## Maths

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• ### Swati A

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A Full Review Of Fractions Of UK As Well As Australian Curriculum.

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FRACTIONS
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WHAT Is A FRACTION When an object is divided into a number of equal parts then each part is called a fraction, The denominator can never be equal to 0. 2 3 numerator denominator
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Math with Fractions Four basic functions Multiply e Divide , Add , Subtract
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Multiplication Multiply the numerators and put in the numerator of the result Multiply the denominators and put in the denominator of the result 7 4 x 8 9 28 72
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210 56 These numbers get pretty big! What if we needed to multiply again? Let's make the fraction more simple, so it will be easier to use in the future.
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Simplification ' Divide by the Greatest Common Factor 28 But what is a 72 Common Factor
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Factors A factor is a number that can be divided into another number with no remainder — 8's factors are: (8/1=8) (8/2 = 4) (8/4 = 2) (8/8 = 1) — 3 is NOT a factor of 8, because 8 is not evenly divisible by 3 (8/3 = 2 with R=3)
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Common Factors common factor is a factor that two numbers have in common — For example, 7 is a factor of both 21 and 105, so it is a common factor of the two. greatest common factor is the largest - The factor that the two number share So let's go back to our simplification problem from before...
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Simplification Divide both numerator and denominator by the Greatest Common Factor Factors are 1, 2, 4 7, 14, 28 28 Factors are 1, 2, 3, 4 6, 9, 12, 18, 24, 48, 72 Greatest Common Factor 28 4 7 28 so 72 7 18
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24 Simplification - Let's Try It! 78 114 19
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Division ' Just like multiplication with one more step ' Invert the second fraction and multiply
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Division - Let's Try It! 21 20 10 44 50
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Addition ' To add two fractions, you must make sure they have a Common Denominator 3 8 5 16 p What is a Common Denominator
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Common Denominator common denominator is a number with which both of the denominators share at least one factor that is not the number 1 — For example, if the denominators are 4 and 7, then a common denominator is 28. — 28 shares the factors 1, 2 and 4 with the number 4, and the factors 1 and 7 with the number 7. So let's go back to our simplification problem from before...
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Addition To add two fractions, you must make sure they have a Common Denominator What can you multiply each fraction by to give the smallest common denominator? 16 goes into 16 one time 8+43 8 goes into 16 two times 69 3 2 8 2 1 1 5 16 The smallest number that has both of these as factors is 16 Once you have a common denominator, add the numerators. 6 5 16 16 11 16
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Subtraction To subtract two fractions, they also must have a Common Denominator What can you multiply each fraction by to give the smallest common denominator? 8 goes into 16 two times 3 2 8 2 16 goes into 16 one time The smallest number that has both of these as factors is 16 Once you have a common denominator, subtract the numerators. 6 16 5 1 1 5 16 5 16 1 16
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Subtraction - Let's Try It!
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Exercise Evaluate — X 'Evaluate 2— X 1 Evaluate 3— X 1 Evaluate 8 + 2 —
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QI. 3/7 x 3/5 + 5/35 Q. 2/3 x 3/8 - 2/24 Q3. 3/7 x 5/9 + 4/63 Q4. 5 x (3/2 + 2/7) 14 X ( Q6. Find the difference between -4/9 and - 2/3 Q7. 5 - -5/9 Q8. find 4/10 of 1000
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Q Christa is making a cake and is adjusting the recipe. The recipe says it will serve 5 people. Christa needs to serve 4 people. a) What fraction of each ingredient listed on the recipe will Christa need to use? b) The original recipe asked for 5/2 cups of flour. How much flour should she use? c) The original recipe asked for 5/16 cups of coconut. How much coconut should she use?
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Answer a) 4/5 b) 4/5 x 5/2 c) 4/5 x 5/16
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Recurring decimals Recurring decimals however have an infinite number of decimal places. In other words, the number of decimal places goes on forever and you'll often see a pattern that forms. 1/3 = 0.333333 0.3. Q Evaluate 4/7 as recurring decimal
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Exercise QI. If 3/5 of a cake is shared equally between 5 people, what fraction of the bun would each receive, Q2. Ajay had to pay \$384 as a deposit on a new sofa. The deposit was 6/7 of the whole price. a) What was the whole price of the sofa? b) how much money does he have left to pay.
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Q3. A class has 10 students. h of the class are boys. a) What fraction of the class is girls? b) How many girls are there? c) How many boys are there? Q4. In a hokey tournament, Adam's team won 1 out of 3 games, and did not tie any games. a) How many games did adam's team lose. b) What fraction of the games did adam's team lose.
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Q7. A bottle is 2/7 full of petrol . If 230 ml of petrol is added to it, the bottle is 5/6 full. How many ml does the bottle hold when full. Q8. In a survey of 270 people, 1/10 said their favourite sport was soccer, and 1/9 said their favourite game was tennis. a) b) c) What is the total fraction of people who said their favourite sport was soccer or tennis? What is the fraction of people who did not put soccer or tennis as their fav sport Number of people who did not put soccer or tennis as their fav sport.
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Q9. Johnny and Elizabeth were playing a video game and trying to get all of the treasure. Johnny got 1/3/3 of the treasure. Elizabeth got 5/9 of the treasure. Together, Johnny and Elizabeth got what fraction of the treasure? QIO. At the party, Aisha and her friends ate 2 1/2 pizzas. After the party, there were 1 1/8 pizzas left. How many pizzas were there at the start of the party?
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Review A fraction has a numerator and a denominator The denominator can never be O ' You can multiply, divide, add and subtract fractions A common factor is a number that both denominators are evenly divisible by A common denominator is a number that both denominators share a factor with

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