Fractions. If the top and bottom numbers of a fraction are the same then you have a whole one.

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1 What do fractions mean? Fractions Academic Skills Advice Look at the bottom of the fraction first this tells you how many pieces the shape (or number) has been cut into. Then look at the top of the fraction this tells you how many pieces you are using. numerator (top) denominator (bottom) means How many pieces are you using? How many EQUAL pieces have you split something into? means split the shape (or number) into and use piece means split the shape (or number) into and use pieces Remember: If the top and bottom numbers of a fraction are the same then you have a whole one. For example means split the shape (or number) into pieces and use of them (in other words the whole thing). halves thirds quarters fifths sixths etc Remember: A fraction is also a way of writing a division calculation. For example is a fraction and it also means (to do this calculation you would write.00 ) H Jackson 0 / ACADEMIC SKILLS

2 Finding Fractions of Numbers: Remember our definition of a fraction: the bottom tells us how many pieces to split (divide) the shape (or number) into and the top tells us how many pieces we are using. So it follows, that we will divide by the bottom number and then multiply by the top number: To find: of a number by of a number by of a number by etc. Always divide by the bottom number: of. (to find a third divide by the bottom number.) of 7. (to find a fifth divide by the bottom number.) Then multiply by the top number: x Answer of x (to find third ) (x to find thirds) bottom number top number of 7 x 7 (to find seventh 7) (x to find sevenths) Work out of then x Work out of then 7 x Work out of then 0 x 0 At this stage you could try question - on the Fraction Practice Sheet. H Jackson 0 / ACADEMIC SKILLS

3 Equivalent Fractions: Some fractions are equivalent to (the same size as) others. For example is the same as. To make an equivalent fraction you can multiply the top number of a fraction by anything as long as you do the same to the bottom number, and vice versa. X X X X 0 7 X0 X The above pairs of fractions are equivalent because the top and bottom have been multiplied by the same number every time. NB you should always work in PAIRS think to yourself have I done the same to the top number as the bottom? Simplifying/Cancelling Fractions: This is the same principle as above but you divide the top and bottom by the same number instead of multiplying To simplify a fraction you need to look for the number that will go into both the top and the bottom number. When you can t simplify any more then the fraction is in its simplest form. You should write fractions in their simplest form wherever possible. Creating Fractions from Real Scenarios: If you are asked to write one number as a fraction of another just write the fraction then simplify if possible. The number that you are writing the fraction of goes on the bottom (normally this is the biggest number), e.g. If I have 0 and spend 7 I have spent 7 out of 0 which is 7 0. Alex scored 0 out of in a test. Write his score as a fraction in it s lowest term. Fraction: 0 simplifies to (top and bottom both divided by ) H Jackson 0 / ACADEMIC SKILLS

4 Improper Fractions & Mixed Numbers: An improper fraction is top heavy (eg ). (read as twelve fifths) A mixed number has both a whole number and a fraction (eg You may be asked to convert from one to the other. ). (read as five and two thirds) Converting from Improper to Mixed: Divide the bottom number into the top then write the remainder as the fraction. Whole ones Fifths 7 How many s in (answer is ) how many left over? (answer is ) ( x 0) ( 0 ) How many s in 7 (answer is ) how many left over? (answer is ) Converting from Mixed to Improper: Multiply the whole number by the bottom number of the fraction then add on the top number of the fraction. Whole number Bottom of fraction Top of fraction x then add the extra on. You have thirds Same denominator 7 x 7 then add the extra on. You have sevenths 7 Try doing all the examples the other way round and see if you get back to where we started. At this stage you could try question - on the Fraction Practice Sheet. H Jackson 0 / ACADEMIC SKILLS

5 Multiplying Fractions: To multiply fractions you need to multiply the top numbers (numerators) together and then multiply the bottom numbers (denominators) together. 7 ( ) ( 7) If possible simplify the numbers in the fractions before you multiply. You can simplify any top number with any bottom number as long as you divide them by the same number. Remember to work in PAIRS you must always divide a top number and a bottom number. (the (top) and the 9 (bottom) will both divide by.) ( ) (7 ) Cancel as many pairs of numbers as you can so that the fractions are as simple as possible before you multiply. However if you miss any it won t matter just simplify at the end. (the (top) and the 9 (bottom) will both divide by.) ( ) ( ) (the (top) and the (bottom) will both divide by.) Dividing Fractions: Dividing fractions is easy once you know how to multiply them. To divide fractions change the divide sign into a multiplication sign and turn the second fraction upside down. Then multiply as explained above. ( ) ( ) becomes x Second fraction is turned upside down. H Jackson 0 / ACADEMIC SKILLS

6 Adding Fractions: Before you add fractions you need to make sure the denominators are the same. To do this you need to be able to find equivalent fractions. If the denominators are the same: it is a straight forward adding of the numerators only: ( + ) (7th is the size of the fractions do not add these) If the denominators are different: you need to use your knowledge of equivalent fractions (see page ) to make them the same. Look for a common denominator (a number that both denominators will go into.) + These cannot just be added as the denominators are different. So find the smallest number that and both go into () then convert both fractions into th s. bottom x X X + X X bottom x 9 Now we have: (the fractions can now be added as the denominators are the same) Remember to finish the question 7 should be written as (see page ). + Make the denominators the same H Jackson 0 / ACADEMIC SKILLS

7 Subtracting Fractions: The method for subtracting fractions is exactly the same as that for adding. Denominators the same: subtract the numerators only. ( ) (th is the size of the fractions do not subtract these) Denominators different: look for a common denominator. These cannot just be subtracted as the denominators are different. So find the smallest number that and both go into () then convert both fractions into th s. bottom x X X X X bottom x Now we have: (the fractions can now be subtracted as the denominators are the same) Make the denominators the same. 0 7 Now try all the questions on the Fraction Practice Sheet. H Jackson 0 / ACADEMIC SKILLS 7

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