Fractions2012
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1. The document discusses fractions including the numerator, denominator, and equal parts of a whole. 2. It provides examples of common fractions like halves, thirds, quarters, and explains how fractions can be added or subtracted. 3. Strategies for solving word problems involving fractions like halves are demonstrated, such as using objects to represent amounts or writing mathematical equations.
Fractions2012
- 2. 1 11 1 11 2 43 5 76 1 11 1 11 8 109 11 1312
- 3. 1 2 The numerator The denominator Tells us how many equal parts our “whole” is broken into. Tells us how many of the equal parts we have or need. What’s in a fraction?
- 4. 1 3 Remember, if you’re adding apples together, they don’t suddenly turn into bananas! When the denominators are the same, add the numerators like normal numbers. Adding fractions with the SAME denominator. 1 3 2 3 + = The denominator stays the SAME, because you are adding the same kind of fraction.
- 5. 2 3 When the numerator is higher than the denominator, it is called an improper fraction. Adding fractions with the numerator larger than the denominator. 2 3 4 3 + = Firstly we see how many “wholes” we have. We know we have one whole because 3/3 is the same as one. There is one left over from the four, so 1 and 1/3. 1 3 = It can be reduced. 1 (Whole) 3 3
- 6. 3 4 Sometimes after reducing, we can reduce again, because the fraction left over is the same as a smaller fraction. These are called equivalent fractions, Adding fractions with the numerator larger than the denominator. 3 4 6 4 + = Firstly we see how many “wholes” we have. We know we have one whole because 4/4 is the same as one. Two is left over from six. 2 4 = It can be reduced again. 1 (Whole) 4 4
- 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 of those equal parts is different. So the answer goes from 1 2/4 to 1 ½ ! 2 4 = It can be reduced again because there is a smaller equivalent fraction. Check out this model. It shows 2/4, or two quarters. 1 (Whole) 4 4 One equal part. The other equal part, but it is a different colour.
- 8. 2 3 Remember, if you’re subtracting apples together, they don’t suddenly turn into bananas! When the denominators are the same, subtract the numerators like normal numbers. SUBTRACTING fractions WITH the SAME denominator. 1 3 1 3 - = The denominator stays the SAME, because you are subtracting the same kind of fraction. (2-1=1)
- 9. 1 2 We start by multiplying the denominator by a number that will make it the same as the second denominator. (2 x ? = 6). When the denominators are NOT the same, we need to change one of the fractions. Try changing the fraction with the smallest denominator. SUBTRACTING fractions WITHOUT the SAME denominator. 1 6 ? ? - = How many times did you multiply the 2 to make 6 in the second fraction? 3 times. Now multiply the top by the same, so 1 x 3 = 3. So ½ becomes 3/6 (This one) 1 2 X ? = 6 Now multiply the top by the same X 3 = ? ½ becomes 3/6 3/6 – 1/6 = 2/6
- 10. 2 3 Remember, if you’re subtracting apples together, they don’t suddenly turn into bananas! Multiply the top numbers together Multiplying fractions WITH the SAME denominator. 1 3 1 3 x = The denominator stays the SAME, because you are subtracting the same kind of fraction. (2-1=1)
- 11. First, we have to figure out what the question is wanting us to find. “Te Kaha had 10 lollies.” Is that telling us what we are trying to find out, or giving 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 be finding. We are trying to find out the number of lollies that Jewel gets! First, we have to figure out what the question is wanting us to find. “Te Kaha had 10 lollies.” Is that telling us what we are trying to find out, or giving 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 be finding. We are trying to find out the number of lollies that Jewel gets! Te Kaha had 10 lollies. He gave half to Jewel. How many lollies does Jewel get? do we start?
- 12. Now that we know what the question wants us to find out, we need to decide on the information we will use to figure this out. “Te Kaha had 10 lollies.” In this sentence, we know there is one person with lollies, and he has 10 lollies. We still need some more information to help us to work out how many lollies Jewel gets. “He gave half to Jewel.” We now know an amount that Jewel gets. He (Te Kaha) gives half of his lollies to Jewel. But we need to find the exact number of lollies Jewel gets. How do we do that? Now that we know what the question wants us to find out, we need to decide on the information we will use to figure this out. “Te Kaha had 10 lollies.” In this sentence, we know there is one person with lollies, and he has 10 lollies. We still need some more information to help us to work out how many lollies Jewel gets. “He gave half to Jewel.” We now know an amount that Jewel gets. He (Te Kaha) gives half of his lollies to Jewel. But we need to find the exact number of lollies Jewel gets. 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. 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. Use what you have learnt about fractions, and your knowledge about halves. For example, if I thought about fractions, I know that they usually are a part of something whole, either a number 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. Use what you have learnt about fractions, and your knowledge about halves. For example, if I thought about fractions, I know that they usually are a part of something whole, either a number or object. do we do this? 1 2 Student’s knowledge about halves: I know that a half is when something has been divided (shared) into two equal parts. Equal means the same, so two parts that are the same size, like this orange that I have cut in half. I also know that a half is written like this:
- 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 two equal 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 two equal 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. I can use my knowledge of 2x tables, because the opposite of dividing by two, is multiplying by two. First I have to write a maths equation from the information from the question: 10 ÷ 2 (10,the lollies Te Kaha has, ÷ 2, sharing into 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. I can use my knowledge of 2x tables, because the opposite of dividing by two, is multiplying by two. First I have to write a maths equation from the information from the question: 10 ÷ 2 (10,the lollies Te Kaha has, ÷ 2, sharing into 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 doubles here, because doubles is the same as multiplying by two. Double something equals 10. Double 5 equals ten, so Jewel gets 5 lollies. Strategy 3: I can use my knowledge of doubles here, because doubles is the same as multiplying by two. Double something equals 10. Double 5 equals ten, so Jewel gets 5 lollies.
- 15. Cruise had 16 raspberry twists. On his way to town, he ate half of the twists all by himself. How many twists did Cruise eat altogether? Identify the main words to make an equation. half quarter 16 There is only one equation here. 16 take away a half. Now apply your fractions knowledge. 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 knowledge One equal group Two equal groups 16 / 2 = 8 2 x something = 16 2 x 8 = 16
- 16. 2 equal parts halves Te Kaha had 10 lollies. He gave half to Monique. How many lollies does Monique get? Put your working out and explanations here.
- 17. • parts can be joined to make a number more than 1 eg. three fourths (quarters) and one fourth and one fourth is equal to one whole and one fourth or 3/4 +1/4 +1/4 = 1 1/4
- 18. numerator denominator Equal parts of a whole