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**Adding, Subtracting, Multiplying and Dividing Fractions**

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EXAMPLES 1) Find the Lowest Common Multiple (LCM) of the following pairs of numbers: 3 and 7 (b) 6 and 9 Write out the multiples of 3 and 7 and circle the lowest common one Write out the multiples of 6 and 9 and circle the lowest common one 3 → 6 → 3, 6, 9, 12, 15, 18, 21, 24 … 6, 12, 18, 7 → 9 → 7, 14, 21, 28 … 9, 18, 27, 36 … LCM = 21 LCM = 18

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**Warm up What is the lowest common multiple of: 2 6 = 3 and 4 12 15 5**

Find a the missing numbers What is the lowest common multiple of: 2 6 = 3 and 4 12 15 5 5 and 6 30 3 15 = 8 4 and 6 12 40 3 and 8 24 25 5 = 6 5 and 10 10 30

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Take out your homework

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Take out your homework

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**Adding, Subtracting, Multiplying and Dividing Fractions**

21/05/14 Learning Objective: To be able to add, subtract, multiple and divide fractions Learning outcome: To be able to add, subtract, multiply and divide the following fractions

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**Adding Fractions There are 3 Simple Steps to add fractions:**

Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put the answer over the denominator. Step 3: Simplify the fraction (if needed).

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Examples = 5 7 2 7 + 3 7 = 6 9 2 9 + 4 9 = 4 11 1 11 + 3 11

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**What if the denominators were different? Any idea?**

We need to make sure the denominator of both fractions is the same before we add. = + = 2 5 + 3 10 4 10 3 10 7 10 We need a number in the 3 and 12 times table to use as our bottom number + 1 3 = = 9 12 + 5 12 4 12 5 12

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**We need a number in the 5 and 6 times table to use as our bottom number**

= 2 5 + 3 6 = 27 30 12 30 + 15 30

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On your own

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**Subtracting Fractions**

= 3 5 4 5 - 1 5 = 7 14 11 14 - 4 14 = 2 11 9 11 - 7 11

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**We need to make sure the denominator of both fractions is the same before we add or subtract**

= 4 5 - 3 15 = - 12 15 3 15 9 15 = - = 4 12 3 4 3 4 - - 5 12 9 12 5 12

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- = 7 8 2 3 - = 21 24 16 24 5 24

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**Multiplying Fractions**

3 4 5 8 15 32 x = 1 2 7 5 6 10 42 5 21 2 7 5 6 5 21 x x = = = 3 3 5 7 9 21 45 7 15 x = =

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**Dividing Fractions 4 7 3 4 4 7 4 3 16 21 ÷ = x = 4 1 2 7 8 1 2 8 7 8**

14 4 7 4 7 1 2 8 7 ÷ = x = = x = 1 2 3 4 5 8 3 4 8 5 24 20 6 5 3 4 8 5 6 5 ÷ x = = x = = 1

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3 32 5 48 1 1 9 1 1 4 25 5 1 7 16 2 65 18 3 11 18 = 2 1 11 1 11 = 1 1 4 2 8 1 8 = 1 1 1 1 1 1 3 = 2 1 1 2 1 1 2 1 2 4 1

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**Mixed numbers and top heavy fractions**

When you see a fraction with a large number in front of it, this is a MIXED NUMBER. 2 2 3 This means, 2 and 2 thirds When we have a fraction where the number at the top (NUMERATOR) is bigger than the number at the bottom (DENOMINATOR) we have a TOP HEAVY FRACTION 5 3 8 4 9 2

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**Mixed numbers and top heavy fractions**

You need to be able to: turn MIXED NUMBERS into TOP HEAVY FRACTIONS turn TOP HEAVY FRACTIONS into MIXED NUMBERS

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**Top heavy fractions to mixed numbers**

14 3 How many 3’s go into 14? 4 What is the remainder? 2 So we can make 4 wholes and we have 2 thirds left over: 14 3 = 4 2 3

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**Top heavy fractions to mixed numbers**

19 5 How many 5’s go into 19? 3 What is the remainder? 4 So we can make 3 wholes and we have 4 fifths left over: 19 5 = 3 4 5

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**Top heavy fractions to mixed numbers**

31 10 How many 10’s go into 31? 3 What is the remainder? 1 So we can make 3 wholes and we have 1 tenth left over: 31 10 = 3 1 10

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**Mixed Numbers to Top heavy fractions**

To turn the mixed numbers into top heavy fractions: 3 1 10 31 10 = Multiply these numbers together= 30 Add on the number at the top= 31 (this will be the top number) The number at the bottom will stay the same

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**Mixed Numbers to Top heavy fractions**

To turn the mixed numbers into top heavy fractions: 5 3 4 23 4 = Multiply these numbers together= 20 Add on the number at the top= 23 (this will be the top number) The number at the bottom will stay the same

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**Mixed Numbers to Top heavy fractions**

To turn the mixed numbers into top heavy fractions: 6 2 5 32 5 = Multiply these numbers together= 30 Add on the number at the top= 32 (this will be the top number) The number at the bottom will stay the same

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3 1 10 5 3 4 x = 31 10 23 4 = x 5 3 4 6 2 5 x = 23 4 32 5 x =

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3 1 10 6 2 5 ÷ = 31 10 32 5 31 10 5 32 ÷ = = x 6 1 4 6 2 5 = ÷ 25 4 32 5 25 4 5 32 = x = ÷

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