Fractions Key Concept: Form Related Concepts: Equivalence, Simplification Global Context: Personal and cultural expression Statement of Inquiry: Different forms can make quantities easier to understand and use in everyday life. Factual Concept Questions How do you simplify a fraction? How do you convert fractions to decimals? What are prime numbers? Conceptual Concept Questions Where are HCF and LCM's useful? How do LCM's relate to adding/ subtracting fractions? Is there a biggest prime number? Content
| Factors and Multiples The factors of a number are all the numbers that divide that number exactly. eg the factors of 12 are 1,2,3,4,6 and 12. The multiples of a number are all the numbers that the number multiplies into exactly. e.g. multiples of 12 are 12,24,36,48 etc The highest common factor (HCF) of two numbers is the biggest number that divides in both numbers. e.g. the HCF of 12 and 18 is 6 to work this out write out all the factors of 12 and all the factors of 18 and see which is the biggest number they both have in common: Factors of 12: 1,2,3,4,6,12 Factors of 18: 1,2,3,6,9,18 common factors highest common factor - the largest number that is a factor of both numbers The lowest common multiple (LCM) of two numbers is the smallest number that both numbers multiply into. e.g. the LCM of 12 and 18 is 36 to work this out start listing the multiples of the two numbers, the LCM is the smallest number that appears in both lists. Multiples of 12: 12,24,36,48,60,72,84 Multiples of 18: 18,36 lowest common multiple of 12 and 18. Workbook 8. Multiples, Factors & Primes Question A [C as extension] Fractions A fraction is a way to describe parts of a whole.
Equivalent Fractions Equivalent fractions are fractions that are equal in value. You can make equivalent fractions by multiplying or dividing the top and bottom of the fraction by the same number. Whatever you do to the top you must do exactly the same to the bottom. eg
We use equivalent fractions to help us simplify fractions (or cancel down fractions) where we divide the top and bottom by the same number. You should always give your fractions in their simplest form when answering questions. This means dividing the top and bottom of your fractions by their highest common factor or dividing until you cannot divide them any more. Workbook 23. Equivalent Fractions Question A [E as extension] 24. Cancelling Fractions Questions A and B [D as extension] Writing Fractions with a Common Denominator This is where we take fractions where the denominator is different and express them as equivalent fractions with the same deonominator. This helps us when comparing, adding or subtracting fractions. To write two fractions with a common denominator you need to find the LCM of the two denominators. This number will be the denominaor for your equivalent fractions. for example: Write ½ and ⅔ as fractions with a common denominator. We first find the LCM of 2 and 3. The LCM of 2 and 3 is 6. So 6 will be the deonominator of our new equivalent fractions. Work with each fraction in turn to find the equivalent fraction with 6 as the denominator. First lets take ½, we need to find the equivalent fraction to 1/2 that has denominator 6 : how many times does 2 go into 6? 2 multiplied by 3 is 6 whatever we do to the top we have to do to the bottom so multiply the numerator by 3 in this case to give the equivalent fraction 3/6.
how many times does 3 go into 6? 3 multiplied by 2 is 6 whatever we do to the top we have to do to the bottom so multiply the numerator by 2 in this case to give the equivalent fraction 4/6.
3/6 and 4/6. Comparing Fractions It is difficult to compare fractions when they have different denominators. Taking the example above which is bigger ½ or ⅔? When we write them as fractions with a common denominator it is very easy to see: which is bigger 3/6 or 4/6? 4 of something is more than 3 of something so 4/6 is bigger than 3/6 which means ⅔ is bigger than ½. Workbook 27. Working with Fractions Questions A and B Adding and Subtracting Fractions To add and subtract fractions firstly you must ensure all the fractions you are working with have a common denominator. You then add or subtract the numerators, the denominator stays the same. Example: Workbook 27. Working with Fractions Questions C Multiplying and Dividing Fractions To multiply fractions You multiply numerators to give the new numerator, You multiply the denominators to give the new denominator. Example: To divide fractions You change the divide to a multiply and 'flip' the second fraction, You then follow the steps for multiplying fractions: You multiply numerators to give the new numerator, You multiply the denominators to give the new denominator. Example: Workbook 27. Working with Fractions Questions C Recipe Activity 1) Get into groups of 2 or 3 2) Choose a recipe book 3) Look through the recipe book for a recipe that uses lots of different fractions (and sounds tasty!) 4) Write down, for your chosen recipe, the title, ingredients list (including quantities) and how many people it serves for. 5) We want to share this wonderful food with the class, write out the ingredients list so that you can serve everyone in the class (20 students). 6*) It was so tasty, we now want to share this wonderful food with the year group, write out the ingredients list so that you can serve everyone in year 7 (72 students). Prime Factors The prime factors of a number are the factors of a number that are also prime numbers. We can write all numbers as a product of prime factors. Drawing a factor tree helps: Example: If you know the product of prime factors of two numbers you can find the HCF and LCM of those numbers. a) By drawing a factor tree, find the product of prime factors of 125. b) By drawing a factor tree, Find the product of prime factors of 300. The HCF of 125 and 300 is 25 - can you work out how I found this using the products of prime factors? The LCM of 125 and 300 is 1500 - can you work out how I found this using the products of prime factors? For the numbers 540 and 135 ... a) draw the factor trees b) write them as products of prime factors c) find the LCM d) find the HCF |
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