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Fractions2012

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Fractions2012

  1. 1. 12151413halvesthirdsquartersfifths16sixths
  2. 2. 1 11 1 112 43 5 761 11 1 118 109 11 1312
  3. 3. 12The numeratorThe denominatorTells us how many equal partsour “whole” is broken into.Tells us how many of the equalparts we have or need.What’s in a fraction?
  4. 4. 13Remember, if you’re addingapples together, they don’tsuddenly turn into bananas!When the denominators are the same, add thenumerators like normal numbers.Adding fractions with the SAME denominator.1323+ =The denominator stays the SAME, becauseyou are adding the same kind of fraction.
  5. 5. 23When the numerator is higher than the denominator, it iscalled an improper fraction.Adding fractions with the numerator larger than the denominator.2343+ =Firstly we see how many “wholes” we have. We know we have one whole because3/3 is the same as one. There is one left over from the four, so 1 and 1/3.13=It can be reduced.1 (Whole)33
  6. 6. 34Sometimes after reducing, we can reduce again, becausethe fraction left over is the same as a smaller fraction. Theseare called equivalent fractions,Adding fractions with the numerator larger than the denominator.3464+ =Firstly we see how many “wholes” we have. We know we have one wholebecause 4/4 is the same as one. Two is left over from six.24=It can be reduced again.1 (Whole)44
  7. 7. The 2 / 4 or two quarters can be reduced again. Why?Adding fractions with the numerator larger than the denominator.Here’s a model chocolate bar, with four pieces. 2 out of the four are a different colour.2/4 can be reduced to ½, because 2/4 can be broken up into two equal parts, and one ofthose equal parts is different. So the answer goes from 1 2/4 to 1 ½ !24=It can be reduced againbecause there is a smallerequivalent fraction. Checkout this model. It shows 2/4,or two quarters.1 (Whole)44One equalpart.The otherequal part,but it is adifferentcolour.
  8. 8. 23Remember, if you’re subtractingapples together, they don’tsuddenly turn into bananas!When the denominators are the same, subtractthe numerators like normal numbers.SUBTRACTING fractions WITH the SAME denominator.1313- =The denominator stays the SAME, because youare subtracting the same kind of fraction.(2-1=1)
  9. 9. 12We start by multiplyingthe denominator by anumber that will make itthe same as the seconddenominator.(2 x ? = 6).When the denominators are NOT the same, weneed to change one of the fractions. Try changingthe fraction with the smallest denominator.SUBTRACTING fractions WITHOUT the SAME denominator.16??- =How many times did you multiply the 2 to make 6in the second fraction? 3 times. Now multiply thetop by the same, so 1 x 3 = 3. So ½ becomes 3/6(This one)12X ? = 6Now multiply the top by the sameX 3 = ?½ becomes 3/63/6 – 1/6 = 2/6
  10. 10. 23Remember, if you’re subtractingapples together, they don’tsuddenly turn into bananas!Multiply the top numbers togetherMultiplying fractions WITH the SAME denominator.1313x =The denominator stays the SAME, because youare subtracting the same kind of fraction.(2-1=1)
  11. 11. First, we have to figure out what the question iswanting us to find.“Te Kaha had 10 lollies.”Is that telling us what we are trying to find out, orgiving us some sort of information?It is giving us information. We might need it again,we might not.“He gave half to Jewel.”This is more information.“How many lollies does Jewel get?”We have found out what we are supposed to befinding. We are trying to find out the number of lolliesthat Jewel gets!First, we have to figure out what the question iswanting us to find.“Te Kaha had 10 lollies.”Is that telling us what we are trying to find out, orgiving us some sort of information?It is giving us information. We might need it again,we might not.“He gave half to Jewel.”This is more information.“How many lollies does Jewel get?”We have found out what we are supposed to befinding. We are trying to find out the number of lolliesthat Jewel gets!Te Kaha had 10 lollies.He gave half to Jewel.How many lollies does Jewel get?do we start?
  12. 12. Now that we know what the question wants us tofind out, we need to decide on the information wewill use to figure this out.“Te Kaha had 10 lollies.”In this sentence, we know there is one person withlollies, and he has 10 lollies.We still need some more information to help us towork out how many lollies Jewel gets.“He gave half to Jewel.”We now know an amount that Jewel gets. He (TeKaha) gives half of his lollies to Jewel.But we need to find the exact number of lollies Jewelgets.How do we do that?Now that we know what the question wants us tofind out, we need to decide on the information wewill use to figure this out.“Te Kaha had 10 lollies.”In this sentence, we know there is one person withlollies, and he has 10 lollies.We still need some more information to help us towork out how many lollies Jewel gets.“He gave half to Jewel.”We now know an amount that Jewel gets. He (TeKaha) gives half of his lollies to Jewel.But we need to find the exact number of lollies Jewelgets.How do we do that?Te Kaha had 10 lollies.He gave half to Jewel.How many lollies does Jewel get?do we do?
  13. 13. Use your knowledge of a “HALF”What is a half?A half or halves is a fractions word.You would have learnt about fractions in class. Usewhat you have learnt about fractions, and yourknowledge about halves.For example, if I thought about fractions, I know thatthey usually are a part of something whole, either anumber or object.Use your knowledge of a “HALF”What is a half?A half or halves is a fractions word.You would have learnt about fractions in class. Usewhat you have learnt about fractions, and yourknowledge about halves.For example, if I thought about fractions, I know thatthey usually are a part of something whole, either anumber or object.do we do this?12Student’s knowledge abouthalves:I know that a half is whensomething has been divided(shared) into two equal parts.Equal means the same, so twoparts that are the same size,like this orange that I havecut in half.I also know that a half iswritten like this:
  14. 14. Strategy 1:Te Kaha needs to share 10 lollies. I can use counters to represent the lollies.I now have to give HALF to Jewel. A half is like splitting up all my lollies into twoequal parts. Here’s 1 part, and here’s the other part.Now I have to share the lollies so that both parts are the same, like this.I’ve counted 5 in each equal part, so Jewel must get 5 lollies.Strategy 1:Te Kaha needs to share 10 lollies. I can use counters to represent the lollies.I now have to give HALF to Jewel. A half is like splitting up all my lollies into twoequal parts. Here’s 1 part, and here’s the other part.Now I have to share the lollies so that both parts are the same, like this.I’ve counted 5 in each equal part, so Jewel must get 5 lollies.Strategy 2:I know the opposite of dividing is multiplying. Ican use my knowledge of 2x tables, becausethe opposite of dividing by two, is multiplying bytwo. First I have to write a maths equation fromthe information from the question:10 ÷ 2 (10,the lollies Te Kaha has, ÷ 2, sharinginto two groups is dividing into two groups)The opposite of 10 ÷ 2 is 2 x something = 10.I know 2 x 5 = 10. So Jewel gets 5 lollies.Strategy 2:I know the opposite of dividing is multiplying. Ican use my knowledge of 2x tables, becausethe opposite of dividing by two, is multiplying bytwo. First I have to write a maths equation fromthe information from the question:10 ÷ 2 (10,the lollies Te Kaha has, ÷ 2, sharinginto two groups is dividing into two groups)The opposite of 10 ÷ 2 is 2 x something = 10.I know 2 x 5 = 10. So Jewel gets 5 lollies.Strategy 3:I can use my knowledge of doubleshere, because doubles is the sameas multiplying by two.Double something equals 10.Double 5 equals ten, so Jewel gets5 lollies.Strategy 3:I can use my knowledge of doubleshere, because doubles is the sameas multiplying by two.Double something equals 10.Double 5 equals ten, so Jewel gets5 lollies.
  15. 15. Cruise had 16 raspberry twists.On his way to town, he ate halfof the twists all by himself.How many twists did Cruise eataltogether?Identify the main words tomake an equation.halfquarter16There is only one equation here.16 take away a half.Now apply your fractionsknowledge.I know halves are TWO equal parts.I can use counters to split 16 into 2 groups.It’s the same as saying 16 divided by 2.I can use my multiplication knowledgeOne equal group Two equal groups16 / 2 = 82 x something = 16 2 x 8 = 16
  16. 16. 2 equal partshalvesTe Kaha had 10 lollies. He gave half to Monique.How many lollies does Monique get?Put your working out and explanations here.
  17. 17. • parts can be joined to make a numbermore than 1 eg. three fourths (quarters)and one fourth and one fourth is equal toone whole and one fourth or 3/4 +1/4 +1/4= 1 1/4
  18. 18. numeratordenominatorEqual partsof a whole
  19. 19. halfthirdsquartershalves
  20. 20. fifthssixthsseventhsfourths
  21. 21. ninthstenthseighths
  22. 22. can bedifferentSizes.Our “whole”

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