© 2006 1 -2008 tutorco.com TOPIC: Fractions Specific Objectives: • The students will be aware of Fractions • The students will be able to compare fractions with same base , different bas • The students will be able to compare the fractions too Recommended time: 15 minutes Explanation and EXAMPLES: Recommended time: 10 minutes Key Concept: Understanding, comparing and ordering fractions. Plan of action: The tutor will start from a fraction and the make them understand how a group of fraction makes a whole, then move into the comparing part depending or looking into the denominator and will at last go to the ordering of fraction thus making them help to understand the arrangement of fractions in order from least to greatest and vice versa What they already know: The students should have the knowledge of fractions or a whole. The should know how to multiply, the multiple facts should be known to them properly. 9/1/1/1 © 2006 2 -2008 tutorco.com Key words for fractions Fraction Any part of a whole. When you divide something into equal pieces, each piece is a fraction of the whole thing. Numerator and denominator Fractions are written as one number on top of another. For example a half is written as 1 on top of 2 like this The parts are given the names numerator and denominator. Common fraction or proper fraction Common fractions are smaller than 1. They are also called proper fractions. E.g. Improper fraction or top heavy fraction A fraction bigger than 1. They are also called top heavy fractions. E.g. Mixed number Mixed numbers are bigger than 1. A mixed number is a combination of a whole number and a common fraction. E.g. 2 Equivalent fraction Fractions that have the same value. For example = You can make equivalent fractions by multiplying or dividing the top and bottom of a fraction by the same number. Reducing, simplifying or cancelling down fractions To simplify a fraction you divide the numerator and the denominator by the © 2006 3 -2008 tutorco.com largest number that divides both exactly. The value of the fraction stays the same. This is also called reducing or simplifying. Comparing unit fractions A unit fraction has a 1 on the top of the fraction. The number on the top is called the numerator. So a unit fraction means a fraction with 1 as the numerator. These are examples of unit fractions: , , , , In a unit fraction the larger the number on the bottom the smaller the value of the fraction. For example, the fraction is smaller than You can see this by looking at this part of the fraction wall For the same reason is larger than You can see this from the fraction wall too Ordering unit fractions If you have many unit fractions you can put them in order of value by comparing the numbers on the bottom, called the denominators. Warning: This only works for unit fractions. So first check that they all have a numerator of 1 Example Put the following in order with the largest first © 2006 4 -2008 tutorco.com The measuring jugs are full to fractions of a whole jug. The amounts in each jug are Putting the jugs in order we get So you can read the fractions from them now in order, largest first From this you can see that the unit fraction with the largest number on the bottom is the smallest in value. Example Put the following in order of value, smallest first , , , , , These are all unit fractions. So the bigger the number on the bottom the smaller the value of the fraction. The question asks for the smallest first so start with the fractions with the biggest number on the bottom. Answer This is the correct order, smallest first < < < < < The symbol < means less than. Compare fractions with the same denominator These fractions all have 4 on the bottom. © 2006 5 -2008 tutorco.com They all have a denominator of 4. This is (one quarter) This is (two quarters) This is (three quarters) You can see that is smaller than , and that is smaller than . We write this using the less than sign like this < < Look at the numbers on the top, 1 2 3. They are in order too. When fractions have the same denominator, you can put them in order using the numbers on the top. Example Put these fractions in order with the smallest first , , , All these fractions have the same denominator, which is 7. The numbers on top are 2, 6, 1 and 4. We can put these in order, smallest first, as 1, 2, 4, 6. So the fractions in order are Example Put these fractions in order with the largest first All these fractions have the same denominator, which is 100. The numbers on top are 20, 43, 8, 85 and 2. We can put these in order, largest first, as 85, 43, 20, 8 and 2. © 2006 6 -2008 tutorco.com So the fractions in order are Compare and order fractions using a fraction wall You can use a fraction wall to compare common fractions. The fraction wall from Factsheet 2 goes down to . Using the fraction wall you can compare fractions. Example Which is larger or ? You can see that is larger than Example Which is larger or ? You can see that is larger than Example Use the fraction wall to compare the following fractions and The answer is that is larger than © 2006 7 -2008 tutorco.com Example Which of the following fractions are larger than ? You can see that and are both larger than But is less than And if you look closely you can see that is the same as Mixed numbers What are mixed numbers? A number like 1 is called a mixed number because it has a mix of a whole number and a fraction. The whole number part is 1 The fraction part is Examples Here are some more examples of mixed numbers 2 6 10 33 99 Comparing mixed numbers When you compare the size of two mixed numbers the first things to check are the whole number parts. If one has a smaller whole number part than the other then it is the smaller number. Example 1 is less than 2 because 1 is less than 2. When the whole number parts are the same then you need to check the fraction parts. Example Which is smaller 1 or 1 ? Both are mixed numbers. First compare the whole number parts. Both have a whole number part of 1. So we need to compare the fraction parts. is less than So 1 is less than 1© 2006 8 -2008 tutorco.com When you compare fractions with mixed numbers the fractions have no whole number part, so they are smaller than the mixed numbers. Example Put these in order, smallest first: 2 , , 1 Answer The smallest is because the others have whole number parts. 1 is smaller than 2 because it has a smaller whole number part. The correct order, smallest first, is , 1 , 2