each sheet has to Each sheet has to be divided into 9 pieces means that; 9 + 9 + 5 = 23 ANSWER: There are 23 pieces of plywood. Example 3 Express the mixed number as an improper fraction. represents 2 whole parts plus of another part. One can use the same method as done in Example 2 and say that there are 23 parts. So in this case can be written as . To convert from mixed numbers to improper fractions faster, multiply the denominator with the whole number and add the answer with the numerator to find the numerator of the answer. Put this answer onto the same denominator. i.e. Example 4 Express as a mixed number. First divide 13 by 4 to find how many times, 4 goes into 13 and see, what is the remainder left. 3 r1 4 13 So can be written as . 3 represents the number of times 4 goes into 13 and 1 represents the remainder left. 2 Fractions Page 3 Name of Lecturer: Mr. J.Agius Course: HVAC1 Manipulating Fractions Q1 Express each of the following fractions as eighths. (Denominator equal to 8) a) b) c) d) e) f) g) h) Q2 Express each of the following fractions as fifteenths. (Denominator equal to 15) a) b) c) d) e) f) g) h) Q3 Find the missing number in each of these. a) b) c) d) e) f) g) h) i) j) k) l) Q4 Write these fractions in their simplest form. a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p) Q5 Change these mixed numbers into improper fractions. a) b) c) d) e) f) g) h) i) j) k) l) Q6 Change these improper fractions into mixed numbers. a) b) c) d) e) f) g) h) i) j) k) l) 2 Fractions Page 4